<?xml version="1.0"?>
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     xml:base="http://www.biomodels.net/kisao/KISAO"
     xmlns:dc="http://purl.org/dc/terms/"
     xmlns:obo="http://purl.obolibrary.org/obo/"
     xmlns:ont="http://www.co-ode.org/ontologies/ont.owl#"
     xmlns:owl="http://www.w3.org/2002/07/owl#"
     xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
     xmlns:xml="http://www.w3.org/XML/1998/namespace"
     xmlns:xsd="http://www.w3.org/2001/XMLSchema#"
     xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
     xmlns:skos="http://www.w3.org/2004/02/skos/core#"
     xmlns:kisao="http://www.biomodels.net/kisao/KISAO#"
     xmlns:protege="http://protege.stanford.edu/plugins/owl/protege#">
    <owl:Ontology rdf:about="http://www.biomodels.net/kisao/KISAO#">
        <protege:defaultLanguage>en</protege:defaultLanguage>
        <dc:rights>Artistic License 2.0</dc:rights>
        <rdfs:comment xml:lang="en">This is a core version which contains all but deprecated classes.</rdfs:comment>
        <rdfs:label xml:lang="en">Kinetic Simulation Algorithm Ontology (KiSAO)</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://co.mbine.org/standards/kisao</rdfs:seeAlso>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/22027554</rdfs:seeAlso>
        <owl:versionInfo rdf:datatype="http://www.w3.org/2001/XMLSchema#decimal">2.13</owl:versionInfo>
        <skos:definition xml:lang="en">The Kinetic Simulation Algorithm Ontology (KiSAO) classifies algorithms available for the simulation and analysis of models in biology, and their characteristics and the parameters required for their use.</skos:definition>
    </owl:Ontology>
    


    <!-- 
    ///////////////////////////////////////////////////////////////////////////////////////
    //
    // Annotation properties
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    <!-- http://protege.stanford.edu/plugins/owl/protege#defaultLanguage -->

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    <!-- http://purl.org/dc/terms/creator -->

    <owl:AnnotationProperty rdf:about="http://purl.org/dc/terms/creator"/>
    


    <!-- http://purl.org/dc/terms/rights -->

    <owl:AnnotationProperty rdf:about="http://purl.org/dc/terms/rights"/>
    


    <!-- http://www.biomodels.net/kisao/KISAO#isImplementedIn -->

    <owl:AnnotationProperty rdf:about="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
    


    <!-- http://www.biomodels.net/kisao/KISAO#isOrganizational -->

    <owl:AnnotationProperty rdf:about="http://www.biomodels.net/kisao/KISAO#isOrganizational"/>
    


    <!-- http://www.w3.org/2004/02/skos/core#altLabel -->

    <owl:AnnotationProperty rdf:about="http://www.w3.org/2004/02/skos/core#altLabel"/>
    


    <!-- http://www.w3.org/2004/02/skos/core#definition -->

    <owl:AnnotationProperty rdf:about="http://www.w3.org/2004/02/skos/core#definition"/>
    


    <!-- 
    ///////////////////////////////////////////////////////////////////////////////////////
    //
    // Datatypes
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    <!-- http://www.w3.org/2001/XMLSchema#date -->

    <rdfs:Datatype rdf:about="http://www.w3.org/2001/XMLSchema#date"/>
    


    <!-- 
    ///////////////////////////////////////////////////////////////////////////////////////
    //
    // Object Properties
    //
    ///////////////////////////////////////////////////////////////////////////////////////
     -->

    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000245 -->

    <owl:ObjectProperty rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000245">
        <owl:inverseOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000268"/>
        <rdfs:domain rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
        <rdfs:range rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000097"/>
        <rdfs:label xml:lang="en">has characteristic</rdfs:label>
        <skos:definition xml:lang="en">&apos;has characteristic&apos; links algorithms to the characteristics, they possess.</skos:definition>
    </owl:ObjectProperty>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000246 -->

    <owl:ObjectProperty rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000246">
        <rdfs:subPropertyOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
        <rdfs:domain>
            <owl:Class>
                <owl:intersectionOf rdf:parseType="Collection">
                    <rdf:Description rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
                    <owl:Restriction>
                        <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                        <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000322"/>
                    </owl:Restriction>
                </owl:intersectionOf>
            </owl:Class>
        </rdfs:domain>
        <rdfs:range rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
        <rdfs:label xml:lang="en">is hybrid of</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1093/bib/bbn050</rdfs:seeAlso>
        <skos:definition xml:lang="en">The basic idea of hybrid simulation methods is to combine the advantages of complementary simulation approaches: the whole system is subdivided into appropriate parts and different simulation methods operate on these parts at the same time.
&apos;is hybrid of&apos; is a relation between the complex simulation method and algorithms it applies to the different parts of the system.</skos:definition>
    </owl:ObjectProperty>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000246"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1093/bib/bbn050</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Biochemical simulations: stochastic, approximate stochastic and hybrid approaches. Pahle J. Brief Bioinform. 2009 Jan;10(1):53-64. Epub 2009 Jan 16.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000250 -->

    <owl:ObjectProperty rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000250">
        <owl:inverseOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
        <rdfs:domain rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000201"/>
        <rdfs:range rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
        <rdfs:label xml:lang="en">is parameter of</rdfs:label>
        <skos:definition xml:lang="en">&apos;is parameter of&apos; is an inverse of &apos;has parameter&apos; and links parameters to the algorithms which use them.</skos:definition>
    </owl:ObjectProperty>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000259 -->

    <owl:ObjectProperty rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000259">
        <rdfs:domain rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
        <rdfs:range rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000201"/>
        <rdfs:label xml:lang="en">has parameter</rdfs:label>
        <skos:definition xml:lang="en">&apos;has parameter&apos; links algorithms to the parameters they use.</skos:definition>
    </owl:ObjectProperty>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000268 -->

    <owl:ObjectProperty rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000268">
        <rdfs:domain rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000097"/>
        <rdfs:range rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
        <rdfs:label xml:lang="en">is characteristic of</rdfs:label>
        <skos:definition xml:lang="en">&apos;is characteristic of&apos; is an inverse of &apos;has characteristic&apos; and links characteristics to the algorithms which possess them.</skos:definition>
    </owl:ObjectProperty>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000359 -->

    <owl:ObjectProperty rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000359">
        <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#SymmetricProperty"/>
        <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#ReflexiveProperty"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-10</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">is similar to</rdfs:label>
        <skos:definition xml:lang="en">A relationship indicating that two entities are similar to each other.</skos:definition>
    </owl:ObjectProperty>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000360 -->

    <owl:ObjectProperty rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000360">
        <owl:inverseOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000399"/>
        <rdfs:domain rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
        <rdfs:range rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-10</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">uses</rdfs:label>
        <skos:definition xml:lang="en">A relation between algorithms indicating that one algorithm uses another one (for example, if the algorithm switches between several algorithms).</skos:definition>
    </owl:ObjectProperty>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000361 -->

    <owl:ObjectProperty rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000361">
        <rdfs:subPropertyOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000359"/>
        <rdfs:domain rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
        <rdfs:range rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-10</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">is generalization of</rdfs:label>
        <skos:definition xml:lang="en">A relation between kinetic simulation algorithms, indicating that one is a generalization of another (e.g.if one extends another to suit systems with more general characteristics ).</skos:definition>
    </owl:ObjectProperty>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000399 -->

    <owl:ObjectProperty rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000399">
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-07-19</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">is used by</rdfs:label>
        <skos:definition xml:lang="en">A relation between algorithms indicating that one algorithm is used by another one (for example, if the algorithm switches between several algorithms). &apos;is used by&apos; is inverse of &apos;uses&apos;.</skos:definition>
    </owl:ObjectProperty>
    


    <!-- 
    ///////////////////////////////////////////////////////////////////////////////////////
    //
    // Data properties
    //
    ///////////////////////////////////////////////////////////////////////////////////////
     -->

    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000251 -->

    <owl:DatatypeProperty rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000251">
        <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#FunctionalProperty"/>
        <rdfs:domain rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000201"/>
        <rdfs:label xml:lang="en">has type</rdfs:label>
        <skos:definition xml:lang="en">Indicates the type of algorithm parameter value, such as, for example, xsd:double for &apos;absolute tolerance&apos;.</skos:definition>
    </owl:DatatypeProperty>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000275 -->

    <owl:DatatypeProperty rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000275">
        <rdfs:domain rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000064"/>
        <rdfs:range rdf:resource="http://www.w3.org/2001/XMLSchema#int"/>
        <rdfs:label xml:lang="en">has Runge-Kutta method order</rdfs:label>
        <skos:definition xml:lang="en">Indicates the order of a &apos;Runge-Kutta based method&apos; [urn.miriam.biomodels.kisao:KISAO_0000064]. A &apos;Runge-Kutta based method&apos; has order p if for sufficiently smooth initial value problems (y&apos;=f(x,y), y(x0)=y0),  ||y(x0 + h)-y1||&lt;=Kh^(p+h).</skos:definition>
    </owl:DatatypeProperty>
    


    <!-- 
    ///////////////////////////////////////////////////////////////////////////////////////
    //
    // Classes
    //
    ///////////////////////////////////////////////////////////////////////////////////////
     -->

    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000000 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000000">
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2008-05-26</dc:created>
        <dc:creator xml:lang="en">dk</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">modelling and simulation algorithm</rdfs:label>
        <skos:altLabel xml:lang="en">modeling and simulation algorithm</skos:altLabel>
        <skos:definition xml:lang="en">Algorithm used to instantiate a simulation from a mathematical model.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000003 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000003">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000333"/>
        <rdfs:subClassOf>
            <owl:Class>
                <owl:complementOf>
                    <owl:Restriction>
                        <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                        <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000102"/>
                    </owl:Restriction>
                </owl:complementOf>
            </owl:Class>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000236"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">24JAN2009</dc:created>
        <dc:creator xml:lang="en">NLN</dc:creator>
        <rdfs:label xml:lang="en">weighted stochastic simulation algorithm</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/19045316</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">weighted SSA</skos:altLabel>
        <skos:definition xml:lang="en">The weighted Stochastic Simulation Algorithm manipulates the probabilities measure of biochemical systems by sampling, in order to increase the fraction of simulation runs exhibiting rare events.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000003"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">weighted SSA</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000003"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/19045316</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Kuwahara H, Mura I. (2008) An efficient and exact stochastic simulation method to analyse rare events in biochemical systems. J Chem Phys. 129(16):165101.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000015 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000015">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000241"/>
        <rdfs:subClassOf>
            <owl:Class>
                <owl:complementOf>
                    <owl:Restriction>
                        <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                        <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000102"/>
                    </owl:Restriction>
                </owl:complementOf>
            </owl:Class>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000236"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2007-11-09</dc:created>
        <dc:creator xml:lang="en">NLN</dc:creator>
        <isImplementedIn xml:lang="en">Cain</isImplementedIn>
        <rdfs:label xml:lang="en">Gillespie first reaction algorithm</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1016/0021-9991(76)90041-3</rdfs:seeAlso>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1021/j100540a008</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Gillespie&apos;s first reaction method</skos:altLabel>
        <skos:definition xml:lang="en">Stochastic simulation algorithm using the reaction probability density function (next-reaction density function), giving the probability that the next reaction will happen in a given time interval. To choose the next reaction to fire, the algorithm calculates a tentative reaction time for each reaction and then select the smallest.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000015"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1016/0021-9991(76)90041-3</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Gillespie DT. A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions. Journal of Computational Physics, Volume 2 , pages 403-434 (1976).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000015"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1021/j100540a008</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Gillespie DT. Exact stochastic simulation of coupled chemical reactions. Journal of Physical Chemistry, Vol. 81, No. 25. (1977), pp. 2340-2361.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000015"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Gillespie&apos;s first reaction method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000017 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000017">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000363"/>
        <rdfs:subClassOf>
            <owl:Class>
                <owl:complementOf>
                    <owl:Restriction>
                        <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                        <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000102"/>
                    </owl:Restriction>
                </owl:complementOf>
            </owl:Class>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000104"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000107"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <isImplementedIn xml:lang="en">StochSim</isImplementedIn>
        <rdfs:label xml:lang="en">multi-state agent-based simulation method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/9628844</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Morton-Firth</skos:altLabel>
        <skos:definition xml:lang="en">The agent-based simulation method instantiates each molecule as an individual software object. The interactions between those objects are determined by interaction probabilities according to experimental data. The probability is depended on the state the molecule is in at that specific time (molecules have multiple-state). Additionally, &apos;&apos;pseudo-molecules&apos;&apos; are introduced to the system in order to simulate unimolecular reactions. For simulation, continuous time is broken down into discrete, independent &apos;&apos;slices&apos;&apos;. During each time slice one molecule is selected randomly, a second molecule or pseudo-molecule is selected afterwards (leading to either a unimolecular or a bimolecular reaction). The reaction will only take place if a produced random number exceeds the reaction probability calculated beforehand. In that case, the system is updated after that reaction.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000017"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/9628844</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Morton-Firth, C.J, Bray, D. Predicting temporal fluctuations in an intracellular signalling pathway. Journal of Theoretical Biology, volume 192, pages 117-128 (1998).</rdfs:comment>
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    </owl:Axiom>
    


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        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2007-11-30</dc:created>
        <dc:creator xml:lang="en">dk</dc:creator>
        <isImplementedIn xml:lang="en">SBML-SAT</isImplementedIn>
        <isImplementedIn xml:lang="en">SUNDIALS</isImplementedIn>
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        <isImplementedIn xml:lang="en">libRoadRunner</isImplementedIn>
        <rdfs:label xml:lang="en">CVODE</rdfs:label>
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        <skos:altLabel xml:lang="en">VODE</skos:altLabel>
        <skos:altLabel xml:lang="en">VODEPK</skos:altLabel>
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        <skos:definition xml:lang="en">The CVODE is a package written in C that solves ODE initial value problems, in real N-space, written as y&apos;=f(t,y),  y(t0)=y0. It is capable for stiff and non-stiff systems and uses two different linear multi-step methods, namely the Adam-Moulton [http://identifiers.org/biomodels.kisao/KISAO_0000280] method and the backward differentiation formula [http://identifiers.org/biomodels.kisao/KISAO_0000288].</skos:definition>
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        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/bionetgen</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">BioNetGen</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000019"/>
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        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/jsim</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">JSim</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000019"/>
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        <rdfs:comment xml:lang="end">OpenCOR</rdfs:comment>
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    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000019"/>
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        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/pysces</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">PySCeS</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000019"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/tellurium</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">tellurium</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000019"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/vcell</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">VCell</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000019"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">citeulike:1832863</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Cohen S, Hindmarsh C. Cvode, A Stiff/nonstiff Ode Solver In C. Computers in Physics, Vol. 10 (2), pages 138-143 (1996).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000019"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1145/1089014.1089020</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Hindmarsh, A. C., et al., SUNDIALS: Suite of Nonlinear and Differential/Algebraic Equation Solvers, ACM Trans. Math. Softw., 31:363-396, 2005.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000019"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">VODE</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">RELATED</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000019"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">VODEPK</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">RELATED</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000019"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">code value ordinary differential equation solver</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000020 -->

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        <owl:disjointWith rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000283"/>
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        <isImplementedIn xml:lang="en">SUNDIALS</isImplementedIn>
        <rdfs:label xml:lang="en">PVODE</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1145/1089014.1089020</rdfs:seeAlso>
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        <skos:altLabel xml:lang="en">parallel code value ordinary differential equation solver</skos:altLabel>
        <skos:definition xml:lang="en">PVODE is a general-purpose solver for ordinary differential equation (ODE) systems that implements methods for both stiff and nonstiff systems. [...] In the stiff case, PVODE uses a backward differentiation formula method [http://identifiers.org/biomodels.kisao/KISAO_0000288] combined with preconditioned GMRES [http://identifiers.org/biomodels.kisao/KISAO_0000253] iteration. Parallelism is achieved by distributing the ODE solution vector into user-specified segments and parallelizing a set of vector kernels accordingly. For PDE-based ODE systems, we provide a module that generates a band block-diagonal preconditioner for use with the GMRES [http://identifiers.org/biomodels.kisao/KISAO_0000253] iteration. PVODE is based on CVODE [http://identifiers.org/biomodels.kisao/KISAO_0000019].</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000020"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1145/1089014.1089020</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Hindmarsh, A. C., et al., SUNDIALS: Suite of Nonlinear and Differential/Algebraic Equation Solvers, ACM Trans. Math. Softw., 31:363-396, 2005.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000020"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1177/109434209901300405</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Byrne GD, Hindmarsh AC. PVODE, an ODE Solver for Parallel Computers. International Journal of High Performance Computing Applications, Vol. 13 (4), pages 354-365 (1999).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000020"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">parallel code value ordinary differential equation solver</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000021 -->

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        </rdfs:subClassOf>
        <rdfs:subClassOf>
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                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <isImplementedIn xml:lang="en">Stochsim 1.2 and more recent versions</isImplementedIn>
        <rdfs:label xml:lang="en">StochSim nearest-neighbour algorithm</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/11395441</rdfs:seeAlso>
        <skos:definition xml:lang="en">The nearest-neighbour algorithm allows for the representation of spatial information, by adding a two-dimensional lattice in the form of a probabilistic cellular automata. That way, nearest neighbour interactions do additionally influence reactions taking place in the systems. Reactions between entities are calculated using the agent-based simulation algorithm [http://identifiers.org/biomodels.kisao/KISAO_0000017].</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000021"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/11395441</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Le Novere N, Shimizu TS. STOCHSIM: modelling of stochastic biomolecular processes. Bioinformatics, volume 17 (6), pages 575-576 (2001).</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000022 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000022">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000095"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000027"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000029"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <owl:disjointWith rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000076"/>
        <isImplementedIn xml:lang="en">MesoRD</isImplementedIn>
        <isImplementedIn xml:lang="en">SmartCell</isImplementedIn>
        <rdfs:label xml:lang="en">Elf and Ehrenberg method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1049/sb:20045021</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Elf algorithm</skos:altLabel>
        <skos:altLabel xml:lang="en">NSM</skos:altLabel>
        <skos:altLabel xml:lang="en">next-subvolume method</skos:altLabel>
        <skos:definition xml:lang="en">Sub-volume stochastic reaction-diffusion method that is a combination of the Direct Method [http://identifiers.org/biomodels.kisao/KISAO_0000029] for sampling the time for a next reaction or diffusion event in each subvolume, with Gibson and Bruck&apos;s Next Reaction Method [http://identifiers.org/biomodels.kisao/KISAO_0000027], which is used to keep track of in which subvolume an event occurs next. The subvolumes are kept sorted in a queue, implemented as a binary tree, according to increasing time of the next event. When an event has occurred in the subvolume at the top of the queue, new event times need to be sampled only for one (the event is a chemical reaction) or two (the event is a diffusion jump) subvolume(s).</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000022"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1049/sb:20045021</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Elf J, Ehrenberg M. Spontaneous separation of bi-stable biochemical systems into spatial domains of opposite phases. Systems Biology, IEE Proceedings, volume 1 (2), pages 230-236 (2004).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000022"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Elf algorithm</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000022"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">NSM</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000022"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">next-subvolume method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000027 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000027">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000333"/>
        <rdfs:subClassOf>
            <owl:Class>
                <owl:complementOf>
                    <owl:Restriction>
                        <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                        <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000102"/>
                    </owl:Restriction>
                </owl:complementOf>
            </owl:Class>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000236"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000359"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000015"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2007-11-10</dc:created>
        <dc:creator xml:lang="en">dk</dc:creator>
        <isImplementedIn xml:lang="en">Cain</isImplementedIn>
        <isImplementedIn xml:lang="en">SmartCell</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/ecell4</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/vcell</isImplementedIn>
        <rdfs:label xml:lang="en">Gibson-Bruck next reaction algorithm</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1021/jp993732q</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Gibson and Bruck algorithm</skos:altLabel>
        <skos:altLabel xml:lang="en">Gibson-Bruck&apos;s next reaction algorithm</skos:altLabel>
        <skos:altLabel xml:lang="en">Gillespie-Gibson stochastic simulation algorithm</skos:altLabel>
        <skos:altLabel xml:lang="en">SSA-GB</skos:altLabel>
        <skos:altLabel xml:lang="en">next reaction method</skos:altLabel>
        <skos:definition xml:lang="en">As with the first reaction method [http://identifiers.org/biomodels.kisao/KISAO_0000015], a putative reaction time is calculated for each reaction, and the reaction with the shortest reaction time will be realized. However, the unused calculated reaction times are not wasted. The set of reactions is organized in a priority queue to allow for the efficient search for the fastest reaction. In addition, by using a so-called dependency graph only those reaction times are recalculated in each step, that are dependent on the reaction, which has been realized.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000027"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/ecell4</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">E-Cell</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000027"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/vcell</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">VCell</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000027"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1021/jp993732q</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Gibson MA, Bruck J. Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels. Journal of Physical Chemistry A, Vol. 104, pages 1876-1889 (2000).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000027"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Gibson and Bruck algorithm</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000027"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Gibson-Bruck&apos;s next reaction algorithm</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000027"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Gillespie-Gibson stochastic simulation algorithm</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000027"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">SSA-GB</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000027"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">next reaction method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000028 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000028">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000333"/>
        <rdfs:subClassOf>
            <owl:Class>
                <owl:complementOf>
                    <owl:Restriction>
                        <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                        <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000102"/>
                    </owl:Restriction>
                </owl:complementOf>
            </owl:Class>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000237"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">slow-scale stochastic simulation algorithm</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/15638651</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">slow-scale stochastic SSA</skos:altLabel>
        <skos:altLabel xml:lang="en">ssSSA</skos:altLabel>
        <skos:definition xml:lang="en">Attempt to overcome the problem of stiff systems by developing an &apos;&apos;approximate theory that allows one to stochastically advance the system in time by simulating the firings of only the slow reaction events&apos;&apos;.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000028"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/15638651</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Cao Y, Gillespie DT, Petzold LR. The slow-scale stochastic simulation algorithm. Journal of Chemical Physics, Vol. 122, No. 1. (1 January 2005).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000028"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">slow-scale stochastic SSA</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000028"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">ssSSA</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000029 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000029">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000241"/>
        <rdfs:subClassOf>
            <owl:Class>
                <owl:complementOf>
                    <owl:Restriction>
                        <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                        <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000102"/>
                    </owl:Restriction>
                </owl:complementOf>
            </owl:Class>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000236"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000359"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000051"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2007-11-10</dc:created>
        <dc:creator xml:lang="en">dk</dc:creator>
        <isImplementedIn xml:lang="en">BetaWB</isImplementedIn>
        <isImplementedIn xml:lang="en">ByoDyn</isImplementedIn>
        <isImplementedIn xml:lang="en">Cain</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/bionetgen</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/ibiosim</isImplementedIn>
        <rdfs:label xml:lang="en">Gillespie direct algorithm</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1016/0021-9991(76)90041-3</rdfs:seeAlso>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1021/j100540a008</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">DM</skos:altLabel>
        <skos:altLabel xml:lang="en">Doob-Gillespie method</skos:altLabel>
        <skos:altLabel xml:lang="en">Gillespie&apos;s direct method</skos:altLabel>
        <skos:altLabel xml:lang="en">SSA</skos:altLabel>
        <skos:altLabel xml:lang="en">stochastic simulation algorithm</skos:altLabel>
        <skos:definition xml:lang="en">Stochastic simulation algorithm using the reaction probability density function (next-reaction density function), giving the probability that the next reaction will happen in a given time interval. To choose the next reaction to fire, the algorithm directly and separately calculates the identity of the reaction and the time it will fire.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000029"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Gillespie&apos;s direct method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000029"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">SSA</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000029"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">stochastic simulation algorithm</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000029"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/bionetgen</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">BioNetGen</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000029"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/ibiosim</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">iBioSim</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000029"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1016/0021-9991(76)90041-3</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Gillespie DT. A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions. Journal of Computational Physics, Volume 2 , pages 403-434 (1976).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000029"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1021/j100540a008</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Gillespie DT. Exact stochastic simulation of coupled chemical reactions. Journal of Physical Chemistry, Vol. 81, No. 25. (1977), pp. 2340-2361.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000029"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">DM</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000029"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Doob-Gillespie method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000030 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000030">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000261"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000239"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <owl:disjointWith rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000031"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2007-11-10</dc:created>
        <dc:creator xml:lang="en">dk</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/ibiosim</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/vcell</isImplementedIn>
        <rdfs:label xml:lang="en">Euler forward method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/052143064X</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">explicit Euler method</skos:altLabel>
        <skos:altLabel xml:lang="en">explicit Gaussian first order Runge-Kutta</skos:altLabel>
        <skos:definition xml:lang="en">The Euler method is an explicit one-step method for the numerical integration of ODES with a given initial value. The calculation of the next integration step at time t+1 is based on the state of the system at time point t.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000030"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/ibiosim</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">iBioSim</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000030"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/vcell</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">VCell</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000030"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/052143064X</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Press WH, Teukolsky SA, Vetterling WT, Flannery BP. Numerical Recipes. Cambridge University Press, New York, 2nd edition (1992).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000030"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">explicit Euler method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000030"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">explicit Gaussian first order Runge-Kutta</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000031 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000031">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000261"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000240"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2007-11-02</dc:created>
        <dc:creator xml:lang="en">dk</dc:creator>
        <isImplementedIn xml:lang="en">GSL</isImplementedIn>
        <rdfs:label xml:lang="en">Euler backward method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/052143064X</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">implicit Euler method</skos:altLabel>
        <skos:altLabel xml:lang="en">implicit Gaussian first order Runge-Kutta</skos:altLabel>
        <skos:definition xml:lang="en">The Euler backward method is an implicit one-step method for the numerical integration of ODES with a given initial value. The next state of a system is calculated by solving an equation that considers both, the current state of the system and the later one.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000031"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/052143064X</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Press WH, Teukolsky SA, Vetterling WT, Flannery BP. Numerical Recipes in Fortran 77. Cambridge University Press (2001).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000031"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">implicit Euler method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000031"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">implicit Gaussian first order Runge-Kutta</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000032 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000032">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000064"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000108"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000239"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000275"/>
                <owl:hasValue rdf:datatype="http://www.w3.org/2001/XMLSchema#integer">4</owl:hasValue>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2007-11-12</dc:created>
        <dc:creator xml:lang="en">dk</dc:creator>
        <isImplementedIn xml:lang="en">GSL</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/jsim</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/vcell</isImplementedIn>
        <rdfs:label xml:lang="en">explicit fourth-order Runge-Kutta method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/0-471-91046-5 </rdfs:seeAlso>
        <skos:altLabel xml:lang="en">ERK4</skos:altLabel>
        <skos:altLabel xml:lang="en">RK4</skos:altLabel>
        <skos:altLabel xml:lang="en">Runge-Kutta method</skos:altLabel>
        <skos:definition xml:lang="en">The Runge-Kutta method is a method for the numerical integration of ODES with a given initial value. The calculation of the next integration step at time t+1 is based on the state of the system at time point t, plus the product of the size of the interval and an estimated slope. The slope is a weighted average of 4 single slope points (beginning of interval-midpoint-midpoint-end of interval).</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000032"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/jsim</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">JSim</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000032"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/vcell</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">VCell</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000032"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/0-471-91046-5 </owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Butcher JC. The Numerical Analysis of Ordinary Differential Equations: Runge-Kutta and General Linear Methods (1987). </rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000032"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">ERK4</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000032"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">RK4</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000032"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Runge-Kutta method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000033 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000033">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000064"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000108"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000240"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2007-11-12</dc:created>
        <dc:creator xml:lang="en">dk</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/ecell4</isImplementedIn>
        <rdfs:label xml:lang="en">Rosenbrock method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1093/comjnl/5.4.329</rdfs:seeAlso>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/052143064X</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Kaps-Rentrop method</skos:altLabel>
        <skos:altLabel xml:lang="en">generalized fourth order Runge-Kutta method</skos:altLabel>
        <skos:definition xml:lang="en">Some general implicit processes are given for the solution of simultaneous first-order differential equations. These processes, which use successive substitution, are implicit analogues of the (explicit) Runge-Kutta processes. They require the solution in each time step of one or more set of simultaneous linear equations, usually of a special and simple form. Processes of any required order can be devised, and they can be made to have a wide margin of stability when applied to a linear problem.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000033"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/ecell4</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">E-Cell</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000033"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1093/comjnl/5.4.329</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Rosenbrock HH. Some general implicit processes for the numerical solution of differential equations. The Computer Journal, pages 329-330 (1963).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000033"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/052143064X</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Press WH, Teukolsky SA, Vetterling WT, Flannery BP. Numerical Recipes. Cambridge University Press, New York, 2nd edition, pages 742-746 (1992).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000033"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Kaps-Rentrop method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000033"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">generalized fourth order Runge-Kutta method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000038 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000038">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000333"/>
        <rdfs:subClassOf>
            <owl:Class>
                <owl:complementOf>
                    <owl:Restriction>
                        <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                        <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000102"/>
                    </owl:Restriction>
                </owl:complementOf>
            </owl:Class>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000236"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">sorting stochastic simulation algorithm</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1016/j.compbiolchem.2005.10.007</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">sorting SSA</skos:altLabel>
        <skos:altLabel xml:lang="en">sorting direct method</skos:altLabel>
        <skos:definition xml:lang="en">In order to overcome the problem of high complexity of the Stochastic Simulation Algorithm [http://identifiers.org/biomodels.kisao/KISAO_0000029] when simulating large systems, the sorting direct method maintains a loosely sorted order of the reactions as the simulation executes.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000038"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1016/j.compbiolchem.2005.10.007</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">McCollum J M, Peterson G D, Cox C D, Simpson M L, Samatova N F. The sorting direct method for stochastic simulation of biochemical systems with varying reaction execution behaviour. Computational Biology and Chemistry, Volume 30 (1), pages 39-49 (2006).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000038"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">sorting SSA</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000038"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">sorting direct method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000039 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000039">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000333"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000237"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:qualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:qualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000228"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2008-07-08</dc:created>
        <dc:creator xml:lang="en">NLN</dc:creator>
        <isImplementedIn xml:lang="en">ByoDyn</isImplementedIn>
        <isImplementedIn xml:lang="en">Cain</isImplementedIn>
        <isImplementedIn xml:lang="en">SmartCell</isImplementedIn>
        <rdfs:label xml:lang="en">tau-leaping method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.1378322</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">tauL</skos:altLabel>
        <skos:definition xml:lang="en">Approximate acceleration procedure of the Stochastic Simulation Algorithm [http://identifiers.org/biomodels.kisao/KISAO_0000029] that divides the time into subintervals and &apos;&apos;leaps&apos;&apos; from one to another, firing all the reaction events in each subinterval.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000039"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.1378322</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Gillespie DT. Approximate accelerated stochastic simulation of chemically reacting systems. The Journal of Chemical Physics, Vol. 115 (4), pages 1716-1733 (2001). Section V.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000039"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">tauL</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000040 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000040">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000039"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000239"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <isImplementedIn xml:lang="en">ByoDyn</isImplementedIn>
        <rdfs:label xml:lang="en">Poisson tau-leaping method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.1378322</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">explicit tau-leaping</skos:altLabel>
        <skos:altLabel xml:lang="en">explicit tau-leaping method with basic pre-leap check</skos:altLabel>
        <skos:altLabel xml:lang="en">explicit tau-leaping method with basic preleap check</skos:altLabel>
        <skos:altLabel xml:lang="en">poisson tau-leaping</skos:altLabel>
        <skos:definition xml:lang="en">Explicit tau-leaping method with basic pre leap check.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000040"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.1378322</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Gillespie DT. Approximate accelerated stochastic simulation of chemically reacting systems. The Journal of Chemical Physics, Vol. 115 (4), pages 1716-1733 (2001). Section V.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000040"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">explicit tau-leaping</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000040"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">explicit tau-leaping method with basic preleap check</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000040"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">poisson tau-leaping</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000045 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000045">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000039"/>
        <rdfs:subClassOf>
            <owl:Class>
                <owl:complementOf>
                    <owl:Restriction>
                        <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                        <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000102"/>
                    </owl:Restriction>
                </owl:complementOf>
            </owl:Class>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000240"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:qualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:qualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000248"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2007-10-12</dc:created>
        <dc:creator xml:lang="en">dk</dc:creator>
        <rdfs:label xml:lang="en">implicit tau-leaping method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.1627296</rdfs:seeAlso>
        <skos:definition xml:lang="en">Contrary to the explicit tau-leaping [http://identifiers.org/biomodels.kisao/KISAO_0000039 and http://identifiers.org/biomodels.kisao/KISAO_0000245 some http://identifiers.org/biomodels.kisao/KISAO_0000239] , the implicit tau-leaping allows for much larger time-steps when simulating stiff systems.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000045"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.1627296</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Rathinam M, Petzold L R, Cao Y, Gillespie D T. Stiffness in stochastic chemically reacting systems: The implicit tau-leaping method. The Journal of Chemical Physics, Volume 119 (24), pages 12784-12794 (2003).</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000046 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000046">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000039"/>
        <rdfs:subClassOf>
            <owl:Class>
                <owl:complementOf>
                    <owl:Restriction>
                        <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                        <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000102"/>
                    </owl:Restriction>
                </owl:complementOf>
            </owl:Class>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000240"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2007-10-16</dc:created>
        <dc:creator xml:lang="en">dk</dc:creator>
        <rdfs:label xml:lang="en">trapezoidal tau-leaping method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">citeulike:1755561</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">trapezoidal implicit tau-leaping method</skos:altLabel>
        <skos:definition xml:lang="en">Formula for accelerated discrete efficient stochastic simulation of chemically reacting system [which] has better accuracy and stiff stability properties than the explicit and implicit [http://identifiers.org/biomodels.kisao/KISAO_0000045] tau-leaping formulas for discrete stochastic systems, and it limits to the trapezoidal rule in the deterministic regime.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000046"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">citeulike:1755561</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Cao Y, Petzold L. Trapezoidal tau-leaping formula for the stochastic simulation of biochemical systems. Foundations of Systems Biology in Engineering (FOSBE), pages 149-152 (2005).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000046"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">trapezoidal implicit tau-leaping method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000048 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000048">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000039"/>
        <rdfs:subClassOf>
            <owl:Class>
                <owl:complementOf>
                    <owl:Restriction>
                        <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                        <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000102"/>
                    </owl:Restriction>
                </owl:complementOf>
            </owl:Class>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000239"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000240"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">adaptive explicit-implicit tau-leaping method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.2745299</rdfs:seeAlso>
        <skos:definition xml:lang="en">Modification of the original tau-selection strategy [http://identifiers.org/biomodels.kisao/KISAO_0000040], designed for explicit tau-leaping, is modified to apply to implicit tau-leaping, allowing for longer steps when the system is stiff. Further, an adaptive strategy is proposed that identifies stiffness and automatically chooses between the explicit and the (new) implicit tau-selection methods to achieve better efficiency.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000048"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.2745299</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Cao Y, Gillespie DT, Petzold LR. Adaptive explicit-implicit tau-leaping method with automatic tau selection. The Journal of Chemical Physics, Vol. 126 (22) (2007).</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000051 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000051">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000241"/>
        <rdfs:subClassOf>
            <owl:Class>
                <owl:complementOf>
                    <owl:Restriction>
                        <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                        <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000102"/>
                    </owl:Restriction>
                </owl:complementOf>
            </owl:Class>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000359"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000029"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">Bortz-Kalos-Lebowitz algorithm</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1016/0021-9991(75)90060-1</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">BKL</skos:altLabel>
        <skos:altLabel xml:lang="en">DMC</skos:altLabel>
        <skos:altLabel xml:lang="en">KMC</skos:altLabel>
        <skos:altLabel xml:lang="en">dynamic Monte Carlo</skos:altLabel>
        <skos:altLabel xml:lang="en">dynamic Monte Carlo method</skos:altLabel>
        <skos:altLabel xml:lang="en">kinetic Monte Carlo</skos:altLabel>
        <skos:altLabel xml:lang="en">kinetic Monte Carlo method</skos:altLabel>
        <skos:altLabel xml:lang="en">n-fold way</skos:altLabel>
        <skos:definition xml:lang="en">The Bortz-Kalos-Lebowitz (or: kinetic Monte-Carlo-) method is a stochastic method for the simulation of time evolution of processes using (pseudo-)random numbers.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000051"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1016/0021-9991(75)90060-1</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Bortz AB, Kalos MH, Lebowitz JL. A new algorithm for Monte Carlo simulation of Ising spin systems. Journal of Computational Physics, Vol. 17 (1), pages 10-18 (1975).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000051"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">BKL</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000051"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">DMC</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000051"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">KMC</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000051"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">dynamic Monte Carlo</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000051"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">dynamic Monte Carlo method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000051"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">kinetic Monte Carlo</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000051"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">kinetic Monte Carlo method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000051"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">n-fold way</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000056 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000056">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000104"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2007-10-29</dc:created>
        <dc:creator xml:lang="en">dk</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">Smoluchowski equation based method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">urn:issn:0942-9352</rdfs:seeAlso>
        <skos:definition xml:lang="en">Method based on the Smoluchowski equation.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000056"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">urn:issn:0942-9352</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Smoluchowski M. Mathematical theory of the kinetics of the coagulation of colloidal solutions. Z. Phys. Chem, Vol. 92, No. 129. (1917).</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000057 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000057">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000056"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000102"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000105"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000108"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:qualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:qualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000254"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:qualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:qualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000257"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:qualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:qualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000258"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:qualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:qualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000260"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <owl:disjointWith rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000058"/>
        <isImplementedIn xml:lang="en">Smoldyn</isImplementedIn>
        <rdfs:label xml:lang="en">Brownian diffusion Smoluchowski method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/16204833</rdfs:seeAlso>
        <skos:definition xml:lang="en">In the Brownian diffusion Smoluchowski method, &apos;&apos;each molecule is treated as a point-like particle that diffuses freely in three-dimensional space. When a pair of reactive molecules collide, such as an enzyme and its substrate, a reaction occurs and the simulated reactants are replaced by products. [..] Analytic solutions are presented for some simulation parameters while others are calculated using look-up tables&apos;&apos;. Supported chemical processes include molecular diffusion, treatment of surfaces, zeroth-order-, unimolecular-, and bimolecular reactions.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000057"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/16204833</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Andrews SS, Bray D. Stochastic simulation of chemical reactions with spatial resolution and single molecule detail. Phys Biol, volume 1 (3-4), pages 137-151 (December 2004).</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000058 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000058">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000056"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000102"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000105"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000107"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000237"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">Greens function reaction dynamics</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.2137716</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">GFRD</skos:altLabel>
        <skos:altLabel xml:lang="en">Green&apos;s function reaction dynamics</skos:altLabel>
        <skos:definition xml:lang="en">Method that simulates biochemical networks on particle level. It considers both changes in time and space by &apos;&apos;exploiting both the exact solution of the Smoluchowski Equation to set up an event-driven algorithm&apos;&apos; which allows for large jumps in time when the considered particles are far away from each other [in space] and thus cannot react. GFRD combines the propagation of particles in space with the reactions taking place between them in one simulation step.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000058"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.2137716</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Van Zon JS, Ten Wolde PR. Green&apos;s-function reaction dynamics: A particle-based approach for simulating biochemical networks in time and space. Journal of Chemical Physics, Volume 123 (23) (2005).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000058"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">GFRD</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000058"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Green&apos;s function reaction dynamics</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000064 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000064">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000377"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000103"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000108"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000374"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000361"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000261"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000275"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#integer"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2007-11-12</dc:created>
        <dc:creator xml:lang="en">dk</dc:creator>
        <isImplementedIn xml:lang="en">ByoDyn</isImplementedIn>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">Runge-Kutta based method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/0-471-91046-5</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">modified Euler method</skos:altLabel>
        <skos:definition xml:lang="en">A method of numerically integrating ordinary differential equations, which uses a sampling of slopes through an interval and takes a weighted average to determine the right end point. This averaging gives a very accurate approximation.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000064"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/0-471-91046-5</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Butcher JC. The Numerical Analysis of Ordinary Differential Equations: Runge-Kutta and General Linear Methods (1987).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000064"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">modified Euler method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">RELATED</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000068 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000068">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000264"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000103"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2007-11-30</dc:created>
        <dc:creator xml:lang="en">dk</dc:creator>
        <rdfs:label xml:lang="en">deterministic cellular automata update algorithm</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-0252000232</rdfs:seeAlso>
        <skos:definition xml:lang="en">A cellular automaton is a discrete model of a regular grid of cells with a finite number of dimensions. Each cell has a finite number of defined states. The automaton changes its state in a discrete manner, meaning that the state of a cell at time t is determined by a function of the states of its neighbours at time t - 1. These neighbours are a selection of cells relative to the specified cell. Famous examples for deterministic cellular automata are Conway&apos;s game of life or Wolfram&apos;s elementary cellular automata.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000068"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-0252000232</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Burks, Arthur W (Editor). Essays on Cellular Automata. University of Illinois Press (1970).</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000071 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000071">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000094"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000239"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000288"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000364"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2007-11-16</dc:created>
        <dc:creator xml:lang="en">dk</dc:creator>
        <rdfs:label xml:lang="en">LSODE</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">citeulike:1774586</rdfs:seeAlso>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1145/1218052.1218054</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Livermore solver for ordinary differential equations</skos:altLabel>
        <skos:definition xml:lang="en">LSODE solves stiff and nonstiff systems of the form dy/dt = f.  In the stiff case, it treats the Jacobian matrix sf/dy as either a dense (full) or a banded matrix, and as either user-supplied or internally approximated by difference quotients. It uses Adams methods (predictor-corrector) [http://identifiers.org/biomodels.kisao/KISAO_0000364] in the nonstiff case, and Backward Differentiation Formula (BDF) methods (the Gear methods) [http://identifiers.org/biomodels.kisao/KISAO_0000288] in the stiff case.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000071"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">citeulike:1774586</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Radhakrishnan K, Hindmarsh AC. Description and Use of LSODE, the Livermore Solver for Ordinary Differential Equations. Lawrence Livermore National Laboratory Report, Vol. UCRL-ID-113855 (1993).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000071"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1145/1218052.1218054</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Hindmarsh AC. LSODE and LSODI, two new initial value ordinary differential equation solvers. SIGNUM Newsletter, Volume 15 (4), pages 10-11 (1980).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000071"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Livermore solver for ordinary differential equations</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000074 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000074">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000039"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000359"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000095"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:qualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:qualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000253"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2007-10-16</dc:created>
        <dc:creator xml:lang="en">dk</dc:creator>
        <rdfs:label xml:lang="en">binomial tau-leaping method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.2771548</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">BtauL</skos:altLabel>
        <skos:altLabel xml:lang="en">binomial tau-leap spatial stochastic simulation algorithm</skos:altLabel>
        <skos:definition xml:lang="en">Coarse grained modified version of the next subvolume method [http://identifiers.org/biomodels.kisao/KISAO_0000022] that allows the user to consider both diffusion and reaction events in relatively long simulation time spans as compared with the original method and other commonly used fully stochastic computational methods.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000074"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.2771548</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Marquez-Lago T., Burrage K. Binomial tau-leap spatial stochastic simulation algorithm for applications in chemical kinetics. The Journal of Chemical Physics, Vol. 127 (10) (2007).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000074"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">BtauL</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000074"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">binomial tau-leap spatial stochastic simulation algorithm</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000075 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000075">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000241"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000102"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000029"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000334"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">Gillespie multi-particle method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/16731694</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">GMP</skos:altLabel>
        <skos:altLabel xml:lang="en">Gillespie&apos;s multi-particle method</skos:altLabel>
        <skos:altLabel xml:lang="en">particle-based spatial stochastic method</skos:altLabel>
        <skos:definition xml:lang="en">Combination of the multiparticle method for diffusion [http://identifiers.org/biomodels.kisao/KISAO_0000334] and the SSA [http://identifiers.org/biomodels.kisao/KISAO_0000029].</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000075"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/16731694</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Rodriguez VJ, Kaandorp JA, Dobrzynski M, Blom JG. Spatial stochastic modelling of the phosphoenolpyruvate-dependent phosphotransferase (PTS) pathway in Escherichia coli. Bioinformatics, Vol. 22 (15), pages 1895-1901 (2006).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000075"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">GMP</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000075"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Gillespie&apos;s multi-particle method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000075"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">particle-based spatial stochastic method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000076 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000076">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000095"/>
        <rdfs:label xml:lang="en">Stundzia and Lumsden method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1006/jcph.1996.0168</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">RD SSA</skos:altLabel>
        <skos:altLabel xml:lang="en">reaction-diffusion stochastic simulation algorithm</skos:altLabel>
        <skos:definition xml:lang="en">Sub-volume stochastic reaction-diffusion method that using Green&apos;s function to link the bulk diffusion coefficient D in Fick&apos;s differential law to the corresponding transition rate probability for diffusion of a particle between finite volume elements. This generalized stochastic algorithm enables to numerically calculate the time evolution of a spatially inhomogeneous mixture of reaction-diffusion species in a finite volume. The time step is stochastic and is generated by a probability distribution determined by the intrinsic reaction kinetics and diffusion dynamics.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000076"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1006/jcph.1996.0168</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Stundzia AB, Lumsden CJ. Stochastic simulation of coupled reaction-diffusion processes. J Comput Phys, Vol. 127 (1), pages 196-207 (1996).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000076"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">RD SSA</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000076"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">reaction-diffusion stochastic simulation algorithm</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000081 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000081">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000039"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000239"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">estimated midpoint tau-leaping method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.1378322</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">explicit tau-leaping method with estimated-mid point technique</skos:altLabel>
        <skos:definition xml:lang="en">Estimated-Midpoint tau-Leap Method: For the selected leaping time tau which satisfies the Leap Condition, compute the expected state change lambda&apos; = tau sumj( aj(x)vj ) during [t, t + tau). Then, with x&apos; =x + [lambda&apos;/2], generate for each j = 1,...,M a sample value kj of the Poisson random variable P(aj(x&apos;), tau). Compute the actual state change, lambda = sumj( kjvj ), and effect the leap by replacing t by t + tau and x by x + lambda.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000081"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.1378322</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Gillespie DT. Approximate accelerated stochastic simulation of chemically reacting systems. The Journal of Chemical Physics, Vol. 115 (4), pages 1716-1733 (2001). Section VI.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000081"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">explicit tau-leaping method with estimated-mid point technique</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000082 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000082">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000333"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000237"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000359"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000039"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">k-alpha leaping method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.1378322</rdfs:seeAlso>
        <skos:definition xml:lang="en">Alternative to the tau-leaping [http://identifiers.org/biomodels.kisao/KISAO_0000039], where one leaps a fixed number of reaction-events.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000082"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.1378322</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Gillespie DT. Approximate accelerated stochastic simulation of chemically reacting systems. The Journal of Chemical Physics, Vol. 115 (4), pages 1716-1733 (2001). Section VIII.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000084 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000084">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000039"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000239"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000359"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000040"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:qualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:qualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000249"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">nonnegative Poisson tau-leaping method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.1992473</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">modified poisson tau-leaping</skos:altLabel>
        <skos:definition xml:lang="en">The explicit tau-leaping procedure attempts to speed up the stochastic simulation of a chemically reacting system by approximating the number of firings of each reaction channel during a chosen time increment Tau as a Poisson random variable. Since the Poisson random variable can have arbitrarily large sample values, there is always the possibility that this procedure will cause one or more reaction channels to fire so many times during Tau that the population of some reactant species will be driven negative. Two recent papers have shown how that unacceptable occurrence can be avoided by replacing the Poisson random variables with binomial random variables, whose values are naturally bounded. This paper describes a modified Poisson tau-leaping procedure that also avoids negative populations, but is easier to implement than the binomial procedure. The new Poisson procedure also introduces a second control parameter, whose value essentially dials the procedure from the original Poisson tau-leaping at one extreme to the exact stochastic simulation algorithm at the other; therefore, the modified Poisson procedure will generally be more accurate than the original Poisson procedure [http://identifiers.org/biomodels.kisao/KISAO_0000040].</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000084"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.1992473</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Cao Y, Gillespie DT, Petzold LR. Avoiding negative populations in explicit Poisson tau-leaping. Journal of Chemical Physics, Vol. 123, 4104 (2005).</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000086 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000086">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000435"/>
        <isImplementedIn xml:lang="en">GSL</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/ecell4</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/ibiosim</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/jsim</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/vcell</isImplementedIn>
        <rdfs:label xml:lang="en">Fehlberg method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1007/BF02241732</rdfs:seeAlso>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/14990450</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">RKF45</skos:altLabel>
        <skos:altLabel xml:lang="en">Runge-Kutta-Fehlberg method</skos:altLabel>
        <skos:definition xml:lang="en">The method was developed by the German mathematician Erwin Fehlberg and is based on the class of Runge-Kutta methods. The Runge-Kutta-Fehlberg method uses an O(h4) method together with an O(h5) method that uses all of the points of the O(h4) method, and hence is often referred to as an RKF45 method. Similar schemes with different orders have since been developed. By performing one extra calculation that would be required for an RK5 method, the error in the solution can be estimated and controlled and an appropriate step size can be determined automatically, making this method efficient for ordinary problems of automated numerical integration of ordinary differential equations.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000086"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/ecell4</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">E-Cell</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000086"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/ibiosim</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">iBioSim</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000086"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/jsim</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">JSim</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000086"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/vcell</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">VCell</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000086"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1007/BF02241732</owl:annotatedTarget>
        <rdfs:comment xml:lang="de">Erwin Fehlberg (1970). Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Wärmeleitungsprobleme, Computing (Arch. Elektron. Rechnen), vol. 6, pp. 61-71.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000086"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/14990450</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Takahashi K, Kaizu K, Hu B, Tomita M. A multi-algorithm, multi-timescale method for cell simulation. Bioinformatics volume 20(4), pages 538-46 (2004).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000086"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">RKF45</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000086"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Runge-Kutta-Fehlberg method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000087 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000087">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000435"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:maxQualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:maxQualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000538"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:maxQualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:maxQualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000539"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:maxQualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:maxQualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000540"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:maxQualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:maxQualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000541"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:maxQualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:maxQualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000559"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2007-11-12</dc:created>
        <dc:creator xml:lang="en">dk</dc:creator>
        <isImplementedIn xml:lang="en">ECell3</isImplementedIn>
        <isImplementedIn xml:lang="en">GSL</isImplementedIn>
        <isImplementedIn xml:lang="en">Matlab</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/ibiosim</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/jsim</isImplementedIn>
        <rdfs:label xml:lang="en">Dormand-Prince method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1016/0771-050X(80)90013-3</rdfs:seeAlso>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/14990450</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">DOPRI</skos:altLabel>
        <skos:altLabel xml:lang="en">Prince-Dormand method</skos:altLabel>
        <skos:definition xml:lang="en">Dormand-Prince is an explicit method for the numerical integration of ODES with a given initial value.
It is an &apos;embedded Runge-Kutta method&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000302] RK5 (4) which (a) has a &apos;small&apos; principal truncation term in the Fifth order and (b) has an extended region of absolute stability.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000087"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/ibiosim</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">iBioSim</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000087"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/jsim</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">JSim</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000087"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1016/0771-050X(80)90013-3</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Dormand J, Prince P. A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics, Volume 6, pages 19-26 (1980).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000087"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/14990450</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Takahashi K, Kaizu K, Hu B, Tomita M. A multi-algorithm, multi-timescale method for cell simulation. Bioinformatics volume 20(4), pages 538-46 (2004).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000087"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Prince-Dormand method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000088 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000088">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000094"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000359"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000071"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000288"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000289"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:qualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:qualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000209"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:qualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:qualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000211"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:qualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:qualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000219"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:qualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:qualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000220"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:maxQualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:maxQualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000559"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2007-11-30</dc:created>
        <dc:creator xml:lang="en">dk</dc:creator>
        <rdfs:label xml:lang="en">LSODA</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1137/0904010</rdfs:seeAlso>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-0444866073</rdfs:seeAlso>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://www.nea.fr/abs/html/uscd1227.html</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Livermore solver for ordinary differential equations with automatic method switching</skos:altLabel>
        <skos:definition xml:lang="en">LSODA solves systems dy/dt = f with a dense or banded Jacobian when the problem is stiff, but it automatically selects between non-stiff (Adams [http://identifiers.org/biomodels.kisao/KISAO_0000289]) and stiff (BDF [http://identifiers.org/biomodels.kisao/KISAO_0000288]) methods. It uses the non-stiff method initially, and dynamically monitors data in order to decide which method to use.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000088"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1137/0904010</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Petzold LR. Automatic Selection of Methods for Solving Stiff and Nonstiff Systems of Ordinary Differential Equations. SIAM Journal on Scientific and Statistical Computing, Vol. 4 (1), pages 136-148 (1983).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000088"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-0444866073</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">A. C. Hindmarsh, ODEPACK, A Systematized Collection of ODE Solvers, in Scientific Computing, R. S. Stepleman et al. (eds.), North-Holland, Amsterdam, 1983 (vol. 1 of IMACS Transactions on Scientific Computation), pp. 55-64.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000088"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://www.nea.fr/abs/html/uscd1227.html</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Petzold LR, Hindmarsh, AC. LSODAR: Livermore solver of ordinary differential equations with automatic method switching and root finding, Computing and Mathematics Research Division, 1-316 Lawerence Livermore National Laboratory (1987).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000088"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Livermore solver for ordinary differential equations with automatic method switching</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000089 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000089">
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            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2007-10-27</dc:created>
        <dc:creator xml:lang="en">dk</dc:creator>
        <rdfs:label xml:lang="en">LSODAR</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-0444866073</rdfs:seeAlso>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://www.nea.fr/abs/html/uscd1228.html</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Livermore solver for ordinary differential equations with automatic method switching and root finding</skos:altLabel>
        <skos:altLabel xml:lang="en">ordinary differential equation solver for stiff or non-stiff systems with root finding</skos:altLabel>
        <skos:definition xml:lang="en">LSODAR is a variant of LSODA [http://identifiers.org/biomodels.kisao/KISAO_0000088] with a root finding capability added. Thus it solves problems dy/dt = f with dense or banded Jacobian and automatic method selection, and at the same time, it finds the roots of any of a set of given functions of the form g(t,y). This is often useful for finding stop conditions, or for finding points at which a switch is to be made in the function f.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000089"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-0444866073</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">A. C. Hindmarsh, ODEPACK, A Systematized Collection of ODE Solvers, in Scientific Computing, R. S. Stepleman et al. (eds.), North-Holland, Amsterdam, 1983 (vol. 1 of IMACS Transactions on Scientific Computation), pp. 55-64.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000089"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://www.nea.fr/abs/html/uscd1228.html</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Petzold LR, Hindmarsh, AC. LSODAR: Livermore solver of ordinary differential equations with automatic method switching and root finding, Computing and Mathematics Research Division, 1-316 Lawerence Livermore National Laboratory (1987).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000089"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Livermore solver for ordinary differential equations with automatic method switching and root finding</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000089"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">ordinary differential equation solver for stiff or non-stiff systems with root finding</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000090 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000090">
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            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">LSODI</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1145/1218052.1218054</rdfs:seeAlso>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-0444866073</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Livermore solver for ordinary differential equations, implicit version</skos:altLabel>
        <skos:definition xml:lang="en">LSODI solves systems given in linearly implicit form, including differential-algebraic systems.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000090"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1145/1218052.1218054</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Hindmarsh AC. LSODE and LSODI, two new initial value ordinary differential equation solvers. SIGNUM Newsletter, Volume 15 (4), pages 10-11 (1980).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000090"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-0444866073</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">A. C. Hindmarsh, ODEPACK, A Systematized Collection of ODE Solvers, in Scientific Computing, R. S. Stepleman et al. (eds.), North-Holland, Amsterdam, 1983 (vol. 1 of IMACS Transactions on Scientific Computation), pp. 55-64.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000090"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Livermore solver for ordinary differential equations, implicit version</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000091 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000091">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000094"/>
        <rdfs:subClassOf>
            <owl:Restriction>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000359"/>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2007-11-30</dc:created>
        <dc:creator xml:lang="en">dk</dc:creator>
        <rdfs:label xml:lang="en">LSODIS</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-0444866073</rdfs:seeAlso>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://www.nea.fr/abs/html/uscd1225.html</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Livermore solver for ordinary differential equations, implicit sparse version</skos:altLabel>
        <skos:definition xml:lang="en">LSODIS is a set of general-purpose FORTRAN routines solver for the initial value problem for ordinary differential equation systems. It is suitable for both stiff and nonstiff systems. LSODIS treat systems in the linearly implicit form A(t,y) dy/dt = g(t,y), A = a square matrix, i.e. with the derivative dy/dt implicit, but linearly so.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000091"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-0444866073</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">A. C. Hindmarsh, ODEPACK, A Systematized Collection of ODE Solvers, in Scientific Computing, R. S. Stepleman et al. (eds.), North-Holland, Amsterdam, 1983 (vol. 1 of IMACS Transactions on Scientific Computation), pp. 55-64.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000091"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://www.nea.fr/abs/html/uscd1225.html</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Seager M, Balsdon S. LSODIS - A sparse implicit ODE solver. 10th World Congress on System Simulation and Scientific Computation, pages 437-439 (1983).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000091"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Livermore solver for ordinary differential equations, implicit sparse version</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000093 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000093">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000094"/>
        <rdfs:subClassOf>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2008-07-08</dc:created>
        <dc:creator xml:lang="en">NLN</dc:creator>
        <rdfs:label xml:lang="en">LSODPK</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-0444866073</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Livermore solver for ordinary differential equations for stiff and nonstiff systems with krylov corrector iteration</skos:altLabel>
        <skos:definition xml:lang="en">LSODPK is a set of FORTRAN subroutines for solving the initial value problem for stiff and nonstiff systems of ordinary differential equations. In solving stiff systems, LSODPK uses a corrector iteration composed of Newton iteration and one of four preconditioned Krylov subspace iteration methods [http://identifiers.org/biomodels.kisao/KISAO_0000354]. The user must select the desired Krylov method and supply a pair of routine to evaluate, preprocess, and solve the (left and/or right) preconditioner matrices. Aside from preconditioning, the implementation is matrix-free, meaning that explicit storage of the Jacobian (or related) matrix is not required. The method is experimental because the scope of problems for which it is effective is not well-known, and users are forewarned that LSODPK may or may not be competitive with traditional methods on a given problem. LSODPK also includes an option for a user-supplied linear system solver to be used without Krylov iteration.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000093"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-0444866073</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">A. C. Hindmarsh, ODEPACK, A Systematized Collection of ODE Solvers, in Scientific Computing, R. S. Stepleman et al. (eds.), North-Holland, Amsterdam, 1983 (vol. 1 of IMACS Transactions on Scientific Computation), pp. 55-64.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000093"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Livermore solver for ordinary differential equations for stiff and nonstiff systems with krylov corrector iteration</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000094 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000094">
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        <rdfs:subClassOf>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000107"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2008-07-08</dc:created>
        <dc:creator xml:lang="en">NLN</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">Livermore solver</rdfs:label>
        <skos:definition xml:lang="en">Method to solve ordinary differential equations developed at the Lawrence Livermore National Laboratory.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000095 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000095">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000335"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000102"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <owl:disjointWith rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000336"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2008-07-08</dc:created>
        <dc:creator xml:lang="en">NLN</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">sub-volume stochastic reaction-diffusion algorithm</rdfs:label>
        <skos:definition xml:lang="en">Stochastic method using a combination of discretisation of compartment volumes into voxels and Gillespie-like algorithm [http://identifiers.org/biomodels.kisao/KISAO_0000241] to simulate the evolution of the system.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000097 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000097">
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">modelling and simulation algorithm characteristic</rdfs:label>
        <skos:altLabel xml:lang="en">modeling and simulation algorithm characteristic</skos:altLabel>
        <skos:definition xml:lang="en">Simulation algorithm property, which can, for example, describe the model, such as the type of variables (discrete or continuous), and information on the treatment of spatial descriptions, or can be a numerical characteristic, such as the system&apos;s behaviour (deterministic or stochastic) as well as the progression mechanism (fixed or adaptive time steps).</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000098 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000098">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000097"/>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">type of variable</rdfs:label>
        <skos:definition xml:lang="en">Type of variables used for the simulation.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000099 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000099">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000097"/>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">type of system behaviour</rdfs:label>
        <skos:definition xml:lang="en">A characteristic describing the rules the algorithm uses to simulate the temporal evolution of a system, specifically whether or not the final state is uniquely determined from a precise initial state.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000100 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000100">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000097"/>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">type of progression time step</rdfs:label>
        <skos:definition xml:lang="en">Type of time steps used by the algorithm.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000102 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000102">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000097"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2008-07-08</dc:created>
        <dc:creator xml:lang="en">NLN</dc:creator>
        <rdfs:label xml:lang="en">spatial description</rdfs:label>
        <skos:definition xml:lang="en">Algorithm, possessing this characteristic, takes into account the location of the reacting components.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000103 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000103">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000099"/>
        <owl:disjointWith rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000104"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2008-07-08</dc:created>
        <dc:creator xml:lang="en">NLN</dc:creator>
        <rdfs:label xml:lang="en">deterministic system behaviour</rdfs:label>
        <skos:definition xml:lang="en">Algorithm, possessing this characteristic, simulates the temporal evolution of a system deterministically, so that from a precise initial state the algorithm will always end up in the same final state.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000104 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000104">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000099"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2008-07-08</dc:created>
        <dc:creator xml:lang="en">NLN</dc:creator>
        <rdfs:label xml:lang="en">stochastic system behaviour</rdfs:label>
        <skos:definition xml:lang="en">Algorithm, possessing this characteristic, simulates the temporal evolution of a system using probabilistic rules, so that between two simulations, the same precise initial state may result in a different final state.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000105 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000105">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000098"/>
        <owl:disjointWith rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000106"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2008-07-08</dc:created>
        <dc:creator xml:lang="en">NLN</dc:creator>
        <rdfs:label xml:lang="en">discrete variable</rdfs:label>
        <skos:definition xml:lang="en">Algorithm, possessing this characteristic, allows values of system&apos;s variables to change by discrete (integral) amounts.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000106 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000106">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000098"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2008-07-08</dc:created>
        <dc:creator xml:lang="en">NLN</dc:creator>
        <rdfs:label xml:lang="en">continuous variable</rdfs:label>
        <skos:definition xml:lang="en">Algorithm, possessing this characteristic, allows the values of a system&apos;s variables to change by continuous (non-integral) amounts.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000107 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000107">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000100"/>
        <owl:disjointWith rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000108"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2008-07-08</dc:created>
        <dc:creator xml:lang="en">NLN</dc:creator>
        <rdfs:label xml:lang="en">progression with adaptive time step</rdfs:label>
        <skos:definition xml:lang="en">Algorithm, possessing this characteristic, does not use fixed time steps to update the state of a system during the whole simulation, but on the contrary adapts the length of the time steps to the local situation.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000108 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000108">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000100"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2008-07-08</dc:created>
        <dc:creator xml:lang="en">NLN</dc:creator>
        <rdfs:label xml:lang="en">progression with fixed time step</rdfs:label>
        <skos:definition xml:lang="en">Algorithm, possessing this characteristic, uses time steps of constant length to update the state of a system during the whole simulation.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000201 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000201">
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">modelling and simulation algorithm parameter</rdfs:label>
        <skos:altLabel xml:lang="en">modeling and simulation algorithm parameter</skos:altLabel>
        <skos:definition xml:lang="en">Parameter that can be used in the simulation experiment settings.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000203 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000203">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000252"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:allValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000231"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#double"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">particle number lower limit</rdfs:label>
        <skos:definition xml:lang="en">This parameter of &apos;Pahle hybrid method&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000231] is a double value specifying the lower limit for particle numbers. Species with a particle number below this value are considered as having a low particle number. The &apos;particle number lower limit&apos; cannot be higher than the &apos;particle number upper limit&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000204].</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000204 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000204">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000252"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:allValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000231"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#double"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">particle number upper limit</rdfs:label>
        <skos:definition xml:lang="en">This parameter of &apos;Pahle hybrid method&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000231] is a double value specifying the upper limit for particle numbers. Species with a particle number above this value are considered as having a high particle number. The &apos;particle number upper limit&apos; cannot be lower than the &apos;particle number lower limit&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000203].</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000205 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000205">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000252"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:allValuesFrom>
                    <owl:Class>
                        <owl:intersectionOf rdf:parseType="Collection">
                            <rdf:Description rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
                            <owl:Restriction>
                                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000322"/>
                            </owl:Restriction>
                        </owl:intersectionOf>
                    </owl:Class>
                </owl:allValuesFrom>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#integer"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">partitioning interval</rdfs:label>
        <skos:definition xml:lang="en">This positive integer value specifies after how many steps the internal partitioning of the system should be recalculated.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000209 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000209">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000597"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:allValuesFrom>
                    <owl:Restriction>
                        <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                        <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000237"/>
                    </owl:Restriction>
                </owl:allValuesFrom>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#double"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">relative tolerance</rdfs:label>
        <skos:altLabel xml:lang="en">RTOL</skos:altLabel>
        <skos:definition xml:lang="en">This parameter is a numeric value specifying the desired relative tolerance the user wants to achieve. A smaller value means that the trajectory is calculated more accurately.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000209"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">RTOL</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000211 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000211">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000597"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:allValuesFrom>
                    <owl:Restriction>
                        <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                        <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000237"/>
                    </owl:Restriction>
                </owl:allValuesFrom>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#double"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">absolute tolerance</rdfs:label>
        <skos:altLabel xml:lang="en">ATOL</skos:altLabel>
        <skos:definition xml:lang="en">This parameter is a positive numeric value specifying the desired absolute tolerance the user wants to achieve.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000211"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">ATOL</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000216 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000216">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000243"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000088"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#boolean"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">integrate reduced model</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/14990466</rdfs:seeAlso>
        <skos:definition xml:lang="en">This parameter is a boolean value to determine whether the integration shall be performed using the mass conservation laws (true), i.e., reducing the number of system variables or to use the complete model (false).</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000219 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000219">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000484"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#integer"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <owl:disjointWith rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000220"/>
        <rdfs:label xml:lang="en">maximum Adams order</rdfs:label>
        <skos:altLabel xml:lang="en">Adams max order</skos:altLabel>
        <skos:altLabel xml:lang="en">maximum non-stiff order</skos:altLabel>
        <skos:definition xml:lang="en">This parameter is a positive integer value specifying the maximal order the non-stiff Adams integration method [http://identifiers.org/biomodels.kisao/KISAO_0000289] shall attempt before switching to the stiff BDF method [http://identifiers.org/biomodels.kisao/KISAO_0000288].</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000220 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000220">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000484"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#integer"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">maximum BDF order</rdfs:label>
        <skos:altLabel xml:lang="en">BDF max order</skos:altLabel>
        <skos:altLabel xml:lang="en">maximum stiff order</skos:altLabel>
        <skos:definition xml:lang="en">This parameter is a positive integer value specifying the maximal order the stiff BDF integration method [http://identifiers.org/biomodels.kisao/KISAO_0000288] shall attempt before switching to smaller internal step sizes.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000223 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000223">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000244"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:someValuesFrom>
                    <owl:Class>
                        <owl:intersectionOf rdf:parseType="Collection">
                            <rdf:Description rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
                            <owl:Restriction>
                                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000375"/>
                            </owl:Restriction>
                        </owl:intersectionOf>
                    </owl:Class>
                </owl:someValuesFrom>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#integer"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">number of history bins</rdfs:label>
        <skos:definition xml:lang="en">The &apos;number of history bins&apos; is only enabled for models that contain delayed or multistep reactions for specifying the granularity with which the delayed reaction solver should retain the history of species values, for species that participate in delayed reactions.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000228 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000228">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000242"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:allValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000039"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#double"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">tau-leaping epsilon</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.1378322</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">epsilon</skos:altLabel>
        <skos:altLabel xml:lang="en">tolerance</skos:altLabel>
        <skos:definition xml:lang="en">The leap condition is chosen such that the expected change in the propensity function aj(x) is bounded by Epsilon * a0 where Epsilon is an error control parameter between 0 and 1. This parameter is the basic error control mechanism for the Tau-Leaping algorithm [http://identifiers.org/biomodels.kisao/KISAO_0000039]. As Epsilon decreases the leaps become shorter and the simulation is more accurate.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000228"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.1378322</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Gillespie DT. Approximate accelerated stochastic simulation of chemically reacting systems. The Journal of Chemical Physics, Vol. 115 (4), pages 1716-1733 (2001). Section V.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000228"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">epsilon</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000230 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000230">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000243"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:allValuesFrom>
                    <owl:Class>
                        <owl:intersectionOf rdf:parseType="Collection">
                            <owl:Restriction>
                                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000246"/>
                                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000029"/>
                            </owl:Restriction>
                            <owl:Restriction>
                                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000246"/>
                                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000039"/>
                            </owl:Restriction>
                        </owl:intersectionOf>
                    </owl:Class>
                </owl:allValuesFrom>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#integer"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">minimum reactions per leap</rdfs:label>
        <skos:altLabel xml:lang="en">threshold</skos:altLabel>
        <skos:definition xml:lang="en">&apos;minimum reactions per leap&apos; parameter is used in hybrid methods, which adaptively switch between the tau-leaping algorithm [http://identifiers.org/biomodels.kisao/KISAO_0000039] to the SSA Direct Method [http://identifiers.org/biomodels.kisao/KISAO_0000029] when the number of reactions in a single tau-leaping leap step is less than the threshold.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000231 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000231">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000352"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000103"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000104"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000322"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000246"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000027"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000246"/>
                <owl:someValuesFrom>
                    <owl:Class>
                        <owl:intersectionOf rdf:parseType="Collection">
                            <rdf:Description rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
                            <owl:Restriction>
                                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000374"/>
                            </owl:Restriction>
                        </owl:intersectionOf>
                    </owl:Class>
                </owl:someValuesFrom>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:qualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:qualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000203"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:qualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:qualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000204"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</isImplementedIn>
        <rdfs:label xml:lang="en">Pahle hybrid method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1093/bioinformatics/btl485</rdfs:seeAlso>
        <skos:definition xml:lang="en">The hybrid method combines the stochastic &apos;Gibson-Bruck&apos;s next reaction method&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000027] with different algorithms for the numerical integration of ODEs [http://identifiers.org/biomodels.kisao/KISAO_0000245 some http://identifiers.org/biomodels.kisao/KISAO_0000374]. The biochemical network is dynamically partitioned into a deterministic and a stochastic subnet depending on the current particle numbers in the system. The user can define limits for when a particle number should be considered low or high. The stochastic subnet contains reactions involving low numbered species as substrate or product. All the other reactions form the deterministic subnet. The two subnets are then simulated in parallel using the stochastic and deterministic solver, respectively. The reaction probabilities in the stochastic subnet are approximated as constant between two stochastic reaction events.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000231"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">COPASI</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000231"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1093/bioinformatics/btl485</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">COPASI--a COmplex PAthway SImulator. Hoops S, Sahle S, Gauges R, Lee C, Pahle J, Simus N, Singhal M, Xu L, Mendes P, Kummer U. Bioinformatics. 2006 Dec 15;22(24):3067-74. Epub 2006 Oct 10.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000232 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000232">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000094"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000240"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000359"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000071"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">LSOIBT</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-0444866073</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Livermore solver for ordinary differential equations given in implicit form, with block-tridiagonal Jacobian treatment</skos:altLabel>
        <skos:definition xml:lang="en">LSOIBT solves linearly implicit systems in which the matrices involved are all assumed to be block-tridiagonal. Linear systems are solved by the LU method.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000232"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-0444866073</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">A. C. Hindmarsh, ODEPACK, A Systematized Collection of ODE Solvers, in Scientific Computing, R. S. Stepleman et al. (eds.), North-Holland, Amsterdam, 1983 (vol. 1 of IMACS Transactions on Scientific Computation), pp. 55-64.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000232"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Livermore solver for ordinary differential equations given in implicit form, with block-tridiagonal Jacobian treatment</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000233 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000233">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000094"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000359"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000071"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">LSODES</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-0444866073</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Livermore solver for ordinary differential equations with general sparse Jacobian matrix</skos:altLabel>
        <skos:definition xml:lang="en">LSODES solves systems dy/dt = f and in the stiff case treats the Jacobian matrix in general sparse form. It determines the sparsity structure on its own, or optionally accepts this information from the user. It then uses parts of the Yale Sparse Matrix Package (YSMP) to solve the linear systems that arise, by a sparse (direct) LU factorization/backsolve method.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000233"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-0444866073</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">A. C. Hindmarsh, ODEPACK, A Systematized Collection of ODE Solvers, in Scientific Computing, R. S. Stepleman et al. (eds.), North-Holland, Amsterdam, 1983 (vol. 1 of IMACS Transactions on Scientific Computation), pp. 55-64.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000233"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Livermore solver for ordinary differential equations with general sparse Jacobian matrix</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000234 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000234">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000094"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000359"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000071"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000359"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000093"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000354"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">LSODKR</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-0444866073</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Livermore solver for ordinary differential equations, with preconditioned Krylov iteration methods for the Newton correction linear systems, and with root finding.</skos:altLabel>
        <skos:definition xml:lang="en">LSODKR is an initial value ODE solver for stiff and nonstiff systems. It is a variant of the LSODPK [http://identifiers.org/biomodels.kisao/KISAO_0000093] and LSODE [http://identifiers.org/biomodels.kisao/KISAO_0000071] solvers, intended mainly for large stiff systems. The main differences between LSODKR and LSODE [http://identifiers.org/biomodels.kisao/KISAO_0000071] are the following: a) for stiff systems, LSODKR uses a corrector iteration composed of Newton iteration and one of four preconditioned Krylov subspace iteration methods. The user must supply routines for the preconditioning operations, b) within the corrector iteration, LSODKR does automatic switching between functional (fixpoint) iteration and modified Newton iteration, c) LSODKR includes the ability to find roots of given functions of the solution during the integration.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000234"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-0444866073</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">A. C. Hindmarsh, ODEPACK, A Systematized Collection of ODE Solvers, in Scientific Computing, R. S. Stepleman et al. (eds.), North-Holland, Amsterdam, 1983 (vol. 1 of IMACS Transactions on Scientific Computation), pp. 55-64.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000234"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Livermore solver for ordinary differential equations, with preconditioned Krylov iteration methods for the Newton correction linear systems, and with root finding.</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000235 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000235">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000097"/>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">type of solution</rdfs:label>
        <skos:definition xml:lang="en">A characteristic describing the type of the solution produced by the method, specifically whether it is exact or approximate.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000236 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000236">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000235"/>
        <owl:disjointWith rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000237"/>
        <rdfs:label xml:lang="en">exact solution</rdfs:label>
        <skos:definition xml:lang="en">Algorithm, possessing this characteristic, provides an exact solution to the initial problem.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000237 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000237">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000235"/>
        <rdfs:label xml:lang="en">approximate solution</rdfs:label>
        <skos:definition xml:lang="en">Approximation algorithms are algorithms used to find approximate solutions to optimization problems. Approximation algorithms are often associated with NP-hard problems; since it is unlikely that there can ever be efficient polynomial time exact algorithms solving NP-hard problems, one settles for polynomial time sub-optimal solutions. Unlike heuristics, which usually only find reasonably good solutions reasonably fast, one wants provable solution quality and provable run time bounds. Ideally, the approximation is optimal up to a small constant factor (for instance within 5% of the optimal solution). Approximation algorithms are increasingly being used for problems where exact polynomial-time algorithms are known but are too expensive due to the input size.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000238 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000238">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000097"/>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">type of method</rdfs:label>
        <skos:definition xml:lang="en">A characteristic describing the way the method finds a solution, specifically whether it solves an equation involving only the current state of the system (explicit) or both the current and the later one (implicit). </skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000239 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000239">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000238"/>
        <owl:disjointWith rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000240"/>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">explicit method type</rdfs:label>
        <skos:definition xml:lang="en">Explicit methods calculate the state of a system at a later time from the state of the system at the current time. Mathematically, if Y(t) is the current system state and Y((t+delta t) is the state at the later time (delta t is a small time step), then, for an explicit method Y(t+delta t) = F(Y(t)), to find Y(t+delta t).</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000240 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000240">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000238"/>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">implicit method type</rdfs:label>
        <skos:definition xml:lang="en">Implicit methods find a solution by solving an equation involving both the current state of the system and the later one. Mathematically, if Y(t) is the current system state and Y((t+delta t) is the state at the later time (delta t is a small time step), then, for an implicit method one solves an equation G(Y(t), Y(t+delta t))=0, to find Y(t+delta t).</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000241 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000241">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000319"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000104"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000105"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000107"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">Gillespie-like method</rdfs:label>
        <skos:definition xml:lang="en">Stochastic simulation algorithm using an approach alike the one described in Gillespie&apos;s papers of 1976 and 1977.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000242 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000242">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000201"/>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">error control parameter</rdfs:label>
        <skos:definition xml:lang="en">Parameter controlling method accuracy.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000243 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000243">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000201"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:allValuesFrom>
                    <owl:Restriction>
                        <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                        <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
                    </owl:Restriction>
                </owl:allValuesFrom>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">method switching control parameter</rdfs:label>
        <skos:definition xml:lang="en">Parameters describing threshold conditions for algorithms that switch between different methods.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000244 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000244">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000201"/>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">granularity control parameter</rdfs:label>
        <skos:definition xml:lang="en">Parameter controlling granularity.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000248 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000248">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000252"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:allValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000045"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#double"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">tau-leaping delta</rdfs:label>
        <skos:definition xml:lang="en">Tau-leaping delta specifies how close two symmetric transition rates must be before we classify them as in partial-equilibrium. Only applies to the implicit tau routine [http://identifiers.org/biomodels.kisao/KISAO_0000045].</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000249 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000249">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000252"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:allValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000084"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#integer"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">critical firing threshold</rdfs:label>
        <skos:altLabel xml:lang="en">nonnegative tau-leaping second control parameter</skos:altLabel>
        <skos:definition xml:lang="en">The &apos;nonnegative Poisson tau-leaping method&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000084] is based on the fact that negative populations typically arise from multiple firings of reactions that are only a few firings away from consuming all the molecules of one of their reactants. To focus on those reaction channels, the modified tau-leaping algorithm introduces a second control parameter nc, a positive integer that is usually set somewhere between 5 and 20. Any reaction channel with a positive propensity function that is currently within nc firings of exhausting one of its reactants is then classified as a critical reaction. The modified algorithm chooses tau in such a way that no more than one firing of all the critical reactions can occur during the leap.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000249"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">nonnegative tau-leaping second control parameter</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000252 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000252">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000201"/>
        <dc:creator xml:lang="en">Parameter describing partitioning of the system.</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">partitioning control parameter</rdfs:label>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000253 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000253">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000244"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:allValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000074"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#double"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">coarse-graining factor</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/15638577</rdfs:seeAlso>
        <skos:definition xml:lang="en">The time in each Monte-Carlo iteration of &apos;binomial tau-leaping method&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000074] is updated with the time increments tau=f/(a1+a2+...+aM). Here 1/(a1+a2+...+aM) is the averaged microscopic increment of the SSA [http://identifiers.org/biomodels.kisao/KISAO_0000029] and f is a coarse-graining factor, controlling the speed-up.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000253"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/15638577</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Chatterjee A, Vlachos DG, Katsoulakis MA. Binomial distribution based tau-leap accelerated stochastic simulation. J Chem Phys. 2005;122(2):024112.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000254 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000254">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000242"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:allValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000057"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#integer"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <isImplementedIn xml:lang="en">Smoldyn</isImplementedIn>
        <rdfs:label xml:lang="en">Brownian diffusion accuracy</rdfs:label>
        <skos:definition xml:lang="en">Accuracy code of &apos;Brownian diffusion Smoluchowski method&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000057], which sets which neighbouring boxes are checked for potential bi-molecular reactions. Consider the reaction A + B -&gt; C and suppose that A and B are within a binding radius of each other. This reaction will always be performed if A and B are in the same virtual box. If accuracy is set to at least 3, then it will also occur if A and B are in nearest-neighbour virtual boxes. If it is at least 7, then the reaction will happen if they are in nearest-neighbour boxes that are separated by periodic boundary conditions. And if it is 9 or 10, then all edge and corner boxes are checked for reactions, which means that no potential reactions are overlooked.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000255 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000255">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000260"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#integer"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <owl:disjointWith rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000256"/>
        <isImplementedIn xml:lang="en">Smoldyn</isImplementedIn>
        <rdfs:label xml:lang="en">molecules per virtual box</rdfs:label>
        <skos:definition xml:lang="en">Target molecules per virtual box is a parameter of &apos;Brownian diffusion Smoluchowski method&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000057], which sets the box sizes so that the average number of molecules per box, at simulation initiation, is close to the requested number.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000256 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000256">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000260"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#double"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <isImplementedIn xml:lang="en">Smoldyn</isImplementedIn>
        <rdfs:label xml:lang="en">virtual box side length</rdfs:label>
        <skos:definition xml:lang="en">The &apos;virtual box side length&apos; is a parameter of &apos;Brownian diffusion Smoluchowski method&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000057]. It requests the length of one side of a box.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000257 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000257">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000252"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:allValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000057"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#double"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">surface-bound epsilon</rdfs:label>
        <skos:definition xml:lang="en">A parameter of &apos;Brownian diffusion Smoluchowski method&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000057]. Molecules that are bound to a surface are given locations that are extremely close to that surface. However, this position does not need to be exactly at the surface, and in fact it usually cannot be exactly at the surface due to round-off error. The tolerance for how  far a surface-bound molecule is allowed to be away from the surface can be set with the epsilon statement.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000258 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000258">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000252"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:allValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000057"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#double"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">neighbour distance</rdfs:label>
        <skos:definition xml:lang="en">A parameter of &apos;Brownian diffusion Smoluchowski method&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000057]. When a surface-bound molecule diffuses off of one surface panel, it can sometimes diffuse onto the neighbouring surface tile. It does so only if the neighbouring panel is declared to be a neighbour and also the neighbour is within a distance that is set with the neighbour distance statement.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000260 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000260">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000252"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:allValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000057"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">virtual box size</rdfs:label>
        <skos:definition xml:lang="en">Target size of virtual boxes for &apos;Brownian diffusion Smoluchowski method&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000057].</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000261 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000261">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000377"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000103"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000106"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000108"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000374"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000376"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000359"/>
                <owl:someValuesFrom>
                    <owl:Class>
                        <owl:intersectionOf rdf:parseType="Collection">
                            <rdf:Description rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000064"/>
                            <owl:Restriction>
                                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000275"/>
                                <owl:hasValue rdf:datatype="http://www.w3.org/2001/XMLSchema#integer">1</owl:hasValue>
                            </owl:Restriction>
                        </owl:intersectionOf>
                    </owl:Class>
                </owl:someValuesFrom>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn xml:lang="en">ByoDyn</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/jsim</isImplementedIn>
        <rdfs:label xml:lang="en">Euler method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/052143064X</rdfs:seeAlso>
        <skos:definition xml:lang="en">The Euler method, named after Leonhard Euler, is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000261"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/jsim</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">JSim</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000261"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/052143064X</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Press WH, Teukolsky SA, Vetterling WT, Flannery BP. Numerical Recipes in Fortran 77. Cambridge University Press (2001).</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000263 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000263">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000017"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000236"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000361"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000029"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <owl:disjointWith rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000362"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-04-07</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/bionetgen</isImplementedIn>
        <rdfs:label xml:lang="en">NFSim agent-based simulation method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1038/nmeth.1546</rdfs:seeAlso>
        <skos:definition xml:lang="en">A generalization a rule-based version of &apos;Gillespie&apos;s direct method&apos; (SSA) [http://identifiers.org/biomodels.kisao/KISAO_0000029]. The method is guaranteed to produce the same results as the exact SSA [http://identifiers.org/biomodels.kisao/KISAO_0000029] by cycling over three primary steps. First, NFsim calculates the probability or propensity for each rule to take effect given the current molecular states. Second, it samples the time to the next reaction event and selects the corresponding reaction rule. Finally, NFsim executes the selected reaction by applying the rule and updating the molecular agents accordingly.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000263"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/bionetgen</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">NFSim</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000263"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1038/nmeth.1546</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Sneddon MW, Faeder JR and Emonet T. Efficient modelling, simulation and coarse-graining of biological complexity with NFsim. Nature Methods (2011) 8(2):177-83.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000264 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000264">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000363"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000102"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000108"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-04-07</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">cellular automata update method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1103/RevModPhys.55.601</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">CA</skos:altLabel>
        <skos:altLabel xml:lang="en">cellular automata</skos:altLabel>
        <skos:altLabel xml:lang="en">cellular spaces</skos:altLabel>
        <skos:altLabel xml:lang="en">cellular structures</skos:altLabel>
        <skos:altLabel xml:lang="en">homogeneous structures</skos:altLabel>
        <skos:altLabel xml:lang="en">iterative arrays</skos:altLabel>
        <skos:altLabel xml:lang="en">tessellation automata</skos:altLabel>
        <skos:altLabel xml:lang="en">tessellation structures</skos:altLabel>
        <skos:definition xml:lang="en">Cellular automata are mathematical idealizations of physical systems in which space and time are discrete, and physical quantities take on a finite set of discrete values. A cellular automaton consists of a regular uniform lattice (or &apos;&apos;array&apos;&apos;), usually infinite in extent, with a discrete variable at each site (&apos;&apos;cell&apos;&apos;). A cellular automaton evolves in discrete time steps, with the value of the variable at one site being affected by the values of variables at sites in its &apos;&apos;neighbourhood&apos;&apos; on the previous time step. The neighbourhood of a site is typically taken to be the site itself and all immediately adjacent sites. The variables at each site are updated simultaneously (&apos;&apos;synchronously&apos;&apos;), based on the values of the variables in their neighbourhood at the preceding time step, and according to a definite set of &apos;&apos;local rules&apos;&apos;.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000264"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1103/RevModPhys.55.601</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Wolfram, Stephen (1983) Statistical mechanics of cellular automata. Reviews of Modern Physics 55 (3): 601-644.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000264"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">CA</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000264"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">cellular automata</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000264"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">cellular spaces</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000264"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">cellular structures</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000264"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">homogeneous structures</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000264"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">iterative arrays</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000264"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">tessellation automata</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000264"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">tessellation structures</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000273 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000273">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000102"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000107"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-05-05</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">hard-particle molecular dynamics</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1016/j.jcp.2004.08.014</rdfs:seeAlso>
        <skos:definition xml:lang="en">A collision-driven molecular dynamics algorithm for a system of non-spherical particles.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000273"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1016/j.jcp.2004.08.014</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Aleksandar Donev, Salvatore Torquato, Frank H. Stillinger, Neighbor list collision-driven molecular dynamics simulation for nonspherical hard particles. I. Algorithmic details, Journal of Computational Physics, v.202 n.2, p.737-764, 20 January 2005</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000274 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000274">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000319"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000102"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000104"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000107"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000236"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-05-05</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">first-passage Monte Carlo algorithm</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1103/PhysRevLett.97.230602</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">AED DKMC</skos:altLabel>
        <skos:altLabel xml:lang="en">AED diffusion kinetic Monte Carlo method</skos:altLabel>
        <skos:altLabel xml:lang="en">asynchronous event-driven diffusion Monte Carlo</skos:altLabel>
        <skos:definition xml:lang="en">We present a novel Monte Carlo algorithm for N diffusing finite particles that react on collisions. Using the theory of first-passage processes and time dependent Green&apos;s functions, we break the difficult N-body problem into independent single- and two-body propagations circumventing numerous diffusion hops used in standard Monte Carlo simulations. The new algorithm is exact, extremely efficient, and applicable to many important physical situations in arbitrary integer dimensions.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000274"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1103/PhysRevLett.97.230602</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">T. Oppelstrup, V. V. Bulatov, G. H. Gilmer, M. H. Kalos, and B. Sadigh. First-passage Monte- Carlo algorithm: Diffusion without all the hops. Physical Review Letters, 97(23):230602, 2006.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000274"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">AED DKMC</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000274"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">AED diffusion kinetic Monte Carlo method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000274"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">asynchronous event-driven diffusion Monte Carlo</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000276 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000276">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000064"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000108"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000239"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000275"/>
                <owl:hasValue rdf:datatype="http://www.w3.org/2001/XMLSchema#integer">4</owl:hasValue>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-05-09</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">Gill method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1017/S0305004100026414</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Gill&apos;s method</skos:altLabel>
        <skos:altLabel xml:lang="en">Runge-Kutta-Gill method</skos:altLabel>
        <skos:definition xml:lang="en">Gill&apos;s fourth order method is a Runge-Kutta method for approximating the solution of the initial value problem y&apos;(x) = f(x,y);  y(x0) = y0 which evaluates the integrand,f(x,y), four times per step. This method is a fourth order procedure for which Richardson extrapolation can be used.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000276"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1017/S0305004100026414</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Gill, S. 1951. A process for the step-by-step integration of differential equations in an automatic digital computing machine. Proc. Cambridge Philos. Soc., 47, pp 96-108.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000276"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Gill&apos;s method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000276"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Runge-Kutta-Gill method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000278 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000278">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000319"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000102"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000104"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000108"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000237"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-05-09</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn xml:lang="en">CompuCell3D</isImplementedIn>
        <rdfs:label xml:lang="en">Metropolis Monte Carlo algorithm</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.1699114</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Metropolis algorithm</skos:altLabel>
        <skos:altLabel xml:lang="en">Metropolis-Hastings algorithm</skos:altLabel>
        <skos:definition xml:lang="en">A general method, suitable for fast computing machines, for investigating such properties as equations of state for substances consisting of interacting individual molecules is described. The method consists of a modified Monte Carlo integration [http://identifiers.org/biomodels.kisao/KISAO_0000051] over configuration space.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000278"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.1699114</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Metropolis, N.; Rosenbluth, A.W.; Rosenbluth, M.N.; Teller, A.H.; Teller, E. (1953). Equations of State Calculations by Fast Computing Machines. Journal of Chemical Physics 21 (6): 1087-1092.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000278"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Metropolis algorithm</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000278"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Metropolis-Hastings algorithm</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000279 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000279">
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        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
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            </owl:Restriction>
        </rdfs:subClassOf>
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        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">Adams-Bashforth method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-3-540-56670-0</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">explicit Adams method</skos:altLabel>
        <skos:definition xml:lang="en">Given an initial value problem: y&apos; = f(x,y),  y(x0) = y0 together with additional starting values y1 = y(x0 + h), . . . , yk-1 = y(x0 + (k-1) h) the k-step Adams-Bashforth method is an explicit linear multistep method that approximates the solution, y(x) at x = x0+kh, of the initial value problem by yk = yk - 1 + h * ( a0 f(xk - 1,yk - 1) + a1 f(xk - 2,yk - 2) + . . . + ak - 1 f(x0,y0) ), where a0, a1, . . . , ak - 1 are constants.</skos:definition>
    </owl:Class>
    <owl:Axiom>
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        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-3-540-56670-0</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Hairer, Ernst; Nørsett, Syvert Paul; Wanner, Gerhard (1993), Solving ordinary differential equations I: Nonstiff problems (2nd ed.), Berlin: Springer Verlag</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000279"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">explicit Adams method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000280 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000280">
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        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/vcell</isImplementedIn>
        <rdfs:label xml:lang="en">Adams-Moulton method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-3-540-56670-0</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">implicit Adams method</skos:altLabel>
        <skos:definition xml:lang="en">The (k-1)-step Adams-Moulton method is an implicit linear multistep method that iteratively approximates the solution, y(x) at x = x0+kh, of the initial value problem by yk = yk - 1 + h * ( b0 f(xk,yk) + b1 f(xk - 1,yk - 1) + . . . + bk - 1 f(x1,y1) ), where b1, . . . , bk - 1 are constants.</skos:definition>
    </owl:Class>
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        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/vcell</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">VCell</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
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        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-3-540-56670-0</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Hairer, Ernst; Nørsett, Syvert Paul; Wanner, Gerhard (1993), Solving ordinary differential equations I: Nonstiff problems (2nd ed.), Berlin: Springer Verlag</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000280"/>
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        <owl:annotatedTarget xml:lang="en">implicit Adams method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000281 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000281">
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        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">multistep method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-3-540-56670-0</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">multi-value method</skos:altLabel>
        <skos:definition xml:lang="en">A numerical method for differential equations which is based on several values of the solution.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000281"/>
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        <rdfs:comment xml:lang="en">Hairer, Ernst; Nørsett, Syvert Paul; Wanner, Gerhard (1993), Solving ordinary differential equations I: Nonstiff problems (2nd ed.), Berlin: Springer Verlag</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000281"/>
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        <owl:annotatedTarget xml:lang="en">multi-value method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000282 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000282">
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        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-05-09</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn xml:lang="en">SUNDIALS</isImplementedIn>
        <rdfs:label xml:lang="en">KINSOL</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1137/0911026</rdfs:seeAlso>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1145/1089014.1089020</rdfs:seeAlso>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.4249/scholarpedia.2860</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">FKINSOL</skos:altLabel>
        <skos:altLabel xml:lang="en">NKSOL</skos:altLabel>
        <skos:altLabel xml:lang="en">Newton-Krylov solver for nonlinear algebraic systems</skos:altLabel>
        <skos:definition xml:lang="en">KINSOL solves algebraic systems in real N-space, written as F(u)=0,  F:RN-&gt;RN, given an initial guess u0. The basic method is either a modified or an inexact Newton iteration [http://identifiers.org/biomodels.kisao/KISAO_0000408]. The linear systems that arise are solved with either a direct (dense or banded) solver (serial version only), or one of the Krylov iterative solvers [http://identifiers.org/biomodels.kisao/KISAO_0000354]. In the Krylov case, the user can (optionally) supply a right preconditioner.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000282"/>
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        <rdfs:comment xml:lang="en">BROWN, P. N. AND SAAD, Y. 1990. Hybrid Krylov methods for nonlinear systems of equations. SIAM  J. Sci. Stat. Comput. 11, 450-481.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000282"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1145/1089014.1089020</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Hindmarsh, A. C., et al., SUNDIALS: Suite of Nonlinear and Differential/Algebraic Equation Solvers, ACM Trans. Math. Softw., 31:363-396, 2005.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000282"/>
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        <rdfs:comment xml:lang="en">Alan C. Hindmarsh and Radu Serban (2007) Sundails equation solvers, Scholarpedia, 2(3):2860.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000282"/>
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    </owl:Axiom>
    <owl:Axiom>
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    </owl:Axiom>
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        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000282"/>
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        <owl:annotatedTarget xml:lang="en">Newton-Krylov solver for nonlinear algebraic systems</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">RELATED</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000283 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000283">
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        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-05-09</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn xml:lang="en">SUNDIALS</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/opencor</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/vcell</isImplementedIn>
        <rdfs:label xml:lang="en">IDA</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1137/0915088</rdfs:seeAlso>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1145/1089014.1089020</rdfs:seeAlso>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.4249/scholarpedia.2860</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">implicit differential-algebraic solver</skos:altLabel>
        <skos:altLabel xml:lang="en">solver for differential-algebraic equation systems</skos:altLabel>
        <skos:definition xml:lang="en">IDA solves real differential-algebraic systems in N-space, in the general form F(t,y,y&apos;)=0,  y(t0)=y0,  y&apos;(t0)=y&apos;0. At each step, a Newton iteration [http://identifiers.org/biomodels.kisao/KISAO_0000408] leads to linear systems Jx=b, which are solved by one of five methods - two direct (dense or band; serial version only) and three Krylov [http://identifiers.org/biomodels.kisao/KISAO_0000354] (GMRES [http://identifiers.org/biomodels.kisao/KISAO_0000353], BiCGStab [http://identifiers.org/biomodels.kisao/KISAO_0000392], or TFQMR [http://identifiers.org/biomodels.kisao/KISAO_0000396]).
IDA is written in C, but derived from the package DASPK [http://identifiers.org/biomodels.kisao/KISAO_0000355] which is written in Fortran.</skos:definition>
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        <rdfs:comment xml:lang="end">OpenCOR</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
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    </owl:Axiom>
    <owl:Axiom>
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        <owl:annotatedTarget xml:lang="en">IDA</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Alan C. Hindmarsh and Radu Serban (2007) Sundails equation solvers, Scholarpedia, 2(3):2860.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000283"/>
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        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1137/0915088</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">BROWN, P. N., HINDMARSH, A. C., AND PETZOLD, L. R. 1994. Using Krylov methods in the solution of large-scale differential-algebraic systems. SIAM J. Sci. Comput. 15, 1467-1488.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000283"/>
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        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1145/1089014.1089020</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Hindmarsh, A. C., et al., SUNDIALS: Suite of Nonlinear and Differential/Algebraic Equation Solvers, ACM Trans. Math. Softw., 31:363-396, 2005.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000283"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.4249/scholarpedia.2860</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Alan C. Hindmarsh and Radu Serban (2007) Sundails equation solvers, Scholarpedia, 2(3):2860.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000283"/>
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        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000283"/>
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        <owl:annotatedTarget xml:lang="en">solver for differential-algebraic equation systems</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">RELATED</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000285 -->

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        <rdfs:label xml:lang="en">finite volume method</rdfs:label>
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        <skos:altLabel xml:lang="en">FVM</skos:altLabel>
        <skos:definition xml:lang="en">The finite volume method is a method for representing and evaluating partial differential equations in the form of algebraic equations, which attempts to emulate continuous conservation laws of physics.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000285"/>
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    <owl:Axiom>
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        <rdfs:comment xml:lang="en">Y. Saad. 2003. Iterative Methods for Sparse Linear Systems (2nd ed.). Soc. for Industrial and Applied Math., Philadelphia, PA, USA.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000285"/>
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        <owl:annotatedTarget xml:lang="en">FVM</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
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    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000286 -->

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        <rdfs:subClassOf>
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        <rdfs:subClassOf>
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        </rdfs:subClassOf>
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        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">Euler-Maruyama method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1098/rspa.2003.1247</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">stochastic Euler scheme</skos:altLabel>
        <skos:definition xml:lang="en">The Euler-Maruyama method is a method for the approximate numerical solution of a stochastic differential equation, which truncates the Ito and Stratonovich Taylor series of the exact solution after the first order stochastic terms. This converges to the Ito solution with strong global order accuracy 1/2 or weak global order accuracy 1. It is a simple generalization of the Euler method [http://identifiers.org/biomodels.kisao/KISAO_0000261] for ordinary differential equations to stochastic differential equations.</skos:definition>
    </owl:Class>
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        <rdfs:comment xml:lang="en">Burrage, K., Burrage, P.M. and Tian, T. (2004) Numerical methods for strong solutions of stochastic differential equations: an overview. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 460 (2041). pp. 373-402.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000286"/>
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        <owl:annotatedTarget xml:lang="en">stochastic Euler scheme</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000287 -->

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        </rdfs:subClassOf>
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        <rdfs:label xml:lang="en">Milstein method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/079233213X</rdfs:seeAlso>
        <skos:definition xml:lang="en">The Milstein method is a technique for the approximate numerical solution of a stochastic differential equation.</skos:definition>
    </owl:Class>
    <owl:Axiom>
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        <rdfs:comment xml:lang="en">Milstein M. G. Numerical Integration of Stochastic Differential Equations (Mathematics and Its Applications) Springer, 2004.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000288 -->

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        <owl:disjointWith rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000289"/>
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        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn xml:lang="en">ByoDyn</isImplementedIn>
        <isImplementedIn xml:lang="en">GSL</isImplementedIn>
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        <rdfs:label xml:lang="en">backward differentiation formula</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/0136266061</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">BDF</skos:altLabel>
        <skos:altLabel xml:lang="en">Gear method</skos:altLabel>
        <skos:altLabel xml:lang="en">Gear&apos;s method</skos:altLabel>
        <skos:definition xml:lang="en">The backward differentiation formulas (BDF) are implicit multistep methods based on the numerical differentiation of a given function and are wildly used for integration of stiff differential equations.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000288"/>
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        <rdfs:comment xml:lang="end">iBioSim</rdfs:comment>
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    <owl:Axiom>
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        <rdfs:comment xml:lang="en">C. William Gear. 1971. Numerical Initial Value Problems in Ordinary Differential Equations. Prentice Hall PTR, Upper Saddle River, NJ, USA.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000288"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">BDF</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000288"/>
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        <owl:annotatedTarget xml:lang="en">Gear method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
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    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000288"/>
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        <owl:annotatedTarget xml:lang="en">Gear&apos;s method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000289 -->

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        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn xml:lang="en">ByoDyn</isImplementedIn>
        <rdfs:label xml:lang="en">Adams method</rdfs:label>
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        <skos:definition xml:lang="en">Adams&apos; methods are multi-step methods used for the numerical integration of initial value problems in Ordinary Differential Equations (ODE&apos;s). Adams&apos; algorithm consists of two parts: firstly, a starting procedure which provides y1, ... , yk-1 ( approximations to the exact solution at the points x0 + h, ... , x0 + (k - 1)h ) and, secondly, a multistep formula to obtain an approximation to the exact solution y(x0 + kh). This is then applied recursively, based on the numerical approximation of k successive steps, to compute y(x0 + (k + 1)h).</skos:definition>
    </owl:Class>
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        <rdfs:comment xml:lang="en">Hairer, Ernst; Nørsett, Syvert Paul; Wanner, Gerhard (1993), Solving ordinary differential equations I: Nonstiff problems (2nd ed.), Berlin: Springer Verlag</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000290 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000290">
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        <skos:altLabel xml:lang="en">KM</skos:altLabel>
        <skos:altLabel xml:lang="en">Kutta-Merson method</skos:altLabel>
        <skos:altLabel xml:lang="en">Merson&apos;s method</skos:altLabel>
        <skos:altLabel xml:lang="en">Runge-Kutta-Merson method</skos:altLabel>
        <skos:definition xml:lang="en">A five-stage Runge-Kutta method with fourth-order accuracy.</skos:definition>
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    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000290"/>
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    </owl:Axiom>
    <owl:Axiom>
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        <rdfs:comment xml:lang="en">R.H. Merson, An operational method for the study of integration processes, in: Proceedings of the Symposium on Data Processing, Weapons Research Establishment, Salisbury, Australia, 1957, pp. 110-1-110-25.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
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        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000290"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Kutta-Merson method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000290"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Merson&apos;s method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000290"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Runge-Kutta-Merson method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000296 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000296">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000064"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000108"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000240"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-05-10</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">Hammer-Hollingsworth method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">urn:issn:0891-6837</rdfs:seeAlso>
        <skos:definition xml:lang="en">The numerical integration of ordinary differential equations by the use of Gaussian quadrature methods.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000296"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">urn:issn:0891-6837</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">P. C. Hammer &amp; J. W. Hollingsworth, Trapezoidal methods of approximating solutions of differential equations, MTAC, v. 9, 1955, pp. 92-96. MR 17, 302.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000297 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000297">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000064"/>
        <rdfs:subClassOf>
            <owl:Class>
                <owl:complementOf>
                    <owl:Restriction>
                        <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                        <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000366"/>
                    </owl:Restriction>
                </owl:complementOf>
            </owl:Class>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000108"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000240"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-05-10</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">Lobatto method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">urn:issn:1088-6842(e)</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">implicit Runge-Kutta method based on Lobatto quadrature</skos:altLabel>
        <skos:definition xml:lang="en">There are three families of Lobatto methods, called IIIA, IIIB and IIIC. These are named after Rehuel Lobatto. All are implicit Runge-Kutta methods, have order 2s − 2 and they all have c1 = 0 and cs = 1.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000297"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">urn:issn:1088-6842(e)</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">J. C. Butcher, Integration processes based on Radau quadrature formulas, Math. Comp., v. 18, 1964, pp. 233-244.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000297"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">implicit Runge-Kutta method based on Lobatto quadrature</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000299 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000299">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000064"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000108"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000240"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000366"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-05-10</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">Butcher-Kuntzmann method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1002/zamm.19660460519</rdfs:seeAlso>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">urn:issn:1088-6842(e)</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Gauss method</skos:altLabel>
        <skos:definition xml:lang="en">From a theoretical point of view, the Butcher-Kuntzmann Runge-Kutta methods belong to the best step-by-step methods for nonstiff problems. These methods integrate first-order initial-value problems by means of formulas based on Gauss-Legendre quadrature, and combine excellent stability features with the property of superconvergence at the step points.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000299"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1002/zamm.19660460519</owl:annotatedTarget>
        <rdfs:comment xml:lang="fr">F. Ceschin, J. Kuntzmann, Problèmes différentiels de conditions initiales. Paris 1963. Dunod.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000299"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">urn:issn:1088-6842(e)</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Butcher, J. C. (1964) Implicit Runge-Kutta processes. Math. Comput. 18, 50-64.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000299"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Gauss method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000301 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000301">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000064"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000108"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000239"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000275"/>
                <owl:hasValue rdf:datatype="http://www.w3.org/2001/XMLSchema#integer">2</owl:hasValue>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-05-10</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">Heun method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-3-540-56670-0</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Heun&apos;s method</skos:altLabel>
        <skos:definition xml:lang="en">The method is named after Karl L. W. M. Heun and is a numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It can be seen as extension of the Euler method [http://identifiers.org/biomodels.kisao/KISAO_0000261] into two-stage second-order Runge-Kutta method.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000301"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-3-540-56670-0</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Hairer, Ernst; Nørsett, Syvert Paul; Wanner, Gerhard (1993), Solving ordinary differential equations I: Nonstiff problems (2nd ed.), Berlin: Springer Verlag</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000301"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Heun&apos;s method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000302 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000302">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000064"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000107"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000239"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-05-10</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">embedded Runge-Kutta method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-3-540-56670-0</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">embedded RK</skos:altLabel>
        <skos:definition xml:lang="en">An embedded Runge-Kutta method is a method in which two Runge-Kutta estimates are obtained using the same auxiliary functions ki but with a different linear combination of these functions so that one estimate has an order one greater than the other.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000302"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-3-540-56670-0</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Hairer, Ernst; Nørsett, Syvert Paul; Wanner, Gerhard (1993), Solving ordinary differential equations I: Nonstiff problems (2nd ed.), Berlin: Springer Verlag</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000302"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">embedded RK</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000303 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000303">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000302"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom>
                    <owl:Class>
                        <owl:intersectionOf rdf:parseType="Collection">
                            <rdf:Description rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000064"/>
                            <owl:Restriction>
                                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000275"/>
                                <owl:hasValue rdf:datatype="http://www.w3.org/2001/XMLSchema#integer">3</owl:hasValue>
                            </owl:Restriction>
                        </owl:intersectionOf>
                    </owl:Class>
                </owl:someValuesFrom>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom>
                    <owl:Class>
                        <owl:intersectionOf rdf:parseType="Collection">
                            <rdf:Description rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000064"/>
                            <owl:Restriction>
                                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000275"/>
                                <owl:hasValue rdf:datatype="http://www.w3.org/2001/XMLSchema#integer">4</owl:hasValue>
                            </owl:Restriction>
                        </owl:intersectionOf>
                    </owl:Class>
                </owl:someValuesFrom>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-05-10</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">Zonneveld method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://trove.nla.gov.au/work/21424455</rdfs:seeAlso>
        <skos:definition xml:lang="en">An embedded Runge-Kutta method [http://identifiers.org/biomodels.kisao/KISAO_0000302] of order 4(3), proposed by J.A. Zonneveld in 1964.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000303"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://trove.nla.gov.au/work/21424455</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Zonneveld, J. A (1970). Automatic numerical integration Mathematisch Centrum, Amsterdam</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000304 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000304">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000064"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000108"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000240"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000484"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000583"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000584"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-05-11</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/jsim</isImplementedIn>
        <rdfs:label xml:lang="en">Radau method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">urn:issn:1088-6842(e)</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">implicit Runge-Kutta method based on Radau quadrature</skos:altLabel>
        <skos:definition xml:lang="en">Implicit Runge-Kutta methods based on Radau quadrature.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000304"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/jsim</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">JSim</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000304"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">urn:issn:1088-6842(e)</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">J. C. Butcher, Integration processes based on Radau quadrature formulas, Math. Comput., 18(1964), 233-244.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000304"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">implicit Runge-Kutta method based on Radau quadrature</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000305 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000305">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000302"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom>
                    <owl:Class>
                        <owl:intersectionOf rdf:parseType="Collection">
                            <rdf:Description rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000064"/>
                            <owl:Restriction>
                                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000275"/>
                                <owl:hasValue rdf:datatype="http://www.w3.org/2001/XMLSchema#integer">5</owl:hasValue>
                            </owl:Restriction>
                        </owl:intersectionOf>
                    </owl:Class>
                </owl:someValuesFrom>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom>
                    <owl:Class>
                        <owl:intersectionOf rdf:parseType="Collection">
                            <rdf:Description rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000064"/>
                            <owl:Restriction>
                                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000275"/>
                                <owl:hasValue rdf:datatype="http://www.w3.org/2001/XMLSchema#integer">6</owl:hasValue>
                            </owl:Restriction>
                        </owl:intersectionOf>
                    </owl:Class>
                </owl:someValuesFrom>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-05-10</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">Verner method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1137/0728027</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Verner&apos;s method</skos:altLabel>
        <skos:definition xml:lang="en">The first high order (6(5)) embedded Runge-Kutta formulas that avoid the drawback of giving identically zero error estimates for quadrature problems y&apos; = f(x) were constructed by Verner in 1978.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000305"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1137/0728027</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">J.H. Verner, Some Runge-Kutta formula pairs, SIAM J. Numer. Anal 28 (1991) 496-511</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000305"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Verner&apos;s method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000306 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000306">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000102"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000106"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000108"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000237"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000372"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-05-11</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/jsim</isImplementedIn>
        <rdfs:label xml:lang="en">Lagrangian sliding fluid element algorithm</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/1449234</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">BTEX</skos:altLabel>
        <skos:altLabel xml:lang="en">LSFEA</skos:altLabel>
        <skos:altLabel xml:lang="en">blood-tissue exchange method</skos:altLabel>
        <skos:definition xml:lang="en">Because the analytic solutions to the partial differential equations require convolution integration, solutions are obtained relatively efficiently by a fast numerical method. Our approach centers on the use of a sliding fluid element algorithm for capillary convection, with the time step set equal to the length step divided by the fluid velocity. Radial fluxes by permeation between plasma, interstitial fluid, and cells and axial diffusion exchanges within each time step are calculated analytically. The method enforces mass conservation unless there is regional consumption.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000306"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/jsim</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">JSim</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000306"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/1449234</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Bassingthwaighte JB, Chan IS, and Wang CY. Computationally efficient algorithms for capillary convection-permeation-diffusion models for blood-tissue exchange. Ann Biomed Eng 20: 687-725, 1992.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000306"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">BTEX</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000306"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">LSFEA</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000306"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">blood-tissue exchange method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000307 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000307">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000369"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000103"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000108"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000237"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000346"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-05-11</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">finite difference method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/0898715342</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">FDM</skos:altLabel>
        <skos:definition xml:lang="en">The finite difference method is based on local approximations of the partial derivatives in a Partial Differential Equation, which are derived by low order Taylor series expansions.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000307"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/0898715342</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Y. Saad. 2003. Iterative Methods for Sparse Linear Systems (2nd ed.). Soc. for Industrial and Applied Math., Philadelphia, PA, USA.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000307"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">FDM</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000308 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000308">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000307"/>
        <owl:disjointWith rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000309"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-05-11</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/jsim</isImplementedIn>
        <rdfs:label xml:lang="en">MacCormack method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.2514/2.6901</rdfs:seeAlso>
        <skos:definition xml:lang="en">In computational fluid dynamics, the MacCormack method is a widely used discretization scheme for the numerical solution of hyperbolic partial differential equations. This second-order finite difference method [http://identifiers.org/biomodels.kisao/KISAO_0000307] is introduced by R. W. MacCormack in 1969.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000308"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/jsim</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">JSim</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000308"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.2514/2.6901</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">MacCormack, R. W., The Effect of viscosity in hypervelocity impact cratering, AIAA Paper, 69-354 (1969).</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000309 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000309">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000307"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000240"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-05-11</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">Crank-Nicolson method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1007/BF02127704</rdfs:seeAlso>
        <skos:definition xml:lang="en">In numerical analysis, the Crank-Nicolson method is a finite difference method [http://identifiers.org/biomodels.kisao/KISAO_0000307] used for numerically solving the heat equation and similar partial differential equations. It is a second-order method in time, implicit in time, and is numerically stable. The method was developed by John Crank and Phyllis Nicolson in the mid 20th century.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000309"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1007/BF02127704</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Crank, J.; Nicolson, P. (1947). A practical method for numerical evaluation of solutions of partial differential equations of the heat conduction type. Proc. Camb. Phil. Soc. 43 (1): 50-67.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000310 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000310">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000369"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000106"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000107"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000346"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-05-11</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">method of lines</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/0126241309</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">MOL</skos:altLabel>
        <skos:altLabel xml:lang="en">NMOL</skos:altLabel>
        <skos:altLabel xml:lang="en">NUMOL</skos:altLabel>
        <skos:definition xml:lang="en">The method of lines is a general technique for solving partial differential equations (PDEs) by typically using finite difference relationships for the spatial derivatives and ordinary differential equations for the time derivative.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000310"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#label"/>
        <owl:annotatedTarget xml:lang="en">method of lines</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000310"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/0126241309</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Schiesser, W. E. (1991). The Numerical Method of Lines. Academic Press.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000310"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">MOL</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000310"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">NMOL</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000310"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">NUMOL</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000311 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000311">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000097"/>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">type of domain geometry handling</rdfs:label>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000314 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000314">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000103"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000107"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000237"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
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            </owl:Restriction>
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        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-05-20</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/ecell4</isImplementedIn>
        <rdfs:label xml:lang="en">S-System power-law canonical differential equations solver</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1137/0727042</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">ESSYNS GMA</skos:altLabel>
        <skos:definition xml:lang="en">Ordinary differential equations can be recast into a nonlinear canonical form called an S-system. Evidence for the generality of this class comes from extensive empirical examples that have been recast and from the discovery that sets of differential equations and functions, recognized as among the most general, are special cases of S-systems. Identification of this nonlinear canonical form suggests a radically different approach to numerical solution of ordinary differential equations. By capitalizing on the regular structure of S-systems, efficient formulas for a variable-order, variable-step Taylor-series method are developed. </skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000314"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/ecell4</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">E-Cell</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000314"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1137/0727042</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Irvine, D.H. and Savageau, M.A., Efficient solution of nonlinear ordinary differential equations expressed in S-System canonical form, Siam. J. Numer. Anal., 27:704-735, 1990.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000314"/>
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        <owl:annotatedTarget xml:lang="en">ESSYNS GMA</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000315 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000315">
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        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">lattice gas automata</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/3-540-66973-6</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">LGA</skos:altLabel>
        <skos:altLabel xml:lang="en">LGCA</skos:altLabel>
        <skos:altLabel xml:lang="en">lattice gas cellular automata</skos:altLabel>
        <skos:definition xml:lang="en">Lattice gas automata methods are a series of cellular automata methods used to simulate fluid flows. From the LGCA, it is possible to derive the macroscopic Navier-Stokes equations.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000315"/>
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        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/3-540-66973-6</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Dieter A. Wolf-Gladrow (2000). Lattice-Gas Cellular Automata and Lattice Boltzmann Models. Springer.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000315"/>
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        <owl:annotatedTarget xml:lang="en">LGA</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000315"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">LGCA</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000315"/>
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        <owl:annotatedTarget xml:lang="en">lattice gas cellular automata</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000316 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000316">
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        <rdfs:subClassOf>
            <owl:Restriction>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
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            </owl:Restriction>
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        <rdfs:subClassOf>
            <owl:Restriction>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-05-23</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">enhanced Greens function reaction dynamics</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1007/978-3-540-88562-7_3</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">eGFRD</skos:altLabel>
        <skos:altLabel xml:lang="en">enhanced Greens function reaction dynamics</skos:altLabel>
        <skos:definition xml:lang="en">GFRD [http://identifiers.org/biomodels.kisao/KISAO_0000058] decomposes the multi­body reaction diffusion problem to a set of single and two body problems. Analytical solutions for two body reaction diffusion are available via Smoluchowski equation. eGFRD allows to solve each sub­problem asynchronously by introducing the concept of first passage processes.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000316"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1007/978-3-540-88562-7_3</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">K. Takahashi, An exact Brownian dynamics method for cell simulation, in Computational Methods in Systems Biology, vol. 5307/2008.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000316"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">eGFRD</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000316"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">enhanced Greens function reaction dynamics</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000317 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000317">
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            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-05-23</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/ecell4</isImplementedIn>
        <rdfs:label xml:lang="en">E-Cell multi-algorithm simulation method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/14990450</rdfs:seeAlso>
        <skos:definition xml:lang="en">A modular meta-algorithm with a discrete event scheduler that can incorporate any type of time-driven simulation algorithm. It was shown that this meta-algorithm can efficiently drive simulation models with different simulation algorithms with little intrusive modification to the algorithms themselves. Only a few additional methods to handle communications between computational modules are required.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000317"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/ecell4</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">E-Cell</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000317"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/14990450</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Takahashi, K., Kaizu, K., Hu, B., and Tomita, M., A multi-algorithm, multi-timescale method for cell simulation. Bioinformatics, in press.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000318 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000318">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000064"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000106"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000108"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000240"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-05-26</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/ibiosim</isImplementedIn>
        <rdfs:label xml:lang="en">Gauss-Legendre Runge-Kutta method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/960-8457-54-8</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Open Formula</skos:altLabel>
        <skos:definition xml:lang="en">So called &apos;Open Formula&apos;, two points formula, three points formula, four points formula, five points formula and six points formula of the Runge-Kutta method to solve the initial value problem of the ordinary differential equation. These formulas use the points and weights from the Gauss-Legendre Quadrature formulas for finding the value of the definite integral.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000318"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/ibiosim</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">iBioSim</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000318"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/960-8457-54-8</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Maitree Podisuk, Sirirat Khuntidilokwongsa, and Witchaya Rattanametawee. 2006. Gauss-Legendre Quadrature formula in Runge-Kutta method with modified model of Newton cooling law. In Proceedings of the 8th WSEAS international conference on Mathematical methods and computational techniques in electrical engineering (MMACTEE&apos;06). World Scientific and Engineering Academy and Society (WSEAS), Stevens Point, Wisconsin, USA, 312-317.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000318"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Open Formula</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000319 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000319">
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            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
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        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-05-26</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">Monte Carlo method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.2307/2280232</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">MC</skos:altLabel>
        <skos:definition xml:lang="en">Monte Carlo methods (or Monte Carlo experiments) are a class of computational algorithms that rely on repeated random sampling to compute their results.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000319"/>
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        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.2307/2280232</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Metropolis, N.; Ulam, S. (1949). &quot;The Monte Carlo Method&quot;. Journal of the American Statistical Association (American Statistical Association) 44 (247): 335-341.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000319"/>
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        <owl:annotatedTarget xml:lang="en">MC</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000320 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000320">
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            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
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        </rdfs:subClassOf>
        <rdfs:subClassOf>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-05-26</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn xml:lang="en">BioRica</isImplementedIn>
        <rdfs:label xml:lang="en">BioRica hybrid method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/19425152</rdfs:seeAlso>
        <skos:definition xml:lang="en">The simulation schema for a given BioRica node is given by a hybrid algorithm that deals with continuous time and allows for discrete events that roll back the time according to these discrete interruptions.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000320"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/19425152</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Cvijovic M, Soueidan H, Sherman DJ, Klipp E, Nikolski M. Exploratory simulation of cell ageing using hierarchical models. Genome Inform. 2008;21:114-25.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000321 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000321">
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        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn xml:lang="en">Cain</isImplementedIn>
        <isImplementedIn xml:lang="en">GSL</isImplementedIn>
        <rdfs:label xml:lang="en">Cash-Karp method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1145/79505.79507</rdfs:seeAlso>
        <skos:definition xml:lang="en">An family of explicit Runge-Kutta formulas, which are very efficient for problems with smooth solution as well as problems having rapidly varying solutions. Each member of this family consists of a fifty-order formula that contains embedded formulas of all orders 1 through 4. By computing solutions at several different orders, it is possible to detect sharp fronts or discontinuities before all the function evaluations defining the full Runge-Kutta step have been computed.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000321"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1145/79505.79507</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">J. R. Cash, A. H. Karp. &quot;A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides&quot;, ACM Transactions on Mathematical Software 16: 201-222, 1990.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000322 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000322">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000097"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-05-27</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">hybridity</rdfs:label>
        <skos:definition xml:lang="en">The basic idea of hybrid simulation methods is to combine the advantages of complementary simulation approaches: the whole system is subdivided into appropriate parts and different simulation methods operate on these parts at the same time.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000323 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000323">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000333"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000325"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000326"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000327"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000328"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-02</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">equation-free probabilistic steady-state approximation</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.2131050</rdfs:seeAlso>
        <skos:definition xml:lang="en">We present a probabilistic steady-state approximation that separates the time scales of an arbitrary reaction network, detects the convergence of a marginal distribution to a quasi-steady-state, directly samples the underlying distribution, and uses those samples to accurately predict the state of the system, including the effects of the slow dynamics, at future times. The numerical method produces an accurate solution of both the fast and slow reaction dynamics while, for stiff systems, reducing the computational time by orders of magnitude. The developed theory makes no approximations on the shape or form of the underlying steady-state distribution and only assumes that it is ergodic. &lt;...&gt; The developed theory may be applied to any type of kinetic Monte Carlo simulation to more efficiently simulate dynamically stiff systems, including existing exact, approximate, or hybrid stochastic simulation techniques.
</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000323"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.2131050</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Salis H, Kaznessis YN. An equation-free probabilistic steady-state approximation: dynamic application to the stochastic simulation of biochemical reaction networks. J Chem Phys. 2005 Dec 1;123(21):214106.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000324 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000324">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000333"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000237"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000029"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-02</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">nested stochastic simulation algorithm</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/16321076</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">nested SSA</skos:altLabel>
        <skos:definition xml:lang="en">This multiscale method is a small modification of the Gillespie&apos;s direct method [http://identifiers.org/biomodels.kisao/KISAO_0000029], in the form of a nested SSA, with inner loops for the fast reactions, and outer loop for the slow reactions. The number of groups can be more than two, and the grouping into fast and slow  variables can be done dynamically in an adaptive version of the scheme.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000324"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/16321076</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">E W., Liu D. and Vanden-Eijnden E. Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates. J Chem Phys. 2005 Nov 15;123(19):194107.
</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000324"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">nested SSA</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000325 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000325">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000242"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:allValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000323"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#integer"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-02</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">minimum fast/discrete reaction occurrences number</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.2131050</rdfs:seeAlso>
        <skos:definition xml:lang="en">Parameter of &apos;equation-free probabilistic steady-state approximation&apos; method  [http://identifiers.org/biomodels.kisao/KISAO_0000323], which describes the minimum number of fast/discrete reaction occurrences before their effects cause convergence to a quasi-steady-state distribution.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000325"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.2131050</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Salis H, Kaznessis YN. An equation-free probabilistic steady-state approximation: dynamic application to the stochastic simulation of biochemical reaction networks. J Chem Phys. 2005 Dec 1;123(21):214106.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000326 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000326">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000242"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:allValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000323"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#integer"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-02</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">number of samples</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.2131050</rdfs:seeAlso>
        <skos:definition xml:lang="en">Parameter of &apos;equation-free probabilistic steady-state approximation&apos; method [http://identifiers.org/biomodels.kisao/KISAO_0000323], which determines the number of samples taken from the distribution.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000326"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.2131050</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Salis H, Kaznessis YN. An equation-free probabilistic steady-state approximation: dynamic application to the stochastic simulation of biochemical reaction networks. J Chem Phys. 2005 Dec 1;123(21):214106.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000327 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000327">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000252"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:allValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000323"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#integer"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-02</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">maximum discrete number</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.2131050</rdfs:seeAlso>
        <skos:definition xml:lang="en">Parameter of &apos;equation-free probabilistic steady-state approximation&apos; method [http://identifiers.org/biomodels.kisao/KISAO_0000323], which controls the maximum number of molecules of some reactant species in order for the reaction to be considered discrete.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000327"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.2131050</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Salis H, Kaznessis YN. An equation-free probabilistic steady-state approximation: dynamic application to the stochastic simulation of biochemical reaction networks. J Chem Phys. 2005 Dec 1;123(21):214106.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000328 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000328">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000252"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:allValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000323"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#double"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-02</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">minimum fast rate</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.2131050</rdfs:seeAlso>
        <skos:definition xml:lang="en">Parameter of &apos;equation-free probabilistic steady-state approximation&apos; method [http://identifiers.org/biomodels.kisao/KISAO_0000323], which controls the minimum rate of the reaction in order for it to be considered fast.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000328"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.2131050</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Salis H, Kaznessis YN. An equation-free probabilistic steady-state approximation: dynamic application to the stochastic simulation of biochemical reaction networks. J Chem Phys. 2005 Dec 1;123(21):214106.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000329 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000329">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000333"/>
        <rdfs:subClassOf>
            <owl:Class>
                <owl:complementOf>
                    <owl:Restriction>
                        <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                        <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000102"/>
                    </owl:Restriction>
                </owl:complementOf>
            </owl:Class>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000236"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-03</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">constant-time kinetic Monte Carlo algorithm</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/18513044</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">SSA-CR</skos:altLabel>
        <skos:definition xml:lang="en">The computational cost of the original SSA [http://identifiers.org/biomodels.kisao/KISAO_0000029] scaled linearly with the number of reactions in the network. Gibson and Bruck developed a logarithmic scaling version of the SSA which uses a priority queue or binary tree for more efficient reaction selection [http://identifiers.org/biomodels.kisao/KISAO_0000027]. More generally, this problem is one of dynamic discrete random variate generation which finds many uses in kinetic Monte Carlo and discrete event simulation. We present here a constant-time algorithm, whose cost is independent of the number of reactions, enabled by a slightly more complex underlying data structure.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000329"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/18513044</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Slepoy A, Thompson AP, Plimpton SJ. A constant-time kinetic Monte Carlo algorithm for simulation of large biochemical reaction networks. J Chem Phys. 2008 May 28;128(20):205101.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000329"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">SSA-CR</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000330 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000330">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000333"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000237"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-03</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">R-leaping algorithm</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/16964997</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">R-leap method</skos:altLabel>
        <skos:definition xml:lang="en">A novel algorithm is proposed for the acceleration of the exact stochastic simulation algorithm by a predefined number of reaction firings (R-leaping) that may occur across several reaction channels. In the present approach, the numbers of reaction firings are correlated binomial distributions and the sampling procedure is independent of any permutation of the reaction channels. This enables the algorithm to efficiently handle large systems with disparate rates, providing substantial computational savings in certain cases.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000330"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/16964997</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Auger A, Chatelain P, Koumoutsakos P. R-leaping: accelerating the stochastic simulation algorithm by reaction leaps. J Chem Phys. 2006 Aug 28;125(8):084103.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000330"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">R-leap method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000331 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000331">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000333"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000236"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000359"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000330"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-03</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">exact R-leaping algorithm</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/2852436</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">ER-leap method</skos:altLabel>
        <skos:altLabel xml:lang="en">exact R-leap method</skos:altLabel>
        <skos:altLabel xml:lang="en">exact accelerated stochastic simulation algorithm</skos:altLabel>
        <skos:definition xml:lang="en">We present a SSA which, similar to R-leap [http://identifiers.org/biomodels.kisao/KISAO_0000330], accelerates SSA [http://identifiers.org/biomodels.kisao/KISAO_0000029] by executing multiple reactions per algorithmic step, but which samples the reactant trajectories from the same probability distribution as the SSA. This &apos;exact R-leap&apos; or &apos;ER-leap&apos; algorithm is a modification of the R-leap algorithm which is both exact and capable of substantial speed-up over SSA.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000331"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/2852436</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Eric Mjolsness, David Orendorff, Philippe Chatelain, and Petros Koumoutsakos. An exact accelerated stochastic simulation algorithm. J Chem Phys. 2009 April 14; 130(14): 144110.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000331"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">ER-leap method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000331"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">exact R-leap method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000331"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">exact accelerated stochastic simulation algorithm</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000332 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000332">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000244"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:allValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000331"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#integer"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-03</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">ER-leap initial leap</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/2852436</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">L</skos:altLabel>
        <skos:definition xml:lang="en">L (initial step) is a parameter of &apos;exact R-leaping method&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000331]. &apos;&apos;We will assume that the reaction event to be bounded occurs within a run of L events in the SSA algorithm[http://identifiers.org/biomodels.kisao/KISAO_0000029], in order to execute L reactions at once in the manner of the R-leap algorithm[http://identifiers.org/biomodels.kisao/KISAO_0000230]&apos;&apos;.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000332"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/2852436</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Eric Mjolsness, David Orendorff, Philippe Chatelain, and Petros Koumoutsakos. An exact accelerated stochastic simulation algorithm. J Chem Phys. 2009 April 14; 130(14): 144110.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000332"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">L</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000333 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000333">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000241"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000359"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000029"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-03</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">accelerated stochastic simulation algorithm</rdfs:label>
        <skos:altLabel xml:lang="en">accelerated SSA</skos:altLabel>
        <skos:definition xml:lang="en">An algorithm, which accelerates SSA [http://identifiers.org/biomodels.kisao/KISAO_0000029] either at the expense of its accuracy or exact.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000333"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">accelerated SSA</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000334 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000334">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000068"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000236"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000359"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000315"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-03</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">multiparticle lattice gas automata</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1142/S0129183194000052</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">multiparticle lattice gas cellular automata</skos:altLabel>
        <skos:definition xml:lang="en">An algorithm which allows  for an arbitrary number of particles, while keeping the benefits of the cellular automata approach [http://identifiers.org/biomodels.kisao/KISAO_0000315].</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000334"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1142/S0129183194000052</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Chopard B., et al.Multiparticle lattice gas automata for reaction diffusion systems. Int. J. Mod. Phys. C 1994;5:47-63.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000334"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">multiparticle lattice gas cellular automata</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000335 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000335">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000241"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000361"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000029"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-03</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">generalized stochastic simulation algorithm</rdfs:label>
        <skos:definition xml:lang="en">Gillespie direct method [http://identifiers.org/biomodels.kisao/KISAO_0000029] follows unit-by-unit changes in the total numbers of each reactant species, it is especially well suited to the study of systems in which reactant densities are low and the application of methods based on continuum approximations, such as the traditional ordinary differential equations of chemical kinetics, is questionable. The &apos;generalized stochastic simulation algorithm&apos; branch presents methods, which extend Gillespie direct method [http://identifiers.org/biomodels.kisao/KISAO_0000029] to suit to systems with other characteristics.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000336 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000336">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000335"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000237"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-03</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">D-leaping method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1016/j.jcp.2009.05.004</rdfs:seeAlso>
        <skos:definition xml:lang="en">We propose a novel, accelerated algorithm for the approximate stochastic simulation of biochemical systems with delays. The present work extends existing accelerated algorithms by distributing, in a time adaptive fashion, the delayed reactions so as to minimize the computational effort while preserving their accuracy.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000336"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1016/j.jcp.2009.05.004</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Bayati B, Chatelain P, Koumoutsakos. D-leaping: Accelerating stochastic simulation algorithms for reactions with delays. Journal of Computational Physics. 2009 Sept;228(16):5909-5918.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000337 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000337">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000369"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000103"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000237"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000346"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-07</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">finite element method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1109/MAP.2007.376627</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">FEA</skos:altLabel>
        <skos:altLabel xml:lang="en">FEM</skos:altLabel>
        <skos:altLabel xml:lang="en">finite element analysis</skos:altLabel>
        <skos:definition xml:lang="en">A numerical technique for finding approximate solutions of partial differential equations (PDE) as well as of integral equations. The solution approach is based either on eliminating the differential equation completely (steady state problems), or rendering the PDE into an approximating system of ordinary differential equations, which are then numerically integrated using standard techniques such as Euler method [http://identifiers.org/biomodels.kisao/KISAO_0000261], Runge-Kutta [http://identifiers.org/biomodels.kisao/KISAO_0000064], etc.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000337"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1109/MAP.2007.376627</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Pelosi G. The finite-element method, Part I: R. L. Courant: Historical Corner. IEEE Antennas and Propagation Magazine, Vol. 49, No. 2. (April 2007), pp. 180-182.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000337"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">FEA</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000337"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">FEM</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000337"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">finite element analysis</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000338 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000338">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000337"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-07</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">h-version of the finite element method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1016/0168-874X(94)90003-5</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">h-FEM</skos:altLabel>
        <skos:altLabel xml:lang="en">h-method</skos:altLabel>
        <skos:definition xml:lang="en">Classical form of the &apos;finite element method&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000337], in which polynomials of fixed degree p are used and the mesh is refined to increase accuracy. Can be considered as a special case of the h-p version [http://identifiers.org/biomodels.kisao/KISAO_0000340].</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000338"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1016/0168-874X(94)90003-5</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Babuska, I., T. Strouboulis, A. Mathur, C. S. Upadhyay, Pollution error in the h-version of the finite element method and the local quality of a-posteriori error estimators, Finite Elements in Analysis and Design, 17: 273-321, 1994.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000338"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">h-FEM</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000338"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">h-method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000339 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000339">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000337"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-07</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">p-version of the finite element method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1137/0718033</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">p-FEM</skos:altLabel>
        <skos:altLabel xml:lang="en">p-method</skos:altLabel>
        <skos:definition xml:lang="en">The p version of &apos;finite element method&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000337] uses a fixed mesh but increases the polynomial degree p to increase accuracy. Can be considered as a special case of the h-p version [http://identifiers.org/biomodels.kisao/KISAO_0000340].</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000339"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1137/0718033</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Babuska, I., B.A. Szabo and I.N. Katz, The p-version of the finite element method, SIAM J. Numer. Anal., 18: 515-545, 1981.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000339"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">p-FEM</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000339"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">p-method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000340 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000340">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000337"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000361"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000338"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000361"/>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <owl:disjointWith rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000341"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-07</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">h-p version of the finite element method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1007/BF00272624</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">hp-FEM</skos:altLabel>
        <skos:altLabel xml:lang="en">hp-method</skos:altLabel>
        <skos:definition xml:lang="en">In h-p version of &apos;finite difference method&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000337] the two approaches of mesh refinement and degree enchacement are combined.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000340"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1007/BF00272624</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Babuska, I., and B. Guo, The h-p version of the finite element method, Comput. Mech., 1: 203-220, 1986.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000340"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">hp-FEM</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000340"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">hp-method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000341 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000341">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000337"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-07</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">mixed finite element method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1016/0045-7825(90)90168-L</rdfs:seeAlso>
        <skos:definition xml:lang="en">A &apos;finite element method&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000337] in which both stress and displacement fields are approximated as primary variables.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000341"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1016/0045-7825(90)90168-L</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">D. N. Arnold. 1990. Mixed finite element methods for elliptic problems. Comput. Methods Appl. Mech. Eng. 82, 1-3 (September 1990), 281-300.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000342 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000342">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000369"/>
        <rdfs:subClassOf>
            <owl:Class>
                <owl:complementOf>
                    <owl:Restriction>
                        <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                        <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000376"/>
                    </owl:Restriction>
                </owl:complementOf>
            </owl:Class>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-07</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">level set method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1016/0021-9991(88)90002-2</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">LSM</skos:altLabel>
        <skos:altLabel xml:lang="en">level-set method</skos:altLabel>
        <skos:definition xml:lang="en">An algorithm for moving surfaces under their curvature. This algorithm rely on numerically solving Hamilton-Jacobi equations with viscous terms, using approximation techniques from hyperbolic conservation laws.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000342"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1016/0021-9991(88)90002-2</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Osher, S.; Sethian, J. A. (1988), &quot;Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations&quot;, J. Comput. Phys. 79: 12-49.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000342"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">LSM</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000342"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">level-set method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000343 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000343">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000369"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000347"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000361"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000337"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-07</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">generalized finite element method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1142/S0219876204000083</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">GFEM</skos:altLabel>
        <skos:altLabel xml:lang="en">PUM</skos:altLabel>
        <skos:altLabel xml:lang="en">partition of unity method</skos:altLabel>
        <skos:definition xml:lang="en">The GFEM is a generalization of the classical &apos;finite element method&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000337] — in its h [http://identifiers.org/biomodels.kisao/KISAO_0000338], p [http://identifiers.org/biomodels.kisao/KISAO_0000339], and h-p versions [http://identifiers.org/biomodels.kisao/KISAO_0000340]— as well as of the various forms of meshless methods used in engineering.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000343"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1142/S0219876204000083</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Babuska, Ivo; Uday Banerjee, John E. Osborn (June 2004). Generalized Finite Element Methods: Main Ideas, Results, and Perspective. International Journal of Computational Methods 1 (1): 67-103.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000343"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">GFEM</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000343"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">PUM</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000343"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">partition of unity method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000345 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000345">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000369"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000237"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000347"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-09</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">h-p cloud method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1002/(SICI)1098-2426(199611)12:6&lt;673::AID-NUM3&gt;3.0.CO;2-P</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">h-p clouds</skos:altLabel>
        <skos:altLabel xml:lang="en">method of clouds</skos:altLabel>
        <skos:definition xml:lang="en">A meshless method, which uses a partition of unity to construct the family of h-p cloud functions. </skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000345"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1002/(SICI)1098-2426(199611)12:6&lt;673::AID-NUM3&gt;3.0.CO;2-P</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Duarte, C. A. and Oden, J. T. (1996), H-p clouds—an h-p meshless method. Numerical Methods for Partial Differential Equations, 12: 673-705.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000345"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">h-p clouds</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000345"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">method of clouds</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000346 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000346">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000311"/>
        <owl:disjointWith rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000347"/>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">mesh-based geometry handling</rdfs:label>
        <skos:definition xml:lang="en">In most large-scale numerical simulations of physical phenomena, a large percentage of the overall computational effort is expended on technical details connected with meshing. These details include, in particular, grid generation, mesh adaptation to domain geometry, element or cell connectivity, grid motion and separation to model fracture, fragmentation, free surfaces, etc.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000347 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000347">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000311"/>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">meshless geometry handling</rdfs:label>
        <skos:definition xml:lang="en">Most meshless methods require a scattered set of nodal points in the domain of interest. In these methods, there may be no fixed connectivities between the nodes, unlike the finite element or finite difference methods. This feature has significant implications in modeling some physical phenomena that are characterized by a continuous change in the geometry of the domain under analysis. </skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000348 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000348">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000369"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000103"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000237"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000347"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000361"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000337"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-09</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">extended finite element method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1007/s00466-002-0391-2</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">X-FEM</skos:altLabel>
        <skos:altLabel xml:lang="en">XFEM</skos:altLabel>
        <skos:definition xml:lang="en">A numerical method to model arbitrary discontinuities in continuous bodies that does not require the mesh to conform to the discontinuities nor significant mesh refinement near singularities. In X-FEM the standard finite element approximation [http://identifiers.org/biomodels.kisao/KISAO_0000337] is enriched and the approximation space is extended by an additional family of functions.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000348"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1007/s00466-002-0391-2</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Stazi, F. L.; Budyn, E.; Chessa, J.; Belytschko, T. An extended finite element method with higher-order elements for curved cracks. Computational Mechanics, Volume 31, Issue 1-2, pp. 38-48 (2003).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000348"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">X-FEM</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000348"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">XFEM</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000349 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000349">
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            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000237"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000347"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-09</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">method of finite spheres</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1007/s004660050481</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">MFS</skos:altLabel>
        <skos:definition xml:lang="en">Method of finite spheres is truly meshless in the sense that the nodes are placed and the numerical integration is performed without a mesh. Some of the novel features of the method of finite spheres are the numerical integration scheme and the way in which the Dirichlet boundary conditions are incorporated.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000349"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1007/s004660050481</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">S. De and K. J. Bathe. The method of finite spheres. Computational Mechanics, Volume 25, Number 4, 329-345.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000349"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">MFS</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000350 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000350">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000333"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-09</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">probability-weighted dynamic Monte Carlo method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1021/jp011404w</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">PW-DMC</skos:altLabel>
        <skos:altLabel xml:lang="en">probability-weighted DMC</skos:altLabel>
        <skos:definition xml:lang="en">We have developed a probability-weighted DMC method by incorporating the weighted sampling algorithm of equilibrium molecular simulations. This new algorithm samples the slow reactions very efficiently and makes it possible to simulate in a computationally efficient manner the reaction kinetics of physical systems in which the rates of reactions vary by several orders of magnitude.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000350"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1021/jp011404w</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Resat H, Wiley HS, Dixon DA. Probability-weighted dynamic Monte Carlo method for reaction kinetics simulations. J Phys Chem B. 2001;105:11026-11034.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000350"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">PW-DMC</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000350"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">probability-weighted DMC</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000351 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000351">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000039"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000361"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000074"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-09</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">multinomial tau-leaping method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/17343434</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">MtauL</skos:altLabel>
        <skos:definition xml:lang="en">The multinomial tau-leaping method  is an extension of the binomial tau-leaping method [http://identifiers.org/biomodels.kisao/KISAO_0000074] to networks with arbitrary multiple-channel reactant dependencies. Improvements were achieved by a combination of three factors: First, tau-leaping steps are determined simply and efficiently using a-priori information and Poisson distribution based estimates of expectation values for reaction numbers. Second, networks are partitioned into closed groups of reactions and corresponding reactants in which no group reactant set is found in any other group. Third, product formation is factored into upper bound estimation of the number of times a particular reaction occurs.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000351"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/17343434</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Pettigrew MF, Resat H. Multinomial tau-leaping method for stochastic kinetic simulations. J Chem Phys. 2007 Feb 28;126(8):084101.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000351"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">MtauL</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000352 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000352">
        <owl:equivalentClass>
            <owl:Class>
                <owl:intersectionOf rdf:parseType="Collection">
                    <rdf:Description rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
                    <owl:Restriction>
                        <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                        <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000322"/>
                    </owl:Restriction>
                </owl:intersectionOf>
            </owl:Class>
        </owl:equivalentClass>
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-09</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">hybrid method</rdfs:label>
        <skos:definition xml:lang="en">A simulation methods which combines the advantages of complementary simulation approaches: the whole system is subdivided into appropriate parts and different simulation methods operate on these parts at the same time.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000353 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000353">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000354"/>
        <rdfs:subClassOf>
            <owl:Class>
                <owl:complementOf>
                    <owl:Restriction>
                        <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                        <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000102"/>
                    </owl:Restriction>
                </owl:complementOf>
            </owl:Class>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000361"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000388"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-10</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">generalized minimal residual algorithm</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1137/0907058</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">GMRES</skos:altLabel>
        <skos:definition xml:lang="en">An iterative method for solving linear systems, which has the property of minimizing at every step the norm of the residual vector over a Krylov subspace. The generalized minimal residual method extends the minimal residual method (MINRES) [http://identifiers.org/biomodels.kisao/KISAO_0000388], which is only applicable to symmetric systems, to non-symmetric systems.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000353"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1137/0907058</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Youcef Saad and Martin H. Schultz, GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems. SIAM J. Sci. and Stat. Comput. 7, 856 (1986).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000353"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">GMRES</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000354 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000354">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000398"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000103"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000106"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-10</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">Krylov subspace projection method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/0898715342</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Krylov subspace method</skos:altLabel>
        <skos:definition xml:lang="en">Krylov subspace method is an iterative linear equation method, which builds up Krylov subspaces and look for good approximations to eigenvectors and invariant subspaces within the Krylov spaces.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000354"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/0898715342</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Y. Saad. 2003. Iterative Methods for Sparse Linear Systems (2nd ed.). Soc. for Industrial and Applied Math., Philadelphia, PA, USA.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000354"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Krylov subspace method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000355 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000355">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000432"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000373"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000359"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000283"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000353"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000356"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000386"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-10</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">DASPK</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1137/0915088</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">DDASPK</skos:altLabel>
        <skos:altLabel xml:lang="en">SDASPK</skos:altLabel>
        <skos:altLabel xml:lang="en">differential algebraic system solver with Krylov preconditioning</skos:altLabel>
        <skos:definition xml:lang="en">In DASPK, we have combined the time-stepping methods of DASSL [http://identifiers.org/biomodels.kisao/KISAO_0000255] with preconditioned iterative method GMRES [http://identifiers.org/biomodels.kisao/KISAO_0000386], for solving large-scale systems of DAEs of the form F(t, y, y&apos;) = 0, where F, y, y&apos; are N-dimensional vectors, and a consistent set of initial conditions y(t0) = y0, y&apos;(t0) = y&apos;0 is given.
DASPK is written in Fortran.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000355"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1137/0915088</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Peter N. Brown, Alan C. Hindmarsh, and Linda R. Petzold. 1994. Using Krylov methods in the solution of large-scale differential-algebraic systems. SIAM J. Sci. Comput. 15, 6 (November 1994), 1467-1488.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000355"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">DDASPK</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">NARROW</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000355"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">SDASPK</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">NARROW</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000355"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">differential algebraic system solver with Krylov preconditioning</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000356 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000356">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000432"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000373"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-10</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">DASSL</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://www.nea.fr/abs/html/nesc9918.html</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">DDASSL</skos:altLabel>
        <skos:altLabel xml:lang="en">SDASSL</skos:altLabel>
        <skos:altLabel xml:lang="en">differential algebraic system solver</skos:altLabel>
        <skos:definition xml:lang="en">DASSL is designed for the numerical solution of implicit systems of differential/algebraic equations written in the form F(t,y,y&apos;)=0, where F, y, and y&apos; are vectors, and initial values for y and y&apos; are given.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000356"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://www.nea.fr/abs/html/nesc9918.html</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Linda R. Petzold: A Description of DASSL: A Differential/Algebraic System Solver, SAND82-8637 (September 1982).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000356"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">DDASSL</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">NARROW</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000356"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">SDASSL</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">NARROW</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000356"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">differential algebraic system solver</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000357 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000357">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000354"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000404"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-10</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">conjugate gradient method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">urn:issn:0091-0635</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">CG</skos:altLabel>
        <skos:definition xml:lang="en">Conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is symmetric and positive-definite. The conjugate gradient method is an iterative method, so it can be applied to sparse systems that are too large to be handled by direct methods. Such systems often arise when numerically solving partial differential equations.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000357"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">urn:issn:0091-0635</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">M. R. Hestenes and E. L. Stiefel, Methods of conjugate gradients for solving linear systems. J. Res. Natl. Bur. Stand. 49 (1952), p. 409.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000357"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">CG</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000358 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000358">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000354"/>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-10</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">biconjugate gradient method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1007/BFb0080109</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">BCG</skos:altLabel>
        <skos:altLabel xml:lang="en">Bi-CG</skos:altLabel>
        <skos:altLabel xml:lang="en">BiCG</skos:altLabel>
        <skos:definition xml:lang="en">The biconjugate gradient method provides a generalization of conjugate gradient method [http://identifiers.org/biomodels.kisao/KISAO_0000357] to non-symmetric matrices.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000358"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1007/BFb0080109</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Fletcher, R. (1976). &quot;Conjugate gradient methods for indefinite systems&quot;. Numerical Analysis. Lecture Notes in Mathematics (Springer Berlin / Heidelberg) 506: 73-89.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000358"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">BCG</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000358"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Bi-CG</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000358"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">BiCG</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000362 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000362">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000017"/>
        <rdfs:subClassOf>
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                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000359"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000021"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000361"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000029"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-13</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">implicit-state Doob-Gillespie algorithm</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/3-540-76636-7 978-3-540-76636-0</rdfs:seeAlso>
        <skos:definition xml:lang="en">The algorithm uses a representation of the system together with a super-approximation of its ‘event horizon’ (all events that may happen next), and a specific correction scheme to obtain exact timings. Being completely local and not based on any kind of enumeration, this algorithm has a per event time cost which is independent of (i) the size of the set of generable species (which can even be infinite), and (ii) independent of the size of the system (ie, the number of agent instances). The algorithm can be refined, using concepts derived from the classical notion of causality, so that in addition to the above one also has that the even cost is depending (iii) only logarithmically on the size of the model (ie, the number of rules).
</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000362"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/3-540-76636-7 978-3-540-76636-0</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">V. Danos, J. Feret, W. Fontana, and J. Krivine. 2007. Scalable simulation of cellular signalling networks. In Proceedings of the 5th Asian conference on Programming languages and systems (APLAS&apos;07), Zhong Shao (Ed.). Springer-Verlag, Berlin, Heidelberg, 139-157.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000363 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000363">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-13</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">rule-based simulation method</rdfs:label>
        <skos:definition xml:lang="en">Rule-based models provide a powerful alternative to approaches that require explicit enumeration of all possible molecular species of a system. Such models consist of formal rules governing interactive behaviour. Rule-based simulation methods simulate such models.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000364 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000364">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000289"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000279"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000280"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-16</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn xml:lang="en">GSL</isImplementedIn>
        <rdfs:label xml:lang="en">Adams predictor-corrector method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">urn:asin:B0000EFQ8B</rdfs:seeAlso>
        <skos:definition xml:lang="en">The combination of evaluating a single explicit integration method (&apos;Adams-Bashforth method&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000279]) (the predictor step) in order to provide a good initial guess for the successive evaluation of an implicit method (&apos;Adams-Moulton method&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000280]) (the corrector step) using iteration.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000364"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">urn:asin:B0000EFQ8B</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Moulton, Forest R. (1926), New methods in exterior ballistics, University of Chicago Press.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000365 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000365">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000352"/>
        <rdfs:subClassOf>
            <owl:Restriction>
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                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000288"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000246"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000310"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000246"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000364"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000246"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000367"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000246"/>
                <owl:someValuesFrom>
                    <owl:Class>
                        <owl:intersectionOf rdf:parseType="Collection">
                            <rdf:Description rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000064"/>
                            <owl:Restriction>
                                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000240"/>
                            </owl:Restriction>
                        </owl:intersectionOf>
                    </owl:Class>
                </owl:someValuesFrom>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-16</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn xml:lang="en">Mathematica</isImplementedIn>
        <rdfs:label xml:lang="en">NDSolve method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-1-57955-058-5</rdfs:seeAlso>
        <skos:definition xml:lang="en">The Mathematica computation system function NDSolve is a general numerical differential equation solver. It can handle a wide range of ordinary differential equations as well as some partial differential equations. NDSolve can also solve some differential-algebraic equations, which are typically a mix of differential and algebraic equations.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000365"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-1-57955-058-5</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Advanced Numerical Differential Equation Solving in Mathematica, Wolfram Mathematica Tutorial Collection, 2008.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000366 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000366">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000097"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-16</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">symplecticness</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1017/S0962492900002282</rdfs:seeAlso>
        <skos:definition xml:lang="en">Roughly speaking, ‘symplecticness’ is a characteristic property possessed by the solutions of Hamiltonian problems. A numerical method is called symplectic if, when applied to Hamiltonian problems, it generates numerical solutions which inherit the property of symplecticness (phase volume preservation).</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000366"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1017/S0962492900002282</owl:annotatedTarget>
        <rdfs:comment xml:lang="en"> J. M. Sanz-Serna (1992). Symplectic integrators for Hamiltonian problems: an overview. Acta Numerica, 1, pp 243-286</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000367 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000367">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000064"/>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
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                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000064"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-16</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">partitioned Runge-Kutta method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1007/BF01389456</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">PRK</skos:altLabel>
        <skos:altLabel xml:lang="en">SPRK</skos:altLabel>
        <skos:altLabel xml:lang="en">symplectic partitioned Runge-Kutta method</skos:altLabel>
        <skos:definition xml:lang="en">If a Hamiltonian system possesses a natural partitioning, it is possible to integrate its certain components using one Runge-Kutta method and other components using a different Runge-Kutta method. The overall s-stage scheme is called a partitioned Runge-Kutta method.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000367"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1007/BF01389456</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">P. Rentrop (1985): Partitioned Runge-Kutta methods with stiffness detection and stepsize control. Numer. Math., Vol. 47, p.545-564.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000367"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">PRK</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000367"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">SPRK</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000367"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">symplectic partitioned Runge-Kutta method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000369 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000369">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
        <rdfs:subClassOf>
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                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-27</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">partial differential equation discretization method</rdfs:label>
        <skos:definition xml:lang="en">A method which solves partial differential equations by discretizing them, i.e. approximating them by equations that involve a finite number of unknowns.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000370 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000370">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000097"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-29</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">type of problem</rdfs:label>
        <skos:definition xml:lang="en">A characteristic describing the type of the problems which can be solved by the algorithm.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000371 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000371">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000405"/>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">stochastic differential equation problem</rdfs:label>
        <skos:altLabel xml:lang="en">SDE problem</skos:altLabel>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000371"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">SDE problem</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000372 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000372">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000405"/>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">partial differential equation problem</rdfs:label>
        <skos:altLabel xml:lang="en">PDE problem</skos:altLabel>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000372"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">PDE problem</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000373 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000373">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000405"/>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">differential-algebraic equation problem</rdfs:label>
        <skos:altLabel xml:lang="en">DAE</skos:altLabel>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000373"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">DAE</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000374 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000374">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000405"/>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">ordinary differential equation problem</rdfs:label>
        <skos:altLabel xml:lang="en">ODE problem</skos:altLabel>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000374"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">ODE problem</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000375 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000375">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000405"/>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">delay differential equation problem</rdfs:label>
        <skos:altLabel xml:lang="en">DDE problem</skos:altLabel>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000376 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000376">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000370"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-07-19</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">linearity of equation</rdfs:label>
        <skos:definition xml:lang="en">Linear differential equations are of the form Ly = f, where the differential operator L is a linear operator, y is the unknown function, and the right hand side f is a given function of the same nature as y.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000377 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000377">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
        <rdfs:subClassOf>
            <owl:Class>
                <owl:complementOf>
                    <owl:Restriction>
                        <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                        <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000102"/>
                    </owl:Restriction>
                </owl:complementOf>
            </owl:Class>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000237"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000483"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-30</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">one-step method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-3-540-56670-0</rdfs:seeAlso>
        <skos:definition xml:lang="en">A numerical method for differential equations which uses one starting value at each step.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000377"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-3-540-56670-0</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Hairer, Ernst; Nørsett, Syvert Paul; Wanner, Gerhard (1993), Solving ordinary differential equations I: Nonstiff problems (2nd ed.), Berlin: Springer Verlag</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000378 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000378">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000064"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000240"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000275"/>
                <owl:hasValue rdf:datatype="http://www.w3.org/2001/XMLSchema#integer">2</owl:hasValue>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-06-30</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn xml:lang="en">GSL</isImplementedIn>
        <rdfs:label xml:lang="en">implicit midpoint rule</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-3-540-56670-0</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">implicit Gaussian second order Runge-Kutta method</skos:altLabel>
        <skos:definition xml:lang="en">The implicit midpoint rule is a second-order case of the more general implicit s-stage Runge-Kutta methods [http://identifiers.org/biomodels.kisao/KISAO_0000064 and (http://identifiers.org/biomodels.kisao/KISAO_0000245 some http://identifiers.org/biomodels.kisao/KISAO_0000240)].</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000378"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-3-540-56670-0</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Hairer, Ernst; Nørsett, Syvert Paul; Wanner, Gerhard (1993), Solving ordinary differential equations I: Nonstiff problems (2nd ed.), Berlin: Springer Verlag.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000378"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">implicit Gaussian second order Runge-Kutta method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000379 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000379">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000380"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000103"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000374"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000382"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-07-01</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">Bulirsch-Stoer algorithm</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1007/BF02165234</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">GBS</skos:altLabel>
        <skos:altLabel xml:lang="en">Gragg-Bulirsch-Stoer algorithm</skos:altLabel>
        <skos:definition xml:lang="en">The Bulirsch-Stoer method is an adaptive method which uses Gragg&apos;s modified midpoint method [http://identifiers.org/biomodels.kisao/KISAO_0000382] to estimate the solution of an initial value problem for various step sizes. The estimates are fit to a &quot;diagonal&quot; rational function or a polynomial as a function of the step size and the limit as the step size tends to zero is taken as the final estimate.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000379"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1007/BF02165234</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Bulirsch R. and Stoer J. (1966) Numerical treatment of ordinary differential equations by extrapolation methods, Numerische Mathematik, Volume 8, Number 1, 1-13.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000379"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">GBS</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000379"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Gragg-Bulirsch-Stoer algorithm</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000380 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000380">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000377"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-07-01</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">Richardson extrapolation based method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1098/rsta.1911.0009</rdfs:seeAlso>
        <skos:definition xml:lang="en">A method based on ideas of Richardson extrapolation, which is a process for obtaining increased accuracy in a discretized approximation by extrapolating results from coarse discretizations to an arbitrarily fine one.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000380"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1098/rsta.1911.0009</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Richardson, L. F. (1911). The approximate arithmetical solution by finite differences of physical problems including differential equations, with an application to the stresses in a masonry dam. Philosophical Transactions of the Royal Society of London, Series A 210 (459-470): 307-357.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000381 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000381">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000064"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000239"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000275"/>
                <owl:hasValue rdf:datatype="http://www.w3.org/2001/XMLSchema#integer">2</owl:hasValue>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-07-01</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">midpoint method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-3-540-56670-0</rdfs:seeAlso>
        <skos:definition xml:lang="en">The midpoint method is an explicit method for approximating the solution of the initial value problem y&apos; = f(x,y);  y(x0) = y0 at x for a given step size h. For the midpoint method the derivative of y(x) is approximated by the symmetric difference y&apos;(x) = ( y(x+h) - y(x-h) ) / 2h + O(h2).</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000381"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-3-540-56670-0</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Hairer, Ernst; Nørsett, Syvert Paul; Wanner, Gerhard (1993), Solving ordinary differential equations I: Nonstiff problems (2nd ed.), Berlin: Springer Verlag.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000382 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000382">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000064"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000239"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-07-01</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">modified midpoint method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/052143064X</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Gragg&apos;s method</skos:altLabel>
        <skos:altLabel xml:lang="en">Gragg&apos;s modified midpoint method</skos:altLabel>
        <skos:definition xml:lang="en">The modified midpoint method is globally a second order method for approximating the solution of the initial value problem y&apos; = f(x, y), y(x0) = y0, which advances a vector of dependent variables y(x) from a point x to a point x + H by a sequence of n substeps each of size h, h = H/n.
</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000382"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/052143064X</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Press WH, Teukolsky SA, Vetterling WT, Flannery BP. Numerical Recipes in Fortran 77. Cambridge University Press (2001).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000382"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Gragg&apos;s method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000383 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000383">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000380"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000374"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000384"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000361"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000379"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-07-01</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn xml:lang="en">GSL</isImplementedIn>
        <rdfs:label xml:lang="en">Bader-Deuflhard method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1007/BF01418331</rdfs:seeAlso>
        <skos:definition xml:lang="en">The Bader-Deuflhard method is an extrapolation method based on a semi-implicit discretization [http://identifiers.org/biomodels.kisao/KISAO_0000387]. It is a generalization of the Bulirsch-Stoer algorithm [http://identifiers.org/biomodels.kisao/KISAO_0000379] for solving ordinary differential equations.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000383"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1007/BF01418331</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Bader, G. and Deuflhard, P. &quot;A Semi-Implicit Mid-Point Rule for Stiff Systems of Ordinary Differential Equations.&quot; Numer. Math. 41, 373-398, 1983.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000384 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000384">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000064"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000240"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-07-01</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">semi-implicit midpoint rule</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1007/BF01418331</rdfs:seeAlso>
        <skos:definition xml:lang="en">A semi-implicit version of the midpoint method that has an even error series [http://identifiers.org/biomodels.kisao/KISAO_0000381].</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000384"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1007/BF01418331</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Bader, G. and Deuflhard, P. &quot;A Semi-Implicit Mid-Point Rule for Stiff Systems of Ordinary Differential Equations.&quot; Numer. Math. 41, 373-398, 1983.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000386 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000386">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000353"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000397"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-07-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">scaled preconditioned generalized minimal residual method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1137/0915088</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">SPGMR</skos:altLabel>
        <skos:definition xml:lang="en">A scaled preconditioned version of &apos;generalized minimal residual algorithm&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000353]. For linear system Ax = b a preconditioner matrix P that approximates A is sought, for which linear system Px = b can be solved easily. Preconditioning is applied on the left only. Scaling is done using diagonal matrix D whose diagonal elements are weights w^i = rtol|y^i| +atol^i, where rtol is &apos;relative tolerance&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000209] and atol is &apos;absolute tolerance&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000211].</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000386"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1137/0915088</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Peter N. Brown, Alan C. Hindmarsh, and Linda R. Petzold. 1994. Using Krylov methods in the solution of large-scale differential-algebraic systems. SIAM J. Sci. Comput. 15, 6 (November 1994), 1467-1488.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000386"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">SPGMR</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000388 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000388">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000354"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000404"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-07-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">minimal residual method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1137/0712047</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">MINRES</skos:altLabel>
        <skos:definition xml:lang="en">The &apos;minimal residual method&apos; is an algorithm for the numerical solution of indefinite symmertic systems of linear equations.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000388"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1137/0712047</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Paige C.C., Saunders M.A. Solution of sparse indefinite systems of linear equations, SIAM Journal on Numerical Analysis (1975) Volume: 12, Issue: 4, Publisher: SIAM, Pages: 617-629.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000388"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">MINRES</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000389 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000389">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000393"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-07-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">quasi-minimal residual method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1007/BF01385726</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">QMR</skos:altLabel>
        <skos:definition xml:lang="en">The QMR algorithm is a robust iterative solver for general nonsingular non-Hermitian linear systems. The method uses a robust implementation of the look-ahead Lanczos algorithm to generate basis vectors for the Krylov subspaces Kn(r0, A). The QMR iterates are characterized by a quasi-minimal residual property over Kn(r0, A).</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000389"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1007/BF01385726</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Roland W. Freund and Noël M. Nachtigal. QMR: a quasi-minimal residual method for non-Hermitian linear systems. NUMERISCHE MATHEMATIK Volume 60, Number 1, 315-339.
</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000389"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">QMR</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000392 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000392">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000395"/>
        <owl:disjointWith rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000393"/>
        <rdfs:label xml:lang="en">biconjugate gradient stabilized method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1137/0913035</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Bi-CGSTAB</skos:altLabel>
        <skos:altLabel xml:lang="en">BiCGSTAB</skos:altLabel>
        <skos:definition xml:lang="en">An iterative method for the numerical solution of nonsymmetric linear systems. It is a variant of the biconjugate gradient method (BiCG) [http://identifiers.org/biomodels.kisao/KISAO_0000358] and has faster and smoother convergence than the original BiCG.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000392"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1137/0913035</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Van der Vorst, H. A. (1992). Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems. SIAM Journal on Scientific and Statistical Computing 13: 631-644.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000392"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Bi-CGSTAB</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000392"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">BiCGSTAB</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000393 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000393">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000395"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-07-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">ingenious conjugate gradients-squared method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1137/0910004</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">CGS</skos:altLabel>
        <skos:definition xml:lang="en">A Lanczos-type method for nonsymmetric sparse linear systems. The method is based on a polynomial variant of the conjugate gradients algorithm [http://identifiers.org/biomodels.kisao/KISAO_0000357]. Although related to the so-called bi-conjugate gradients (Bi-CG) algorithm [http://identifiers.org/biomodels.kisao/KISAO_0000358], it does not involve adjoint matrix-vector multiplications, and the expected convergence rate is about twice that of the Bi-CG algorithm.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000393"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1137/0910004</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Peter Sonneveld. 1989. CGS, a fast Lanczos-type solver for nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 10, 1 (January 1989), 36-52.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000393"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">CGS</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000394 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000394">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000392"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-07-19</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">quasi-minimal residual variant of biconjugate gradient stabilized method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1137/0915023</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">QMRCGSTAB</skos:altLabel>
        <skos:definition xml:lang="en">QMRCGSTAB is a quasi-minimal residual (QMR) variant of the Bi-CGSTAB algorithm [http://identifiers.org/biomodels.kisao/KISAO_0000394] of van der Vorst for solving nonsymmetric linear systems. The motivation for the QMR variant is to obtain smoother convergence behavior of the underlying method.
</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000394"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1137/0915023</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">T. F. Chan, E. Gallopoulos, V. Simoncini, T. Szeto, and C. H. Tong. 1994. A quasi-minimal residual variant of the Bi-CGSTAB algorithm for nonsymmetric systems. SIAM J. Sci. Comput. 15, 2 (March 1994), 338-347.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000394"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">QMRCGSTAB</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000395 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000395">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000354"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000359"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000358"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-07-19</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">improved biconjugate gradient method</rdfs:label>
        <skos:definition xml:lang="en">An &apos;improved biconjugate gradient method&apos; branch contains algorithms which can be viewed as improvements over some of drawbacks of BCG [http://identifiers.org/biomodels.kisao/KISAO_0000358], such as (1) the need for matrix-vector multiplications with A^T (which can be inconvenient as well as doubling the number of matrix-vector multiplications compared to CG [http://identifiers.org/biomodels.kisao/KISAO_0000357] for each increase in the degree of the underlying Krylov subspace), (2) the possibility of breakdowns and (3) erratic convergence behavior.
</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000396 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000396">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000389"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-07-19</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">transpose-free quasi-minimal residual algorithm</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1137/0914029</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">TFQMR</skos:altLabel>
        <skos:definition xml:lang="en">A version of CGS [http://identifiers.org/biomodels.kisao/KISAO_0000393] which &apos;quasi-minimizes&apos; the residual in the space spanned by the vectors generated by the CGS iteration.
</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000396"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1137/0914029</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Roland W. Freund. 1993. A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems. SIAM J. Sci. Comput. 14, 2 (March 1993), 470-482.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000396"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">TFQMR</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000397 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000397">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000399"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000398"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-07-19</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">preconditioning technique</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/0898715342</rdfs:seeAlso>
        <skos:definition xml:lang="en">Preconditioning is simply a means of transforming the original linear system into one which has the same solution, but which is likely to be easier to solve with an iterative solver.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000397"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/0898715342</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Saad, Yousef (2003). Iterative methods for sparse linear systems (2nd ed.). SIAM.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000398 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000398">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000237"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000373"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000376"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-07-19</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">iterative method for linear system</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/0898715342</rdfs:seeAlso>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000398"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/0898715342</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Saad, Yousef (2003). Iterative methods for sparse linear systems (2nd ed.). SIAM.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000403 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000403">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000376"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-07-19</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">homogeneousness of equation</rdfs:label>
        <skos:definition xml:lang="en">Homogeneous equations are of the form Ly = 0, where the differential operator L is a linear operator and y is the unknown function.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000404 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000404">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000370"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-07-19</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">symmetricity of matrix</rdfs:label>
        <skos:definition xml:lang="en">In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000405 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000405">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000370"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2011-07-19</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">type of differential equation</rdfs:label>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000407 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000407">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000106"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2012-01-17</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:comment xml:lang="en">Requested by Frank T. Bergmann on Sunday, November 27, 2011 4:45:30 PM.</rdfs:comment>
        <rdfs:label xml:lang="en">steady state method</rdfs:label>
        <skos:definition xml:lang="en">A method looking for a steady state of a dynamic system.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000408 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000408">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000106"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000209"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000211"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000415"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2012-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:comment xml:lang="en">Requested by Frank T. Bergmann on Sunday, November 27, 2011 4:45:30 PM.</rdfs:comment>
        <rdfs:label xml:lang="en">Newton-type method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/9783540210993</rdfs:seeAlso>
        <skos:definition xml:lang="en">A method which attacks the solution of a nonlinear problem F(x) = 0 by solving a sequence of liner problems of the same kind.
The solution of the system F(x)=0 can be interpreted as a steady state of a dynamic system x&apos;(t)=F(x(t)). The Newton approach will only work if the fixed point [http://identifiers.org/biomodels.teddy/TEDDY_0000086] of the dinamic system is attractive [http://identifiers.org/biomodels.teddy/TEDDY_0000094].</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000408"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/9783540210993</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Deuflhard, P. Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms, Springer Series in Computational Mathematics, Vol. 35, 1st ed. 2004.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000409 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000409">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000408"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2012-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">ordinary Newton method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/9783540210993</rdfs:seeAlso>
        <skos:definition xml:lang="en">A &apos;Newton-type method&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000408] which solves the general nonlinear problem F(x)=0 by applying successive linearization F&apos;(x[k])deltax[k]=-F(x[k]), x[k+1]=x[k]+deltax[k], k=0,1,...</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000409"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/9783540210993</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Deuflhard, P. Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms, Springer Series in Computational Mathematics, Vol. 35, 1st ed. 2004.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000410 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000410">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000408"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2012-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">simlified Newton method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/9783540210993</rdfs:seeAlso>
        <skos:definition xml:lang="en">A &apos;Newton-type method&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000408] which is characterized by keeping the initial derivative throughout the whole iteration: F&apos;(x[0])deltax[k]=-F(x[k]), x[k+1]=x[k]+deltax[k], k=0,1,...</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000410"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/9783540210993</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Deuflhard, P. Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms, Springer Series in Computational Mathematics, Vol. 35, 1st ed. 2004.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000411 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000411">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000408"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2012-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">Newton-like method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/9783540210993</rdfs:seeAlso>
        <skos:definition xml:lang="en">A &apos;Newton-type method&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000408] which is characterized by the fact that, in finite dimension, the Jacodian matrices are either replaced by some fixed &apos;close by&apos; Jacobian F&apos;(z) with z not equal to the initial guess x[0], or by some approximation so that: M&apos;(x[0])deltax[k]=-F(x[k]), x[k+1]=x[k]+deltax[k], k=0,1,...</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000411"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/9783540210993</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Deuflhard, P. Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms, Springer Series in Computational Mathematics, Vol. 35, 1st ed. 2004.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000412 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000412">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000408"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom>
                    <owl:Class>
                        <owl:intersectionOf rdf:parseType="Collection">
                            <rdf:Description rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
                            <owl:Restriction>
                                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000237"/>
                            </owl:Restriction>
                        </owl:intersectionOf>
                    </owl:Class>
                </owl:someValuesFrom>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2012-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">inexact Newton method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/9783540210993</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">iterative Newton method</skos:altLabel>
        <skos:altLabel xml:lang="en">truncated Newton method</skos:altLabel>
        <skos:definition xml:lang="en">For extremely large scale nonlinear problems the arising linear systems for the Newton corrections can no longer be solved directly (&apos;exactly&apos;), but must be solved iterativly (&apos;inexactly) - which gives the name inexact Newton methods. The whole scheme then consists of an inner iteration (at Newton step k): 
F&apos;(x[k])deltaxi[k]=-F(x[k])+ri[k], k=0,1,...
xi[k+1]=x[k]+deltaxi[k], i=0,1,..,imax[k]
in terms of residuals ri[k] and an outer iteration where, given x[0], the iterates are defined as x[k+1]=xi[k+1] for i=imax[k], k=0,1,...</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000412"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/9783540210993</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Deuflhard, P. Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms, Springer Series in Computational Mathematics, Vol. 35, 1st ed. 2004.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000412"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">iterative Newton method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000412"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">truncated Newton method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000413 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000413">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000408"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom>
                    <owl:Class>
                        <owl:intersectionOf rdf:parseType="Collection">
                            <rdf:Description rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
                            <owl:Restriction>
                                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000236"/>
                            </owl:Restriction>
                        </owl:intersectionOf>
                    </owl:Class>
                </owl:someValuesFrom>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2012-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">exact Newton method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/9783540210993</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">direct Newton method</skos:altLabel>
        <skos:definition xml:lang="en">Any of the finite dimensional Newton-type methods [http://identifiers.org/biomodels.kisao/KISAO_0000408] requires the numerical solution of the linear equations F&apos;(x[k])deltax[k]=-F(x[k]). Whenever direct elimination methods are applicable, we speak of exact Newton methods.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000413"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/9783540210993</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Deuflhard, P. Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms, Springer Series in Computational Mathematics, Vol. 35, 1st ed. 2004.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000415 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000415">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000244"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:allValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000408"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#integer"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2012-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">maximum number of steps</rdfs:label>
        <skos:altLabel xml:lang="en">maximum steps</skos:altLabel>
        <skos:definition xml:lang="en">The limit on number of internal steps before an output point.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000416 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000416">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000423"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:qualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:qualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000420"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:qualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:qualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000421"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2012-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:comment xml:lang="en">Requested by Kristin Tøndel on Thursday, October 13, 2011 10:46:04 AM.</rdfs:comment>
        <rdfs:label xml:lang="en">partial least squares regression method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/biomodels.kisao/10.1007/BFb0062108</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">PLSR</skos:altLabel>
        <skos:altLabel xml:lang="en">PLSR method</skos:altLabel>
        <skos:definition xml:lang="en">Multivariate regression method based on estimated latent variables. Related to Principal Component Analysis (PCA) and Principal Component Regression (PCR).</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000416"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/biomodels.kisao/10.1007/BFb0062108</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Wold S, Martens H, Wold H (1983) The multivariate calibration method in chemistry solved by the PLS method. In: Lecture notes in Mathematics, Matrix Pencils. Heidelberg: Springer-Verlag. pp. 286-293.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000416"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">PLSR</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000416"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">PLSR method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000417 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000417">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000423"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000322"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000424"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000425"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000416"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:qualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:qualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000428"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2012-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:comment xml:lang="en">Requested by Kristin Tøndel on Thursday, October 13, 2011 11:13:17 AM.</rdfs:comment>
        <rdfs:label xml:lang="en">hierarchical cluster-based partial least squares regression method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1186/1752-0509-5-90</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">HC-PLSR</skos:altLabel>
        <skos:altLabel xml:lang="en">Multivariate regression method based on separating the observations into clusters and generating Partial Least Squares Regression (PLSR) [http://identifiers.org/biomodels.kisao/KISAO_0000416] models within each cluster. This local regression analysis is suitable for very non-linear systems. PLSR is a regression method based on estimated latent variables, related to Principal Component Analysis (PCA) and Principal Component Regression (PCR).
Hierarchical cluster-based partial least squares regression method uses fuzzy C-means clustering, PLSR and Linear Discriminant Analysis (LDA), Quadratic Discriminant Analysis (QDA) or Naive Bayes for classification of new observations to be predicted.</skos:altLabel>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000417"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1186/1752-0509-5-90</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Tøndel K, Indahl UG, Gjuvsland AB, Vik JO, Hunter P, et al. (2011) Hierarchical Cluster-based Partial Least Squares Regression is an efficient tool for metamodelling of nonlinear dynamic models. BMC Systems Biology 5: 90.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000418 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000418">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000423"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:qualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:qualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000422"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2012-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:comment xml:lang="en">Requested by Kristin Tøndel on Thursday, October 13, 2011 11:33:06 AM.</rdfs:comment>
        <rdfs:label xml:lang="en">N-way partial least squares regression method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1002/(SICI)1099-128X(199601)10:1&lt;47::AID-CEM400&gt;3.0.CO;2-C</rdfs:seeAlso>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://www.models.life.ku.dk/nwaytoolbox</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">N-PLS</skos:altLabel>
        <skos:altLabel xml:lang="en">N-way PLSR</skos:altLabel>
        <skos:altLabel xml:lang="en">N-way partial least squares method</skos:altLabel>
        <skos:definition xml:lang="en">Multivariate regression method that can be used on N-way data. Based on Partial Least Squares Regression (PLSR) [http://identifiers.org/biomodels.kisao/KISAO_0000416], which is a regression method based on estimated latent variables. PLSR is related to Principal Component Analysis (PCA) and Principal Component Regression (PCR).</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000418"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1002/(SICI)1099-128X(199601)10:1&lt;47::AID-CEM400&gt;3.0.CO;2-C</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Bro R (1996) Multiway calibration. Multilinear PLS. J. Chemometrics 10: 47-6.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000418"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://www.models.life.ku.dk/nwaytoolbox</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">N-way toolbox website</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000418"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">N-PLS</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000418"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">N-way PLSR</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000418"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">N-way partial least squares method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000419 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000419">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000103"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2012-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">metamodelling method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1186/1752-0509-5-90</rdfs:seeAlso>
        <skos:definition xml:lang="en">Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs) to variation in features of the trajectories of the state variables (outputs) throughout the entire biologically relevant input space.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000419"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1186/1752-0509-5-90</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Tøndel K, Indahl UG, Gjuvsland AB, Vik JO, Hunter P, et al. (2011) Hierarchical Cluster-based Partial Least Squares Regression is an efficient tool for metamodelling of nonlinear dynamic models. BMC Systems Biology 5: 90.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000420 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000420">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000201"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:allValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000423"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#integer"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2012-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">number of partial least squares components</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/biomodels.kisao/10.1007/BFb0062108</rdfs:seeAlso>
        <skos:definition xml:lang="en">Parameter used by &apos;partial least squares regression method&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000416] describing number of PLS components to include in the regression analysis.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000420"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/biomodels.kisao/10.1007/BFb0062108</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Wold S, Martens H, Wold H (1983) The multivariate calibration method in chemistry solved by the PLS method. In: Lecture notes in Mathematics, Matrix Pencils. Heidelberg: Springer-Verlag. pp. 286-293.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000421 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000421">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000201"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:allValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000423"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2012-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">type of validation</rdfs:label>
        <skos:definition xml:lang="en">Parameter of &apos;partial least squares regression method&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000416] describing how validation is performed. Possible values include cross-validation and test set validation.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000422 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000422">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000201"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:allValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000418"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#integer"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2012-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">number of N-way partial least squares regression factors</rdfs:label>
        <skos:altLabel xml:lang="en">number of factors</skos:altLabel>
        <skos:definition xml:lang="en">Parameter of &apos;N-way partial least squares regression method&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000369] describing the number of factors to compute.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000422"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">number of factors</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000423 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000423">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000419"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:qualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:qualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000421"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2012-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">partial least squares regression-like method</rdfs:label>
        <skos:definition xml:lang="en">Method for building regression models between independent and dependent variables.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000424 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000424">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000430"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:allValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000423"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#boolean"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <owl:disjointWith rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000425"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2012-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">mean-centring of variables</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1186/1752-0509-5-90</rdfs:seeAlso>
        <skos:definition xml:lang="en">A boolean parameter of the &apos;hierarchical cluster-based partial least squares regression method&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000417] specifying whether the variables were mean-centred prior to the regression analysis.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000424"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1186/1752-0509-5-90</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Tøndel K, Indahl UG, Gjuvsland AB, Vik JO, Hunter P, et al. (2011) Hierarchical Cluster-based Partial Least Squares Regression is an efficient tool for metamodelling of nonlinear dynamic models. BMC Systems Biology 5: 90.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000425 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000425">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000430"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:allValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000423"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#boolean"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2012-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">standardising of variables</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1186/1752-0509-5-90</rdfs:seeAlso>
        <skos:definition xml:lang="en">A boolean parameter of the &apos;hierarchical cluster-based partial least squares regression method&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000417] specifying whether the variables were standardised (divided by their standard deviations) prior to the regression analysis.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000425"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1186/1752-0509-5-90</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Tøndel K, Indahl UG, Gjuvsland AB, Vik JO, Hunter P, et al. (2011) Hierarchical Cluster-based Partial Least Squares Regression is an efficient tool for metamodelling of nonlinear dynamic models. BMC Systems Biology 5: 90.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000427 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000427">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000429"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#integer"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <owl:disjointWith rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000428"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2012-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">number of clusters</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1186/1752-0509-5-90</rdfs:seeAlso>
        <skos:definition xml:lang="en">Parameter specifying the number of clusters used by C-means algorithm.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000427"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1186/1752-0509-5-90</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Tøndel K, Indahl UG, Gjuvsland AB, Vik JO, Hunter P, et al. (2011) Hierarchical Cluster-based Partial Least Squares Regression is an efficient tool for metamodelling of nonlinear dynamic models. BMC Systems Biology 5: 90.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000428 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000428">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000429"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:allValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000417"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2012-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">matrix for clusterization</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1186/1752-0509-5-90</rdfs:seeAlso>
        <skos:definition xml:lang="en">A matrix to do the clustering in &apos;hierarchical cluster-based partial least squares regression method&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000417].</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000428"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1186/1752-0509-5-90</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Tøndel K, Indahl UG, Gjuvsland AB, Vik JO, Hunter P, et al. (2011) Hierarchical Cluster-based Partial Least Squares Regression is an efficient tool for metamodelling of nonlinear dynamic models. BMC Systems Biology 5: 90.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000429 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000429">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000201"/>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">clusterization parameter</rdfs:label>
        <skos:definition xml:lang="en">Parameter used by algorithms performing clusterization.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000430 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000430">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000201"/>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">variables preprocessing parameter</rdfs:label>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000432 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000432">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000408"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:qualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:qualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000467"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2012-05-24</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">IDA-like method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1145/1089014.1089020</rdfs:seeAlso>
        <skos:definition xml:lang="en">Solves real differential-algebraic systems in N-space, in the general form F(t,y,y&apos;)=0,  y(t0)=y0,  y&apos;(t0)=y&apos;0. At each step, a Newton iteration [http://identifiers.org/biomodels.kisao/KISAO_0000408] leads to linear systems Jx=b, which are solved by one of five methods - two direct (dense or band; serial version only) and three Krylov [http://identifiers.org/biomodels.kisao/KISAO_0000354] (GMRES [http://identifiers.org/biomodels.kisao/KISAO_0000353], BiCGStab [http://identifiers.org/biomodels.kisao/KISAO_0000392], or TFQMR [http://identifiers.org/biomodels.kisao/KISAO_0000396]).</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000432"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1145/1089014.1089020</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Hindmarsh, A. C., et al., SUNDIALS: Suite of Nonlinear and Differential/Algebraic Equation Solvers, ACM Trans. Math. Softw., 31:363-396, 2005.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000433 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000433">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
        <rdfs:subClassOf>
            <owl:Class>
                <owl:unionOf rdf:parseType="Collection">
                    <owl:Restriction>
                        <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                        <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000280"/>
                    </owl:Restriction>
                    <owl:Restriction>
                        <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                        <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000288"/>
                    </owl:Restriction>
                </owl:unionOf>
            </owl:Class>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000374"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:qualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:qualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000467"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:maxQualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:maxQualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000559"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2012-05-24</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">CVODE-like method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1145/1089014.1089020</rdfs:seeAlso>
        <skos:definition xml:lang="en">Solves ODE initial value problems, in real N-space, written as y&apos;=f(t,y),  y(t0)=y0. It is capable for stiff and non-stiff systems and uses two different linear multi-step methods, namely the Adam-Moulton [http://identifiers.org/biomodels.kisao/KISAO_0000280] method and the backward differentiation formula [http://identifiers.org/biomodels.kisao/KISAO_0000288].</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000433"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1145/1089014.1089020</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Hindmarsh, A. C., et al., SUNDIALS: Suite of Nonlinear and Differential/Algebraic Equation Solvers, ACM Trans. Math. Softw., 31:363-396, 2005.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000434 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000434">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000435"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2012-09-25</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">Higham-Hall method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1016/0377-0427(90)90192-3</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">RK5(4)7FEql</skos:altLabel>
        <skos:definition xml:lang="en">The equilibrium theory of Hall and Higham (1988) can be used to determine whether a Runge-Kutta algorithm will perform smoothly when stability restricts the stepsize. Higham-Hall method is a fifth order embedded Runge-Kutta method [http://identifiers.org/biomodels.kisao/KISAO_0000302], which behaves smoothly with respect to the standard type of stepsize controllers.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000434"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1016/0377-0427(90)90192-3</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Higham, D.J. and Hall, G. (1990) Embedded Runge-Kutta formulae with stable equilibrium states. Journal of Computational and Applied Mathematics, 29 (1). pp. 25-33.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000435 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000435">
        <owl:equivalentClass>
            <owl:Class>
                <owl:intersectionOf rdf:parseType="Collection">
                    <rdf:Description rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000302"/>
                    <owl:Restriction>
                        <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                        <owl:someValuesFrom>
                            <owl:Class>
                                <owl:intersectionOf rdf:parseType="Collection">
                                    <rdf:Description rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000064"/>
                                    <owl:Restriction>
                                        <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000275"/>
                                        <owl:hasValue rdf:datatype="http://www.w3.org/2001/XMLSchema#integer">4</owl:hasValue>
                                    </owl:Restriction>
                                </owl:intersectionOf>
                            </owl:Class>
                        </owl:someValuesFrom>
                    </owl:Restriction>
                    <owl:Restriction>
                        <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                        <owl:someValuesFrom>
                            <owl:Class>
                                <owl:intersectionOf rdf:parseType="Collection">
                                    <rdf:Description rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000064"/>
                                    <owl:Restriction>
                                        <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000275"/>
                                        <owl:hasValue rdf:datatype="http://www.w3.org/2001/XMLSchema#integer">5</owl:hasValue>
                                    </owl:Restriction>
                                </owl:intersectionOf>
                            </owl:Class>
                        </owl:someValuesFrom>
                    </owl:Restriction>
                </owl:intersectionOf>
            </owl:Class>
        </owl:equivalentClass>
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000302"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2012-09-26</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">embedded Runge-Kutta 5(4) method</rdfs:label>
        <skos:altLabel xml:lang="en">RK5(4)</skos:altLabel>
        <skos:definition xml:lang="en">An embedded Runge-Kutta integrator of order 5(4).</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000436 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000436">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000302"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom>
                    <owl:Class>
                        <owl:intersectionOf rdf:parseType="Collection">
                            <rdf:Description rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000064"/>
                            <owl:Restriction>
                                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000275"/>
                                <owl:hasValue rdf:datatype="http://www.w3.org/2001/XMLSchema#integer">5</owl:hasValue>
                            </owl:Restriction>
                        </owl:intersectionOf>
                    </owl:Class>
                </owl:someValuesFrom>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom>
                    <owl:Class>
                        <owl:intersectionOf rdf:parseType="Collection">
                            <rdf:Description rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000064"/>
                            <owl:Restriction>
                                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000275"/>
                                <owl:hasValue rdf:datatype="http://www.w3.org/2001/XMLSchema#integer">8</owl:hasValue>
                            </owl:Restriction>
                        </owl:intersectionOf>
                    </owl:Class>
                </owl:someValuesFrom>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:maxQualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:maxQualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000538"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:maxQualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:maxQualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000539"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:maxQualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:maxQualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000540"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:maxQualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:maxQualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000541"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:maxQualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:maxQualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000559"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2012-09-26</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">Dormand-Prince 8(5,3) method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-3-540-56670-0</rdfs:seeAlso>
        <skos:definition xml:lang="en">This method is based on an 8(6) method by Dormand and Prince (i.e. order 8 for the integration and order 6 for error estimation) modified by Hairer and Wanner to use a 5th order error estimator with 3rd order correction.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000436"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/978-3-540-56670-0</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Hairer, Ernst; Nørsett, Syvert Paul; Wanner, Gerhard (1993), Solving ordinary differential equations I: Nonstiff problems (2nd ed.), Berlin: Springer Verlag</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000437 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000437">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000407"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2012-11-29</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:comment xml:lang="en">Requested by Frank T. Bergmann on Thursday, November 29, 2012 9:51:58 AM.</rdfs:comment>
        <rdfs:label xml:lang="en">flux balance analysis</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1038/nbt.1614</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">FBA</skos:altLabel>
        <skos:definition xml:lang="en">Flux balance analysis is a mathematical approach for analyzing the flow of metabolites through a metabolic network.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000437"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1038/nbt.1614</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Jeffrey D Orth, Ines Thiele and Bernhard O Palsson (2010) What is flux balance analysis? Nature Biotechnology 28, 245–248</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000447 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000447">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000352"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000015"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000039"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom>
                    <owl:Class>
                        <owl:intersectionOf rdf:parseType="Collection">
                            <rdf:Description rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
                            <owl:Restriction>
                                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000103"/>
                            </owl:Restriction>
                        </owl:intersectionOf>
                    </owl:Class>
                </owl:someValuesFrom>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:qualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:qualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000211"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2013-01-28</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:comment xml:lang="en">Requested by Mark Moeller on Friday, January 25, 2013 11:11:30 AM.</rdfs:comment>
        <rdfs:label xml:lang="en">COAST</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/17100426</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">controllable approximative stochastic reaction algorithm</skos:altLabel>
        <skos:definition xml:lang="en">An approximative algorithm for stochastic simulations of chemical reaction systems based on three different modeling levels: for small numbers of particles an exact [http://identifiers.org/biomodels.kisao/KISAO_0000236] stochastic [http://identifiers.org/biomodels.kisao/KISAO_0000104] model; for intermediate numbers an approximative [http://identifiers.org/biomodels.kisao/KISAO_0000237], but computationally more efficient stochastic [http://identifiers.org/biomodels.kisao/KISAO_0000104] model based on discrete Gaussian distributions; and for large numbers the deterministic [http://identifiers.org/biomodels.kisao/KISAO_0000103] reaction kinetics. In every simulation time step, the subdivision of the reaction channels into the three different modeling levels is done automatically, where all approximations applied can be controlled by a single error parameter for which an appropriate value can easily be found.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000447"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/17100426</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Holger Wagner, Mark Moeller, and Klaus Prank (2006) COAST: Controllable approximative stochastic reaction algorithm. J. Chem. Phys. 125, 174104</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000448 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000448">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000105"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000107"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:maxQualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:maxQualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000572"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2013-01-28</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">logical model simulation method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://www.identifiers.org/pubmed/22141422</rdfs:seeAlso>
        <skos:definition xml:lang="en">Qualitative (logical) models specify the evolution rules of their components. In each state a number of transitions are enabled. A &apos;logical model simulation method&apos; guides the choice of the transitions processed at each step.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000448"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://www.identifiers.org/pubmed/22141422</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Daniel Machado et al. Modeling formalisms in Systems Biology. AMB Express 2011, 1:45</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000449 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000449">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000448"/>
        <owl:disjointWith rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000450"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2013-01-28</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">synchronous logical model simulation method</rdfs:label>
        <skos:definition xml:lang="en">Qualitative (logical) models specify the evolution rules of their components. In the case of a synchronous updating all enabled transitions are processed simultaneously. </skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000450 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000450">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000448"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000574"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2013-01-28</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">asynchronous logical model simulation method</rdfs:label>
        <skos:definition xml:lang="en">Qualitative (logical) models specify the evolution rules of their components. It the case of an asynchronous updating all enabled transitions are performed independently: a state has as many successors as the number of transitions enabled in this state. An &apos;asynchronous logical model simulation method&apos; specifies a rule to guide the choice of a unique transition at each step (for example random).</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000451 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000451">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000097"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2013-01-28</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">type of updating policy</rdfs:label>
        <skos:definition xml:lang="en">A rule to guide the choice of a unique transition at each step used by an &apos;asynchronous logical model simulation method&apos; [http://identifiers.org/biomodels.kisao/KISAO_0000450].</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000452 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000452">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000451"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000268"/>
                <owl:someValuesFrom>
                    <owl:Class>
                        <owl:intersectionOf rdf:parseType="Collection">
                            <rdf:Description rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000450"/>
                            <owl:Restriction>
                                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000104"/>
                            </owl:Restriction>
                        </owl:intersectionOf>
                    </owl:Class>
                </owl:someValuesFrom>
            </owl:Restriction>
        </rdfs:subClassOf>
        <owl:disjointWith rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000453"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2013-01-28</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">random updating policy</rdfs:label>
        <skos:definition xml:lang="en">An updating policy that chooses a transition randomly.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000453 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000453">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000451"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000268"/>
                <owl:someValuesFrom>
                    <owl:Class>
                        <owl:intersectionOf rdf:parseType="Collection">
                            <rdf:Description rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000450"/>
                            <owl:Restriction>
                                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000103"/>
                            </owl:Restriction>
                        </owl:intersectionOf>
                    </owl:Class>
                </owl:someValuesFrom>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2013-01-28</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">ordered updating policy</rdfs:label>
        <skos:definition xml:lang="en">An updating policy that chooses a transition in a definite way.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000454 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000454">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000453"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2013-01-28</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">constant updating policy</rdfs:label>
        <skos:definition xml:lang="en">An updating policy that chooses a transition in a constant way.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000455 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000455">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000453"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2013-01-28</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">prioritized updating policy</rdfs:label>
        <skos:definition xml:lang="en">An updating policy that chooses a transition in a prioritized way.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000467 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000467">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000242"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#double"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2013-07-05</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:comment xml:lang="en">Requested by Andrew Miller on Tuesday, June 4, 2013 2:33:51 AM.</rdfs:comment>
        <rdfs:label xml:lang="en">maximum step size</rdfs:label>
        <skos:definition xml:lang="en">An upper limit, in the units of the bound variable over which a numerical integration is being performed, that an adaptive step size numerical integration algorithm should take.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000468 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000468">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000352"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000104"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000469"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000027"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000039"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2014-04-25</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:comment xml:lang="en">Requested by Andrzej Kierzek on Thursday, April 24, 2014 12:40:35 PM</rdfs:comment>
        <rdfs:comment xml:lang="en">Used to simulate systems involving reactions with propensities varying by many orders of magnitude.</rdfs:comment>
        <rdfs:label xml:lang="en">maximal timestep method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/14990466</rdfs:seeAlso>
        <skos:definition xml:lang="en">Hybrid simulation algorithm [http://www.biomodels.net/kisao/KISAO#KISAO_0000352] combining Gibson and Bruck algorithm [http://www.biomodels.net/kisao/KISAO#KISAO_0000027] with the Gillespie tau-leap method [http://www.biomodels.net/kisao/KISAO#KISAO_0000039].</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000468"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/14990466</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Puchalka J, Kierzek AM. Bridging the gap between stochastic and deterministic regimes in the kinetic simulations of the biochemical reaction networks. Biophys J. 2004 Mar;86(3):1357-72.
</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000469 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000469">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000243"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2014-04-25</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">maximal timestep</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/14990466</rdfs:seeAlso>
        <skos:definition xml:lang="en">Key parameter of the &apos;maximal timestep method&apos; [http://www.biomodels.net/kisao/KISAO#KISAO_0000468]. If Gillespie [http://www.biomodels.net/kisao/KISAO#KISAO_0000027] waiting time is longer than maximal timestep, slow reaction is not fired and tau-leap [http://www.biomodels.net/kisao/KISAO#KISAO_0000039] step is executed for fast reactions. Otherwise, slow reaction is fired and tau-leap [http://www.biomodels.net/kisao/KISAO#KISAO_0000039] is executed with shorter time step.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000469"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/pubmed/14990466</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Puchalka J, Kierzek AM. Bridging the gap between stochastic and deterministic regimes in the kinetic simulations of the biochemical reaction networks. Biophys J. 2004 Mar;86(3):1357-72.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000470 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000470">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000237"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2015-04-23</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">optimization algorithm</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://en.wikipedia.org/wiki/Mathematical_optimization#Optimization_algorithms</rdfs:seeAlso>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/0691102872</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">optimization method</skos:altLabel>
        <skos:definition xml:lang="en">An optimization algorithm tries to find the minumum or maximum of an arbitrary function. It takes a function of one or several variables and determines the values for the variables so that the function value is optimal.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000470"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/0691102872</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Brinkhuis J, Tikhomirov V. Optimization: Insights and Applications
Princeton Series in Applied Mathematics (illustrated), Princeton University Press, 2005.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000471 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000471">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000470"/>
        <owl:disjointWith rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000472"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2015-04-23</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">local optimization algorithm</rdfs:label>
        <skos:altLabel xml:lang="en">local optimiation method</skos:altLabel>
        <skos:definition xml:lang="en">A local optimization algorithm is an optimisation algorithm [http://www.biomodels.net/kisao/KISAO#KISAO_0000470] that only finds a local optimum of a function. If several optima exist for the function, it usually depends on the starting values for the variables which optimum is found.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000472 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000472">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000470"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000488"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2015-04-23</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">global optimization algorithm</rdfs:label>
        <skos:altLabel xml:lang="en">global optimization method</skos:altLabel>
        <skos:definition xml:lang="en">A global optimization algorithm is an optimization algorithm [http://www.biomodels.net/kisao/KISAO#KISAO_0000470] that tries to find the global optimum of a function. If a function has several minima/maxima with in the allowed range of variable values, the global minimum/maximum is the one with the smallest/largest function value.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000473 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000473">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2015-04-23</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">Bayesian inference algorithm</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://en.wikipedia.org/wiki/Bayesian_inference</rdfs:seeAlso>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/111803144X</rdfs:seeAlso>
        <skos:definition xml:lang="en">A bayesian inference algorithm calculates a posterior probability distribution from a prior probability distribution and some additional evidence in the form of a likelyhood function.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000473"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/111803144X</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">George E. P. Box, George C. Tiao. Bayesian Inference in Statistical Analysis, Volume 40 of Wiley Classics Library. John Wiley &amp; Sons (reprint, revised), 2011.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000475 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000475">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000201"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2015-09-10</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/opencor</isImplementedIn>
        <rdfs:label xml:lang="en">integration method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.3389/fphys.2015.00026</rdfs:seeAlso>
        <skos:definition xml:lang="en">the integration method used by the solver</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000475"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/opencor</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">OpenCOR</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000475"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.3389/fphys.2015.00026</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Garny A and Hunter PJ (2015) OpenCOR: a modular and interoperable approach to computational biology. Front. Physiol. 6:26</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000476 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000476">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000201"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2015-09-10</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/opencor</isImplementedIn>
        <rdfs:comment xml:lang="en">Requested in https://sourceforge.net/p/kisao/feature-requests/12/</rdfs:comment>
        <rdfs:label xml:lang="en">iteration type</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.3389/fphys.2015.00026</rdfs:seeAlso>
        <skos:definition xml:lang="en">the type of iteration used by the solver</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000476"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/opencor</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">OpenCOR</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000476"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.3389/fphys.2015.00026</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Garny A and Hunter PJ (2015) OpenCOR: a modular and interoperable approach to computational biology. Front. Physiol. 6:26</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000477 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000477">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000201"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2015-09-10</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/opencor</isImplementedIn>
        <rdfs:comment xml:lang="en">Requested in https://sourceforge.net/p/kisao/feature-requests/12/</rdfs:comment>
        <rdfs:label xml:lang="en">linear solver</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.3389/fphys.2015.00026</rdfs:seeAlso>
        <skos:definition xml:lang="en">the linear solver used by the solver during a Newton iteration</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000477"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/opencor</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">OpenCOR</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000477"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.3389/fphys.2015.00026</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Garny A and Hunter PJ (2015) OpenCOR: a modular and interoperable approach to computational biology. Front. Physiol. 6:26</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000478 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000478">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000201"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2015-09-10</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/opencor</isImplementedIn>
        <rdfs:comment xml:lang="en">Requested in https://sourceforge.net/p/kisao/feature-requests/12/</rdfs:comment>
        <rdfs:label xml:lang="en">preconditioner</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.3389/fphys.2015.00026</rdfs:seeAlso>
        <skos:definition xml:lang="en">the preconditioner, if any, used by the solver when using a GMRES, BiCGStab or TFQMR linear solver during a Newton iteration.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000478"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/opencor</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">OpenCOR</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000478"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.3389/fphys.2015.00026</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Garny A and Hunter PJ (2015) OpenCOR: a modular and interoperable approach to computational biology. Front. Physiol. 6:26</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000479 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000479">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000482"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#integer"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <owl:disjointWith rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000480"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2015-09-10</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/opencor</isImplementedIn>
        <rdfs:comment xml:lang="en">Requested in https://sourceforge.net/p/kisao/feature-requests/12/</rdfs:comment>
        <rdfs:label xml:lang="en">upper half-bandwidth</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.3389/fphys.2015.00026</rdfs:seeAlso>
        <skos:definition xml:lang="en">the upper half-bandwidth value used by the Banded linear solver or preconditioner (a value between 0 and n-1 with n the number of ODEs/DAEs in the model).</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000479"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.3389/fphys.2015.00026</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Garny A and Hunter PJ (2015) OpenCOR: a modular and interoperable approach to computational biology. Front. Physiol. 6:26</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000479"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/opencor</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">OpenCOR</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000480 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000480">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000482"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#integer"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2015-09-10</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/opencor</isImplementedIn>
        <rdfs:comment xml:lang="en">Requested in https://sourceforge.net/p/kisao/feature-requests/12/</rdfs:comment>
        <rdfs:label xml:lang="en">lower half-bandwidth</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.3389/fphys.2015.00026</rdfs:seeAlso>
        <skos:definition xml:lang="en">the lower half-bandwidth value used by the Banded linear solver or preconditioner (a value between 0 and n-1 with n the number of ODEs/DAEs in the model).</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000480"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/opencor</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">OpenCOR</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000480"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.3389/fphys.2015.00026</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Garny A and Hunter PJ (2015) OpenCOR: a modular and interoperable approach to computational biology. Front. Physiol. 6:26</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000481 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000481">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000201"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#boolean"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2015-09-10</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/opencor</isImplementedIn>
        <rdfs:comment xml:lang="en">Requested in https://sourceforge.net/p/kisao/feature-requests/12/</rdfs:comment>
        <rdfs:label xml:lang="en">interpolate solution</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.3389/fphys.2015.00026</rdfs:seeAlso>
        <skos:definition xml:lang="en">whether the solver returns an interpolated solution.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000481"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/opencor</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">OpenCOR</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000481"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.3389/fphys.2015.00026</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Garny A and Hunter PJ (2015) OpenCOR: a modular and interoperable approach to computational biology. Front. Physiol. 6:26</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000482 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000482">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000201"/>
        <rdfs:label xml:lang="en">half-bandwith parameter</rdfs:label>
        <skos:definition xml:lang="en">the parameter related to the half-bandwidth value used by the Banded linear solver or preconditioner.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000483 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000483">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000242"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2015-09-10</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:comment xml:lang="en">Requested in https://sourceforge.net/p/kisao/feature-requests/13/</rdfs:comment>
        <rdfs:label xml:lang="en">step size</rdfs:label>
        <skos:definition xml:lang="en">the size of every step of the algorithm</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000484 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000484">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000594"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#integer"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn xml:lang="en">Roadrunner</isImplementedIn>
        <rdfs:label xml:lang="en">maximum order</rdfs:label>
        <skos:definition xml:lang="en">Maximum order of method. For example, in Roadrunner it can be used for two parameters that one can set for deterministic runs: &apos;maximum_bdf_order&apos; and &apos;maximum_adams_order&apos;.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000485 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000485">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000242"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#double"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">minimum step size</rdfs:label>
        <skos:definition xml:lang="en">A lower limit, in the units of the bound variable over which a numerical integration is being performed, that a numerical integration algorithm with variable step size should take.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000486 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000486">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000244"/>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">maximum iterations</rdfs:label>
        <skos:altLabel xml:lang="en">iteration limit</skos:altLabel>
        <skos:definition xml:lang="en">For algorithms that iterate to a solution (steady state finders in particular), a limit on the number of iterations that should be performed.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000487 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000487">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000201"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#double"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <isImplementedIn xml:lang="en">Roadrunner</isImplementedIn>
        <rdfs:comment xml:lang="en">The damping factor is a variable for at least some steady state algorithms: roadrunner allows you to set the minimum value for this.</rdfs:comment>
        <rdfs:label xml:lang="en">minimum damping</rdfs:label>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000488 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000488">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000201"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:someValuesFrom>
                    <owl:Class>
                        <owl:intersectionOf rdf:parseType="Collection">
                            <rdf:Description rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
                            <owl:Restriction>
                                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000104"/>
                            </owl:Restriction>
                        </owl:intersectionOf>
                    </owl:Class>
                </owl:someValuesFrom>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">seed</rdfs:label>
        <skos:altLabel xml:lang="en">random seed</skos:altLabel>
        <skos:definition xml:lang="en">Random seed of a stochastic algorithm. Setting it allows one to reproduce their results while running the same algorithm on the same computer.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000491 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000491">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000105"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">discrete event simulation algorithm</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/0387333320</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">DES</skos:altLabel>
        <skos:definition xml:lang="en">Discrete Event Simulation algorithm refers to the simulation of systems whose (countable) discrete states change over time and are event-driven.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000491"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/0387333320</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">C.G. Cassandras &amp; S. Lafortune &quot;Introduction to Discrete Event Systems&quot;, Chapt 1 2nd Ed 2008. Springer</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000492 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000492">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000451"/>
        <owl:disjointWith rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000493"/>
        <rdfs:label xml:lang="en">asynchronous updating policy</rdfs:label>
        <skos:definition xml:lang="en">An updating policy where all enabled transitions (events) occur independently. Thus a state has as many successors as the number of transitions enabled in this state.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000493 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000493">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000451"/>
        <rdfs:label xml:lang="en">synchronous updating policy</rdfs:label>
        <skos:definition xml:lang="en">An updating policy where all enabled transitions occur simultaneously. Thus a state will have at most one successor.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000494 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000494">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000492"/>
        <rdfs:label xml:lang="en">fully asynchronous updating policy</rdfs:label>
        <skos:definition xml:lang="en">An updating policy where all enabled transitions occur either independently or (partially) simultaneously. (i.e. considering all possible combinations of enabled transitions). Thus a state has as many successors as the number of combinations of transitions enabled in this state.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000495 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000495">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000452"/>
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000492"/>
        <rdfs:label xml:lang="en">random asynchronous updating policy</rdfs:label>
        <skos:definition xml:lang="en">An updating policy where a single transition is picked randomly from the set of transitions enabled in this state. Thus a state will have at most one successor.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000496 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000496">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000433"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000359"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000019"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000497"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:maxQualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:maxQualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000543"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:maxQualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:maxQualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000555"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:maxQualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:maxQualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000556"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:maxQualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:maxQualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000557"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:maxQualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:maxQualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000558"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <isImplementedIn xml:lang="en">SUNDIALS</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/amici</isImplementedIn>
        <rdfs:comment xml:lang="en">CVODES is a superset of CVODE [http://identifiers.org/biomodels.kisao/KISAO_0000019] and hence all options available to CVODE (with the exception of the FCVODE interface module) are also available for CVODES. Both integration methods (Adams-Moulton [http://identifiers.org/biomodels.kisao/KISAO_0000280] and BDF [http://identifiers.org/biomodels.kisao/KISAO_0000288]) and the corresponding nonlinear iteration methods, as well as all linear solver and preconditioner modules, are available for the integration of the original ODEs, the sensitivity systems, or the adjoint system.</rdfs:comment>
        <rdfs:label xml:lang="en">CVODES</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://computation.llnl.gov/projects/sundials/cvodes</rdfs:seeAlso>
        <skos:definition xml:lang="en">CVODES is a solver for stiff and nonstiff ODE systems (initial value problem) given in explicit form y’ = f(t,y,p) with sensitivity analysis capabilities (both forward and adjoint modes).</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000496"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/amici</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">AMICI</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000497 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000497">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2017-01-09</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">KLU</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1145/1824801.1824814</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">&quot;Clark Kent&quot; LU factorization algorithm</skos:altLabel>
        <skos:definition xml:lang="en">KLU is a software package and an algorithm for solving sparse unsymmetric linear systems of equations that arise in circuit simulation applications. It relies on a permutation to Block Triangular Form (BTF), several methods for finding a fill-reducing ordering (variants of approximate minimum degree and nested dissection), and Gilbert/Peierls’ sparse left-looking LU factorization algorithm to factorize each block. The package is written in C and includes a MATLAB interface.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000497"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1145/1824801.1824814</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Davis, Timothy A., and Ekanathan Palamadai Natarajan. &quot;Algorithm 907: KLU, a direct sparse solver for circuit simulation problems.&quot; ACM Transactions on Mathematical Software (TOMS) 37.3 (2010): 36.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000498 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000498">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000201"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2017-07-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:comment xml:lang="en">Requested in https://sourceforge.net/p/kisao/feature-requests/31/</rdfs:comment>
        <rdfs:label xml:lang="en">number of runs</rdfs:label>
        <skos:definition xml:lang="en">The number of runs that a simulation should perform. Typically used to specify the number of runs for a stochastic simulation.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000499 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000499">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000000"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2017-09-12</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn xml:lang="en">DFBAlab</isImplementedIn>
        <rdfs:comment xml:lang="en">Ticket 32</rdfs:comment>
        <rdfs:label xml:lang="en">dynamic flux balance analysis</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1186/s12859-014-0409-8</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">DFBA</skos:altLabel>
        <skos:definition xml:lang="en">Dynamic flux balance analysis (DFBA) enables the simulation of dynamic biological systems by assuming organisms reach steady state rapidly in response to changes in the extracellular environment. DFBA couples flux balance analysis (FBA) [http://identifiers.org/biomodels.kisao/KISAO_0000437] model approaches with dynamic model approaches.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000499"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1186/s12859-014-0409-8</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">DFBAlab: a fast and reliable MATLAB code for dynamic flux balance analysis.
Gomez JA, Höffner K, Barton PI. BMC Bioinformatics. 2014 Dec 18;15:409.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000500 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000500">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000499"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000360"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000030"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2017-09-12</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn xml:lang="en">DFBAlab</isImplementedIn>
        <rdfs:comment xml:lang="en">Ticket 32</rdfs:comment>
        <rdfs:label xml:lang="en">SOA-DFBA</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1186/s12859-014-0409-8</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">SOA</skos:altLabel>
        <skos:altLabel xml:lang="en">static optimization approach dynamic flux balance analysis</skos:altLabel>
        <skos:definition xml:lang="en">Dynamic Flux Balance Analysis (DFBA) [http://identifiers.org/biomodels.kisao/KISAO_0000499] couples flux balance analysis (FBA) [http://identifiers.org/biomodels.kisao/KISAO_0000437] model approaches with dynamic model approaches. The static optimization approach (SOA) uses the Euler forward method [http://identifiers.org/biomodels.kisao/KISAO_0000030], solving the embedded LPs at each time step. The FBA fluxes are assumed to be constant during the time step.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000500"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1186/s12859-014-0409-8</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">DFBAlab: a fast and reliable MATLAB code for dynamic flux balance analysis.
Gomez JA, Höffner K, Barton PI. BMC Bioinformatics. 2014 Dec 18;15:409.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000501 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000501">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000499"/>
        <rdfs:subClassOf>
            <owl:Class>
                <owl:complementOf>
                    <owl:Restriction>
                        <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                        <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000376"/>
                    </owl:Restriction>
                </owl:complementOf>
            </owl:Class>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2017-09-12</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn xml:lang="en">DFBAlab</isImplementedIn>
        <rdfs:comment xml:lang="en">Ticket 32</rdfs:comment>
        <rdfs:label xml:lang="en">DOA-DFBA</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1186/s12859-014-0409-8</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">DOA</skos:altLabel>
        <skos:altLabel xml:lang="en">dynamic optimization approach dynamic flux balance analysis</skos:altLabel>
        <skos:definition xml:lang="en">Dynamic Flux Balance Analysis (DFBA) [http://identifiers.org/biomodels.kisao/KISAO_0000499] couples flux balance analysis (FBA) [http://identifiers.org/biomodels.kisao/KISAO_0000437] model approaches with dynamic model approaches. The dynamic optimization approach (DOA) discretizes the time horizon and optimizes simultaneously over the entire time period of interest by solving a nonlinear programming problem (NLP).</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000501"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1186/s12859-014-0409-8</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">DFBAlab: a fast and reliable MATLAB code for dynamic flux balance analysis.
Gomez JA, Höffner K, Barton PI. BMC Bioinformatics. 2014 Dec 18;15:409.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000502 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000502">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000499"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000374"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2017-09-12</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn xml:lang="en">DFBAlab</isImplementedIn>
        <rdfs:comment xml:lang="en">Ticket 32</rdfs:comment>
        <rdfs:label xml:lang="en">DA-DFBA</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1186/s12859-014-0409-8</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">DA</skos:altLabel>
        <skos:altLabel xml:lang="en">direct approach dynamics flux balance analysis</skos:altLabel>
        <skos:definition xml:lang="en">Dynamic Flux Balance Analysis (DFBA) [http://identifiers.org/biomodels.kisao/KISAO_0000499] couples flux balance analysis (FBA) [http://identifiers.org/biomodels.kisao/KISAO_0000437] model approaches with dynamic model approaches. The direct approach (DA) includes the LP solver in the right-hand side evaluator for the ordinary differential equations (ODEs) and takes advantage of reliable implicit ODE integrators with adaptive step size for error control.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000502"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1186/s12859-014-0409-8</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">DFBAlab: a fast and reliable MATLAB code for dynamic flux balance analysis.
Gomez JA, Höffner K, Barton PI. BMC Bioinformatics. 2014 Dec 18;15:409.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000503 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000503">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000472"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000211"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000522"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000523"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2019-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</isImplementedIn>
        <rdfs:label xml:lang="en">simulated annealing</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1126/science.220.4598.671</rdfs:seeAlso>
        <skos:definition xml:lang="en">Simulated annealing is an optimization algorithm first proposed by Kirkpatrick et al. and was inspired by statistical mechanics and the way in which perfect crystals are formed. Perfect crystals are formed by first melting the substance of interest, and then cooling it very slowly. At large temperatures the particles vibrate with wide amplitude and this allows a search for global optimum. As the temperature decreases so do the vibrations until the system settles to the global optimum (the perfect crystal).

The simulated annealing optimization algorithm uses a similar concept: the objective function is considered a measure of the energy of the system and this is maintained constant for a certain number of iterations (a temperature cycle). In each iteration, the parameters are changed to a nearby location in parameter space and the new objective function value calculated; if it decreased, then the new state is accepted, if it increased then the new state is accepted with a probability that follows a Boltzmann distribution (higher temperature means higher probability of accepting the new state). After a fixed number of iterations, the stopping criterion is checked; if it is not time to stop, then the system&apos;s temperature is reduced and the algorithm continues.

Simulated annealing is a stochastic algorithm that is guaranteed to converge if ran for an infinite number of iterations. It is one of the most robust global optimization algorithms, although it is also one of the slowest. (Be warned that simulated annealing can run for hours or even days!).</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000503"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">COPASI</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000503"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1126/science.220.4598.671</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">S. Kirkpatrick, J., C.D. Gelatt, and M. P. Vecchi. Optimization by simulated annealing. Science. 220. 671 - 680. 1983.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000504 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000504">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000472"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000486"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2019-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</isImplementedIn>
        <rdfs:label xml:lang="en">random search</rdfs:label>
        <skos:definition xml:lang="en">Random search is an optimization method that attempts to find the optimum by testing the objective function&apos;s value on a series of combinations of random values of the adjustable parameters. The random values are generated complying with any boundaries selected by the user, furthermore, any combinations of parameter values that do not fulfill constraints on the variables are excluded. This means that the method is capable of handling bounds on the adjustable parameters and fulfilling constraints.

For infinite number of iterations this method is guaranteed to find the global optimum of the objective function. In general one is interested in processing a very large number of iterations.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000504"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">COPASI</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000505 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000505">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000472"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000486"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2019-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</isImplementedIn>
        <rdfs:label xml:lang="en">particle swarm</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1109/ICNN.1995.488968</rdfs:seeAlso>
        <skos:definition xml:lang="en">The particle swarm optimization method suggested by Kennedy and Eberhart is inspired by a flock of birds or a school of fish searching for food. Each particle has a position Xi and a velocity Vi in the parameter space. Additionally, it remembers its best achieved objective value O and position Mi. Dependent on its own information and the position of its best neighbor (a random subset of particles of the swarm) a new velocity is calculated. With this information the position is updated.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000505"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">COPASI</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000505"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1109/ICNN.1995.488968</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">J. Kennedy and R. Eberhart. Particle Swarm Optimization. Proceedings of the Fourth IEEE International Conference on Neural Networks, Perth, Australia. 1942 - 1948. 1995.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000506 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000506">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000520"/>
        <owl:disjointWith rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000508"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2019-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</isImplementedIn>
        <rdfs:label xml:lang="en">genetic algorithm</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/9780750308953</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">GA</skos:altLabel>
        <skos:definition xml:lang="en">The genetic algorithm (GA) is a computational technique that mimics evolution and is based on reproduction and selection. A GA is composed of individuals that reproduce and compete, each one is a potential solution to the (optimization) problem and is represented by a &quot;genome&quot; where each gene corresponds to one adjustable parameter. At each generation of the GA, each individual is paired with one other at random for reproduction. Two offspring are produced by combining their genomes and allowing for &quot;cross-over&quot;, i.e., the two new individuals have genomes that are formed from a combination of the genomes of their parents. Also each new gene might have mutated, i.e. the parameter value might have changed slightly. At the end of the generation, the algorithm has double the number of individuals. Then each of the individuals is confronted with a number of others to count how many does it outperform (the number of wins is the number of these competitors that represent worse solutions than itself). All the individuals are ranked by their number of wins, and the population is again reduced to the original number of individuals by eliminating those which have worse fitness (solutions).</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000506"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">COPASI</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000506"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/9780750308953</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">T. Bäck, D.B. Fogel, and Z. Michalewicz. Handbook of evolutionary computation. Oxford: IOP Publishing/Oxford University Press. 1997.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000507 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000507">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000506"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2019-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</isImplementedIn>
        <rdfs:label xml:lang="en">genetic algorithm SR</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1109/4235.873238</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">genetic algorithm with stochastic ranking</skos:altLabel>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000507"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">COPASI</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000507"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1109/4235.873238</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">T. Runarsson and X. Yao. Stochastic ranking for constrained evolutionary optimization. EEE Transactions on Evolutionary Computation. 4. 284 - 294. 2000.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000508 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000508">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000520"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2019-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</isImplementedIn>
        <rdfs:label xml:lang="en">evolutionary programming</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/9780750308953</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">EP</skos:altLabel>
        <skos:definition xml:lang="en">Evolutionary programming (EP) is a computational technique that mimics evolution and is based on reproduction and selection. An EP algorithm is composed of individuals that reproduce and compete, each one is a potential solution to the (optimization) problem and is represented by a &quot;genome&quot; where each gene corresponds to one adjustable parameter. At each generation of the EP, each individual reproduces asexually, i.e. divides into two individuals. One of these contains exactly the same &quot;genome&quot; as the parent while the other suffers some mutations (the parameter values of each gene change slightly). At the end of the generation, the algorithm has double the number of individuals. Then each of the individuals is confronted with a number of others to count how many does it outperform (the number of wins is the number of these competitors that represent worse solutions than itself). All the individuals are ranked by their number of wins, and the population is again reduced to the original number of individuals by eliminating those which have worse fitness (solutions).</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000508"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">COPASI</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000508"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/9780750308953</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">T. Bäck, D.B. Fogel, and Z. Michalewicz. Handbook of evolutionary computation. Oxford: IOP Publishing/Oxford University Press. 1997.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000509 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000509">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000508"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2019-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</isImplementedIn>
        <rdfs:label xml:lang="en">evolutionary strategy</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1109/4235.873238</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">SRES</skos:altLabel>
        <skos:altLabel xml:lang="en">evolutionary strategies with stochastic ranking</skos:altLabel>
        <skos:definition xml:lang="en">Evolutionary Strategies with Stochastic Ranking (SRES) is similar to Evolutionary Programming. However, a parent has multiple offsprings during each generation. Each offspring will contain a recombination of genes with another parent and additional mutations. The algorithm assures that each parameter value will be within its boundaries. But constraints to the solutions may be violated.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000509"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">COPASI</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000509"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1109/4235.873238</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">T. Runarsson and X. Yao. Stochastic ranking for constrained evolutionary optimization. EEE Transactions on Evolutionary Computation. 4. 284 - 294. 2000.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000510 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000510">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000471"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2019-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</isImplementedIn>
        <rdfs:label xml:lang="en">truncated Newton</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/0122839528</rdfs:seeAlso>
        <skos:definition xml:lang="en">The Truncated Newton method is a sophisticated variant of the Newton optimization method. The Newton optimization method searches for the minimum of a nonlinear function by following descent directions determined from the function&apos;s first and second partial derivatives. The Truncated Newton method does an incomplete (truncated) solution of a system of linear equations to calculate the Newton direction. This means that the actual direction chosen for the descent is between the steepest descent direction and the true Newton direction.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000510"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">COPASI</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000510"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/0122839528</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">P.E. Gill, W. Murray, and M.H. Wright. Practical Optimization. London, Academic Press. 1981.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000511 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000511">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000471"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000209"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000486"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2019-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">steepest descent</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1109/ACSSC.1991.186507</rdfs:seeAlso>
        <skos:definition xml:lang="en">Steepest descent is an optimization method that follows the direction of steepest descent on the hyper-surface of the objective function to find a local minimum. The direction of steepest descent is defined by the negative of the gradient of the objective function.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000511"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1109/ACSSC.1991.186507</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">D.B. Fogel, L.J. Fogel, and J.W. Atmar. Meta-evolutionary programming. 25th Asiloma Conference on Signals, Systems and Computers. IEEE Computer Society, Asilomar . 540 - 545. 1992.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000512 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000512">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000471"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000209"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2019-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</isImplementedIn>
        <rdfs:label xml:lang="en">praxis</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/0486419983</rdfs:seeAlso>
        <skos:definition xml:lang="en">Praxis is a direct search method that searches for the minimum of a nonlinear function without requiring (or attempting to calculate) derivatives of that function. Praxis was developed by Brent after the method proposed by Powell. The inspiration for Praxis was the well-known method of minimising each adjustable parameter (direction) at a time - the principal axes method. In Praxis directions are chosen that do not coincide with the principal axes, in fact if the objective function is quadratic then these will be conjugate directions, assuring a fast convergence rate.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000512"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">COPASI</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000512"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/isbn/0486419983</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">P.R. Brent. A new algorithm for minimizing a function of several variables without calculating derivatives. In Algorithms for minimization without derivatives, (Englewood Cliffs, NJ: Prentice-Hall, Inc.). 117 - 167. 1973.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000513 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000513">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000471"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000486"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2019-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</isImplementedIn>
        <rdfs:label xml:lang="en">NL2SOL</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1145/355958.355966</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">adaptive nonlinear least-squares algorithm</skos:altLabel>
        <skos:definition xml:lang="en">The NL2SOL method is based on an adaptive nonlinear least-squares algorithm, devised by Dennis and colleagues. For problems with large number of residuals, this algorithm is known to be more reliable than Gauss-Newton or Levenberg-Marquardt method and more efficient than the secant or variable metric algorithms that are intended for general function minimization.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000513"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">COPASI</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000513"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1145/355958.355966</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">J. E. Dennis, D. M. Gay, and R. E. Welsch. An adaptive nonlinear least-squares algorithm. ACM Trans. Math. Softw.. 7(3). 348 - 368. 1981.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000514 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000514">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000471"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000211"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000486"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2019-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</isImplementedIn>
        <rdfs:label xml:lang="en">Nelder-Mead</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1093/comjnl/7.4.308</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">simplex method</skos:altLabel>
        <skos:definition xml:lang="en">This method also known as the simplex method is due to Nelder and Mead. A simplex is a polytope of N+1 vertices in N dimensions. The objective function is evaluated at each vertex. Dependent on these calculated values a new simplex is constructed. The simplest step is to replace the worst point with a point reflected through the centroid of the remaining N points. If this point is better than the best current point, then we can try stretching exponentially out along this line. On the other hand, if this new point isn&apos;t much better than the previous value then we are stepping across a valley, so we shrink the simplex towards the best point.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000514"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">COPASI</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000514"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1093/comjnl/7.4.308</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">J. A. Nelder and R. Mead. A simplex method for function minimization. Computer Journal. 7. 308 - 313. 1965.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000515 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000515">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000471"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000322"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000209"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000486"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2019-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</isImplementedIn>
        <rdfs:label xml:lang="en">Levenberg-Marquardt</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1090/qam/10666</rdfs:seeAlso>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1137/0111030</rdfs:seeAlso>
        <skos:definition xml:lang="en">Levenberg-Marquardt is a gradient descent method. It is a hybrid between the steepest descent and the Newton methods.
Levenberg first suggested an improvement to the Newton method in order to make it more robust, i.e. to overcome the problem of non-convergence. His suggestion was to add a factor to the diagonal elements of the Hessian matrix of second derivatives when not close to the minimum (this can be judged by how positive definite the matrix is). The effect when this factor is large compared to the elements of Hessian is that the method then becomes the steepest descent method. Later Marquardt suggested that the factor should be multiplicative rather than additive and also defined a heuristic to make this factor increase or decrease. The method known as Levenberg-Marquardt is thus an adaptive method that effectively changes between the steepest descent to the Newton method.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000515"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">COPASI</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000515"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1090/qam/10666</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">K. Levenberg. A method for the solution of certain nonlinear problems in least squares. Quart. Appl. Math.. 2. 164 - 168. 1944.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000515"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1137/0111030</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">D.W. Marquardt. An algorithm for least squares estimation of nonlinear parameters. SIAM Journal. 11. 431 - 441. 1963.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000516 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000516">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000471"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000209"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000486"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2019-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</isImplementedIn>
        <rdfs:label xml:lang="en">Hooke&amp;Jeeves</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1145/321062.321069</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Hooke and Jeeves method</skos:altLabel>
        <skos:altLabel xml:lang="en">method of Hooke and Jeeves</skos:altLabel>
        <skos:definition xml:lang="en">The method of Hooke and Jeeves is a direct search algorithm that searches for the minimum of a nonlinear function without requiring (or attempting to calculate) derivatives of the function. Instead it is based on a heuristic that suggests a descent direction using the values of the function calculated in a number of previous iterations.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000516"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">COPASI</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000516"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1145/321062.321069</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">R. Hooke and T. A. Jeeves. &quot;Direct search&quot; solution of numerical and statistical problems. Journal of the Association for Computing Machinery. 8. 212 - 229. 1961.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000517 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000517">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000518"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:qualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:qualifiedCardinality>
                <owl:onDataRange rdf:resource="http://www.w3.org/2001/XMLSchema#integer"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <owl:disjointWith rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000519"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2019-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">number of generations</rdfs:label>
        <skos:definition xml:lang="en">The parameter is a positive integer value to determine the number of generations the evolutionary algorithm shall evolve the population.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000518 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000518">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000201"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000520"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2019-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">evolutionary algorithm parameter</rdfs:label>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000519 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000519">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000518"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#integer"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2019-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">population size</rdfs:label>
        <skos:definition xml:lang="en">The parameter is a positive integer value to determine the size of the population, i.e., the number of individuals that survive after each generation.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000520 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000520">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000472"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000517"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000519"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2019-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational xml:lang="en">true</isOrganizational>
        <rdfs:label xml:lang="en">evolutionary algorithm</rdfs:label>
        <skos:definition xml:lang="en">An optimisation algorithm that mimics evolution and is based on reproduction and selection.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000521 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000521">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000201"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000250"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000503"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2019-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
        <rdfs:label xml:lang="en">simulated annealing parameter</rdfs:label>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000522 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000522">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000521"/>
        <owl:disjointWith rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000523"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2019-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">start temperature</rdfs:label>
        <skos:definition xml:lang="en">Initial temperature of the system. The higher the temperature, the larger the probability that a global optimum is found. Note that the temperature should be very high in the beginning of the method (the system should be above the &quot;melting&quot; temperature). This value has the same units as the objective function, so what represents &quot;high&quot; is different from problem to problem.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000523 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000523">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000521"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#double"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2019-01-18</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <rdfs:label xml:lang="en">cooling factor</rdfs:label>
        <skos:definition xml:lang="en">Rate by which the temperature is reduced from one cycle to the next, given by the formula: Tnew=Told*&quot;Cooling Factor&quot;. The simulated annealing algorithm works best if the temperature is reduced at a slow rate, so this value should be close to 1.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000524 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000524">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000039"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000488"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-05-29</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/bionetgen</isImplementedIn>
        <rdfs:label xml:lang="en">partitioned leaping method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.2354085</rdfs:seeAlso>
        <skos:definition xml:lang="en">Multiscale simulation approach for modeling stochasticity in chemical reaction networks. The approach seamlessly integrates exact-stochastic and &quot;leaping&quot; methodologies into a single partitioned leaping algorithmic framework. The technique correctly accounts for stochastic noise at significantly reduced computational cost, requires the definition of only three modelindependent parameters and is particularly well-suited for simulating systems containing widely disparate species populations.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000524"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/bionetgen</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">BioNetGen</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000524"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1063/1.2354085</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Harris LA, Clancy P. A &quot;partitioned leaping&quot; approach for multiscale modeling of chemical reaction dynamics. J Chem Phys. 125 (14), 144107 (2006).</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000525 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000525">
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        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/bionetgen</isImplementedIn>
        <rdfs:label xml:lang="en">stop condition</rdfs:label>
        <skos:definition xml:lang="en">A condition upon which a simulation should terminate.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000525"/>
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        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/bionetgen</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">BioNetGen</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000526 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000526">
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        </rdfs:subClassOf>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
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                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000534"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-08-11</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/cobrapy</isImplementedIn>
        <rdfs:label xml:lang="en">flux variability analysis</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1016/j.ymben.2003.09.002</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">FVA</skos:altLabel>
        <skos:definition xml:lang="en">Method for determining the minimum and maximum flux of each reaction that satisfies the flux constraints of the flux balance analysis (FBA) [http://identifiers.org/biomodels.kisao/KISAO_0000437] model.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000526"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/cobrapy</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">COBRApy</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000526"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1016/j.ymben.2003.09.002</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Mahadevan R, Schilling CH. The effects of alternate optimal solutions in constraint-based genome-scale metabolic models. Metab Eng. 2003;5(4):264-276.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000527 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000527">
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            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-08-11</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/cobrapy</isImplementedIn>
        <rdfs:label xml:lang="en">geometric flux balance analysis</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1016/j.jtbi.2009.01.027</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">gFBA</skos:altLabel>
        <skos:altLabel xml:lang="en">geometric FBA</skos:altLabel>
        <skos:definition xml:lang="en">Method for determining the central flux distribution among all flux distributions that satisfy the constraints of the  flux balance analysis (FBA) [http://identifiers.org/biomodels.kisao/KISAO_0000437] model.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000527"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/cobrapy</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">COBRApy</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000527"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1016/j.jtbi.2009.01.027</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Smallbone K, Simeonidis E. Flux balance analysis: a geometric perspective. J Theor Biol. 2009;258(2):311-315.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000528 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000528">
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            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-08-11</dc:created>
        <dc:creator xml:lang="en">AZ</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/cbmpy</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/cobrapy</isImplementedIn>
        <rdfs:label xml:lang="en">parsimonious enzyme usage flux balance analysis (minimum sum of absolute fluxes)</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1038/msb.2010.47</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">pFBA</skos:altLabel>
        <skos:altLabel xml:lang="en">parsimonious FBA</skos:altLabel>
        <skos:altLabel xml:lang="en">parsimonious flux balance analysis</skos:altLabel>
        <skos:definition xml:lang="en">Method for determining the smallest flux distribution among all flux distributions that satisfy the constraints of the flux balance analysis (FBA) [http://identifiers.org/biomodels.kisao/KISAO_0000437] model.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000528"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/cbmpy</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">CBMPy</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000528"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/cobrapy</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">COBRApy</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000528"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://identifiers.org/doi/10.1038/msb.2010.47</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Lewis NE, Hixson KK, Conrad TM, et al. Omic data from evolved E. coli are consistent with computed optimal growth from genome-scale models. Mol Syst Biol. 2010;6:390.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000529 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000529">
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        </rdfs:subClassOf>
        <rdfs:subClassOf>
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        <rdfs:subClassOf>
            <owl:Restriction>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">parallelism</rdfs:label>
        <skos:definition xml:lang="en">Number of parallel processes to use.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000531 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000531">
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            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">fraction of optimum</rdfs:label>
        <skos:definition xml:lang="en">Fraction of the optimum solution which must be maintained.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000532 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000532">
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            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
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                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#boolean"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">loopless</rdfs:label>
        <skos:definition xml:lang="en">Whether to return only loopless flux solutions.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000533 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000533">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000201"/>
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            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000251"/>
                <owl:someValuesFrom rdf:resource="http://www.w3.org/2001/XMLSchema#float"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">pFBA factor</rdfs:label>
        <skos:definition xml:lang="en">Maximum permissible sum of absolute fluxes.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000534 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000534">
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            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:label xml:lang="en">reactions</rdfs:label>
        <skos:definition xml:lang="en">FVA algorithm [http://www.biomodels.net/kisao/KISAO#KISAO_0000526] parameter: reactions to compute the variablity of.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000535 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000535">
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            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
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                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000019"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn xml:lang="en">Odespy</isImplementedIn>
        <isImplementedIn xml:lang="en">SciPy</isImplementedIn>
        <isImplementedIn xml:lang="en">deSolve</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/gillespy2</isImplementedIn>
        <rdfs:label xml:lang="en">VODE</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1137/0910062</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">DVODE</skos:altLabel>
        <skos:altLabel xml:lang="en">Real-valued Variable-coefficient Ordinary Differential Equation solver, with fixed-leading-coefficient implementation</skos:altLabel>
        <skos:definition xml:lang="en">VODE provides implicit Adams method (for non-stiff problems) and a method based on backward differentiation formulas (BDF) (for stiff problems).</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000535"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/gillespy2</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">GillesPy2</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000535"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1137/0910062</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Peter N. Brown, George D. Byrne &amp; Alan C. Hindmarsh. VODE: A Variable-Coefficient ODE Solver. SIAM J. Sci. and Stat. Comput., 10(5), 1038–1051 (1988).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000535"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">DVODE</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">RELATED</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000535"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Real-valued Variable-coefficient Ordinary Differential Equation solver, with fixed-leading-coefficient implementation</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000536 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000536">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000433"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:maxQualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:maxQualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000542"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000359"/>
                <owl:maxQualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:maxQualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000019"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn xml:lang="en">Odespy</isImplementedIn>
        <isImplementedIn xml:lang="en">SciPy</isImplementedIn>
        <isImplementedIn xml:lang="en">deSolve</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/gillespy2</isImplementedIn>
        <rdfs:label xml:lang="en">ZVODE</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1137/0910062</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Complex-valued Variable-coefficient Ordinary Differential Equation solver, with fixed-leading-coefficient implementation</skos:altLabel>
        <skos:definition xml:lang="en">ZVODE provides implicit Adams method (for non-stiff problems) and a method based on backward differentiation formulas (BDF) (for stiff problems).</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000536"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/gillespy2</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">GillesPy2</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000536"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1137/0910062</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Peter N. Brown, George D. Byrne &amp; Alan C. Hindmarsh. VODE: A Variable-Coefficient ODE Solver. SIAM J. Sci. and Stat. Comput., 10(5), 1038–1051 (1988).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000536"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Complex-valued Variable-coefficient Ordinary Differential Equation solver, with fixed-leading-coefficient implementation</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000537 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000537">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000064"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn xml:lang="en">MATLAB</isImplementedIn>
        <isImplementedIn xml:lang="en">Octave</isImplementedIn>
        <isImplementedIn xml:lang="en">Odespy</isImplementedIn>
        <isImplementedIn xml:lang="en">SciPy</isImplementedIn>
        <isImplementedIn xml:lang="en">deSolve</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/gillespy2</isImplementedIn>
        <rdfs:label xml:lang="en">explicit Runge-Kutta method of order 3(2)</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1016/0893-9659(89)90079-7</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">RK23</skos:altLabel>
        <skos:definition xml:lang="en">RK23 uses the Bogacki-Shampine pair of formulas [1]. The error is controlled assuming accuracy of the second-order method, but steps are taken using the third-order accurate formula (local extrapolation is done). A cubic Hermite polynomial is used for the dense output.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000537"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/gillespy2</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">GillesPy2</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000537"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1016/0893-9659(89)90079-7</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">P. Bogacki &amp; L. F. Shampine. A 3(2) pair of Runge - Kutta formulas. Applied Mathematics Letters 2(4), 321-325 (1989).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000537"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">RK23</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000538 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000538">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000242"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn xml:lang="en">JModelica</isImplementedIn>
        <isImplementedIn xml:lang="en">Odespy</isImplementedIn>
        <isImplementedIn xml:lang="en">SciPy</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/gillespy2</isImplementedIn>
        <rdfs:label xml:lang="en">safety factor on new step selection</rdfs:label>
        <skos:altLabel xml:lang="en">safe</skos:altLabel>
        <skos:altLabel xml:lang="en">safety</skos:altLabel>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000538"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/gillespy2</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">GillesPy2</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000538"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">safe</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000538"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">safety</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000539 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000539">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000242"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn xml:lang="en">JModelica</isImplementedIn>
        <isImplementedIn xml:lang="en">Odespy</isImplementedIn>
        <isImplementedIn xml:lang="en">SciPy</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/gillespy2</isImplementedIn>
        <rdfs:label xml:lang="en">minimum factor to change step size by</rdfs:label>
        <skos:altLabel xml:lang="en">dfactor</skos:altLabel>
        <skos:altLabel xml:lang="en">fac1</skos:altLabel>
        <skos:definition xml:lang="en">Minimum factor to increase/decrease step size by in one step. The new step-size is chosen subject to the restriction fac1 &lt;= current step-size / old step-size &lt;= fac2.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000539"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/gillespy2</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">GillesPy2</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000539"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">dfactor</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000539"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">fac1</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000540 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000540">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000242"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn xml:lang="en">JModelica</isImplementedIn>
        <isImplementedIn xml:lang="en">Odespy</isImplementedIn>
        <isImplementedIn xml:lang="en">SciPy</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/gillespy2</isImplementedIn>
        <rdfs:label xml:lang="en">maximum factor to change step size by</rdfs:label>
        <skos:altLabel xml:lang="en">fac2</skos:altLabel>
        <skos:altLabel xml:lang="en">ifactor</skos:altLabel>
        <skos:definition xml:lang="en">Maximum factor to increase/decrease step size by in one step. The new step-size is chosen subject to the restriction fac1 &lt;= current step-size / old step-size &lt;= fac2.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000540"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/gillespy2</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">GillesPy2</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000540"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">fac2</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000540"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">ifactor</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000541 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000541">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000242"/>
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000243"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn xml:lang="en">JModelica</isImplementedIn>
        <isImplementedIn xml:lang="en">Odespy</isImplementedIn>
        <isImplementedIn xml:lang="en">SciPy</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/gillespy2</isImplementedIn>
        <rdfs:label xml:lang="en">Beta parameter for stabilized step size control</rdfs:label>
        <skos:altLabel xml:lang="en">beta</skos:altLabel>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000541"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/gillespy2</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">GillesPy2</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000541"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">beta</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000542 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000542">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000243"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn xml:lang="en">SciPy</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/gillespy2</isImplementedIn>
        <rdfs:label xml:lang="en">correction step should use internally generated full Jacobian</rdfs:label>
        <skos:altLabel xml:lang="en">MF=22</skos:altLabel>
        <skos:altLabel xml:lang="en">with Jacobian</skos:altLabel>
        <skos:definition xml:lang="en">Specifies whether the iteration method of the ODE solver’s correction step is chord iteration with an internally generated full Jacobian or functional iteration with no Jacobian. Option is only considered when the user has not supplied a Jacobian function and has not indicated (by setting either upper or lower band) that the Jacobian is banded.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000542"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/gillespy2</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">GillesPy2</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000542"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">MF=22</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000542"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">with Jacobian</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000543 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000543">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000242"/>
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000243"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn xml:lang="en">SUNDIALS</isImplementedIn>
        <rdfs:label xml:lang="en">stability limit detection flag</rdfs:label>
        <skos:definition xml:lang="en">Flag to activate stability limit detection.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000544 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000544">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000432"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:maxQualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:maxQualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000545"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn xml:lang="en">SUNDIALS</isImplementedIn>
        <rdfs:label xml:lang="en">IDAS</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1145/1089014.1089020</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">implicit differential-algebraic solver with sensitivity analysis</skos:altLabel>
        <skos:definition xml:lang="en">IDAS solves real differential-algebraic systems in N-space, in the general form F(t,y,y&apos;)=0, y(t0)=y0, y&apos;(t0)=y&apos;0 with sensitivity analysis.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000544"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1145/1089014.1089020</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers. Alan C. Hindmarsh, Peter N. Brown, Keith E. Grant, Steven L. Lee, Radu Serban, Dana E. Shumaker &amp; Carol S. Woodward. ACM Transactions on Mathematical Software 31(3), 363-396 (2005).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000544"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">implicit differential-algebraic solver with sensitivity analysis</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000545 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000545">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000242"/>
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000243"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn xml:lang="en">SUNDIALS</isImplementedIn>
        <rdfs:label xml:lang="en">include sensitivity variables in error control mechanism</rdfs:label>
        <skos:altLabel xml:lang="en">errconS</skos:altLabel>
        <skos:definition xml:lang="en">Specifies whether sensitivity variables are included or not in the error control mechanism.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000545"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">errconS</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000546 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000546">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000472"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <rdfs:label xml:lang="en">convex optimization algorithm</rdfs:label>
        <skos:definition xml:lang="en">Optimization of a convex function over a convex set. Convex optimization is subclass of global optimization because conveness gaurantees that each local optimum is a global optimum.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000547 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000547">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000546"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn xml:lang="en">CPLEX</isImplementedIn>
        <isImplementedIn xml:lang="en">CVXOPT</isImplementedIn>
        <isImplementedIn xml:lang="en">ConvOpt</isImplementedIn>
        <isImplementedIn xml:lang="en">GLPK</isImplementedIn>
        <isImplementedIn xml:lang="en">Gurobi</isImplementedIn>
        <isImplementedIn xml:lang="en">MATLAB</isImplementedIn>
        <isImplementedIn xml:lang="en">Mosek</isImplementedIn>
        <isImplementedIn xml:lang="en">OptLang</isImplementedIn>
        <isImplementedIn xml:lang="en">SciPy</isImplementedIn>
        <isImplementedIn xml:lang="en">SoPlex</isImplementedIn>
        <isImplementedIn xml:lang="en">XPRESS</isImplementedIn>
        <rdfs:label xml:lang="en">linear programming</rdfs:label>
        <skos:altLabel xml:lang="en">LP</skos:altLabel>
        <skos:definition xml:lang="en">Method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000547"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">LP</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000548 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000548">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000549"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn xml:lang="en">CPLEX</isImplementedIn>
        <isImplementedIn xml:lang="en">CVXOPT</isImplementedIn>
        <isImplementedIn xml:lang="en">ConvOpt</isImplementedIn>
        <isImplementedIn xml:lang="en">Gurobi</isImplementedIn>
        <isImplementedIn xml:lang="en">MATLAB</isImplementedIn>
        <isImplementedIn xml:lang="en">Mosek</isImplementedIn>
        <isImplementedIn xml:lang="en">OptLang</isImplementedIn>
        <isImplementedIn xml:lang="en">XPRESS</isImplementedIn>
        <rdfs:label xml:lang="en">quadratic programming</rdfs:label>
        <skos:altLabel xml:lang="en">QP</skos:altLabel>
        <skos:definition xml:lang="en">Process of solving a quadratic optimization problem.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000548"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">QP</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000549 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000549">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000472"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <rdfs:label xml:lang="en">non-linear programming</rdfs:label>
        <skos:definition xml:lang="en">Process of solving an optimization problem where some of the constraints or the objective function are nonlinear.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000550 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000550">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000547"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn xml:lang="en">CPLEX</isImplementedIn>
        <isImplementedIn xml:lang="en">GLPK</isImplementedIn>
        <isImplementedIn xml:lang="en">Gurobi</isImplementedIn>
        <rdfs:label xml:lang="en">simplex method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://projecteuclid.org/euclid.pjm/1103044531</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Dantzig&apos;s simplex algorithm</skos:altLabel>
        <skos:definition xml:lang="en">Approach to solving linear programming models by hand using slack variables, tableaus, and pivot variables as a means to finding the optimal solution of an optimization problem.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000550"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Dantzig&apos;s simplex algorithm</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000551 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000551">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000547"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn xml:lang="en">CPLEX</isImplementedIn>
        <isImplementedIn xml:lang="en">GLPK</isImplementedIn>
        <isImplementedIn xml:lang="en">Gurobi</isImplementedIn>
        <rdfs:label xml:lang="en">primal-dual interior point method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1137/0802028</rdfs:seeAlso>
        <skos:definition xml:lang="en">The Interior Point method approximates the constraints of a linear programming model as a set of boundaries surrounding a region.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000551"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1137/0802028</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Sanjay Mehrotra. On the Implementation of a Primal-Dual Interior Point Method. SIAM Journal on Optimization, 2(4), 575–601(1991).</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000552 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000552">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000243"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn xml:lang="en">CPLEX</isImplementedIn>
        <isImplementedIn xml:lang="en">GLPK</isImplementedIn>
        <isImplementedIn xml:lang="en">Gurobi</isImplementedIn>
        <rdfs:label xml:lang="en">optimization method</rdfs:label>
        <skos:definition xml:lang="en">Optimization method such as the revised simplex method [http://identifiers.org/biomodels.kisao/KISAO_0000550] or primal-dual interior point method [http://identifiers.org/biomodels.kisao/KISAO_0000551].</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000553 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000553">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000243"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn xml:lang="en">ConvOpt</isImplementedIn>
        <isImplementedIn xml:lang="en">OptLang</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/cbmpy</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/cobrapy</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/raven</isImplementedIn>
        <rdfs:label xml:lang="en">optimization solver</rdfs:label>
        <skos:definition xml:lang="en">Optimization solver such as CPLEX, GLPK, or Gurobi.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000553"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/cbmpy</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">CBMPy</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000553"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/cobrapy</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">COBRApy</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000553"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/raven</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">RAVEN</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000554 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000554">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000437"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/cbmpy</isImplementedIn>
        <rdfs:label xml:lang="en">parsimonius flux balance analysis (minimum number of active fluxes)</rdfs:label>
        <skos:altLabel xml:lang="en">pFBA</skos:altLabel>
        <skos:altLabel xml:lang="en">parsimonious FBA</skos:altLabel>
        <skos:altLabel xml:lang="en">parsimonious flux balance analysis</skos:altLabel>
        <skos:definition xml:lang="en">A technique for selecting a parsimonious flux distribution which has a minimal number of active fluxes.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000554"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/cbmpy</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">CBMPy</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000555 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000555">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000211"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn xml:lang="en">SUNDIALS</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/amici</isImplementedIn>
        <rdfs:label xml:lang="en">absolute quadrature tolerance</rdfs:label>
        <skos:definition xml:lang="en">Absolute error tolerance of the adjoint solution.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000555"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/amici</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">AMICI</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000556 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000556">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000209"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn xml:lang="en">SUNDIALS</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/amici</isImplementedIn>
        <rdfs:label xml:lang="en">relative quadrature tolerance</rdfs:label>
        <skos:definition xml:lang="en">Relative error tolerance of the adjoint solution.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000556"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/amici</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">AMICI</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000557 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000557">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000211"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn xml:lang="en">SUNDIALS</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/amici</isImplementedIn>
        <rdfs:label xml:lang="en">absolute steady-state tolerance</rdfs:label>
        <skos:definition xml:lang="en">Absolute error tolerance of the steady-state.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000557"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/amici</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">AMICI</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000558 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000558">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000209"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn xml:lang="en">SUNDIALS</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/amici</isImplementedIn>
        <rdfs:label xml:lang="en">relative steady-state tolerance</rdfs:label>
        <skos:definition xml:lang="en">Relative error tolerance of the steady-state.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000558"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/amici</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">AMICI</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000559 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000559">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000242"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn xml:lang="en">SUNDIALS</isImplementedIn>
        <isImplementedIn xml:lang="en">SciPy</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/gillespy2</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/tellurium</isImplementedIn>
        <isImplementedIn xml:lang="en">libRoadRunner</isImplementedIn>
        <rdfs:label xml:lang="en">initial step size</rdfs:label>
        <skos:definition xml:lang="en">Initial time step size.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000559"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">COPASI</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000559"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/gillespy2</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">GillesPy2</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000559"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/tellurium</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">tellurium</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000560 -->

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        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000245"/>
                <owl:maxQualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:maxQualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000371"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <rdfs:label xml:lang="en">stochastic Runge-Kutta method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_method_(SDE)</rdfs:seeAlso>
        <skos:definition xml:lang="en">Technique for the approximate numerical solution of a systems of stochastic differential equations (SDEs). The method is a generalisation of the Runge-Kutta method for ordinary differential equations to stochastic differential equations.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000565 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000565">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000211"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</isImplementedIn>
        <rdfs:label xml:lang="en">absolute tolerance for root finding</rdfs:label>
        <skos:definition xml:lang="en">Absolute error tolerance for root finding.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000565"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">COPASI</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000566 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000566">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000564"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:maxQualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:maxQualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000565"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:maxQualifiedCardinality rdf:datatype="http://www.w3.org/2001/XMLSchema#nonNegativeInteger">1</owl:maxQualifiedCardinality>
                <owl:onClass rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000567"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</isImplementedIn>
        <rdfs:label xml:lang="en">stochastic second order Runge-Kutta method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1137/060673308</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">RI5</skos:altLabel>
        <skos:definition xml:lang="en">Technique for the second order approximate numerical solution of a systems of stochastic differential equations (SDEs). The method is a generalisation of the Runge-Kutta method for ordinary differential equations to stochastic differential equations.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000566"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">COPASI</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000566"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1137/060673308</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Andreas Rößler. Second order Runge-Kutta methods for Itô stochastic differential equations. SIAM Journal Numerical Analysis 47 (3), 1713–1738 (2009).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000566"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">RI5</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000567 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000567">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000243"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</isImplementedIn>
        <rdfs:label xml:lang="en">force physical correctness</rdfs:label>
        <skos:definition xml:lang="en">Indicates whether to force physical correctness.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000567"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/copasi</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">COPASI</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000568 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000568">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000408"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/tellurium</isImplementedIn>
        <rdfs:label xml:lang="en">NLEQ1</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.43.3751</rdfs:seeAlso>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1007/978-3-642-23899-4</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Newton-type method for solveing non-linear (NL) equations (EQ)</skos:altLabel>
        <skos:altLabel xml:lang="en">Numerical solution of nonlinear (NL) equations (EQ) especially designed for numerically sensitive problems</skos:altLabel>
        <skos:definition xml:lang="en">Damped Newton-algorithm with rank strategy for systems of highly nonlinear equations.

Global Newton method with error oriented convergence criterion; arbitrary selection of direct linear equation solver.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000568"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/tellurium</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">tellurium</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000568"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.43.3751</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Ulrich Nowak &amp; Lutz Weimann. A family of Newton codes for systems of highly nonlinear equations - algorithm, implementation, application. Konrad-Zuse-Zentrum für Informationstechnik Berlin 91-10 (1991).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000568"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1007/978-3-642-23899-4</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Peter Deuflhard. Newton methods for nonlinear problems. Affine Invariance and Adaptive Algorithms (2004).</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000569 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000569">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000408"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/tellurium</isImplementedIn>
        <rdfs:label xml:lang="en">NLEQ2</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.43.3751</rdfs:seeAlso>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1007/978-3-642-23899-4</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Newton-type method for solveing non-linear (NL) equations (EQ)</skos:altLabel>
        <skos:altLabel xml:lang="en">Numerical solution of nonlinear (NL) equations (EQ) especially designed for numerically sensitive problems</skos:altLabel>
        <skos:definition xml:lang="en">Damped Newton-algorithm with rank strategy for systems of highly nonlinear equations.

Global Newton method with error oriented convergence criterion; QR-decomposition with subcondition number estimate.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000569"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/tellurium</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">tellurium</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000569"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.43.3751</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Ulrich Nowak &amp; Lutz Weimann. A family of Newton codes for systems of highly nonlinear equations - algorithm, implementation, application. Konrad-Zuse-Zentrum für Informationstechnik Berlin 91-10 (1991).</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000569"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1007/978-3-642-23899-4</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Peter Deuflhard. Newton methods for nonlinear problems. Affine Invariance and Adaptive Algorithms (2004).</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000570 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000570">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000242"/>
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000243"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/pysces</isImplementedIn>
        <rdfs:label xml:lang="en">auto reduce tolerances</rdfs:label>
        <skos:definition xml:lang="en">Whether to automatically reduce tolerances.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000570"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/pysces</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">PySCeS</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000571 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000571">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000597"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/pysces</isImplementedIn>
        <rdfs:label xml:lang="en">absolute tolerance adjustment factor</rdfs:label>
        <skos:definition xml:lang="en">How much to adjust the absolute tolerance.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000571"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/pysces</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">PySCeS</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000572 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000572">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000201"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/boolnet</isImplementedIn>
        <rdfs:label xml:lang="en">level of superimposed noise</rdfs:label>
        <skos:altLabel xml:lang="en">noise level</skos:altLabel>
        <skos:definition xml:lang="en">Standard deviation of the Gaussian noise which is added to each prediction.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000572"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/boolnet</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">BoolNet</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000572"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">noise level</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000573 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000573">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000448"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/boolnet</isImplementedIn>
        <rdfs:label xml:lang="en">probabilistic logical model simulation method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1093/bioinformatics/btq124</rdfs:seeAlso>
        <skos:definition xml:lang="en">Qualitative (logical) models specify the evolution rules of their components. Probabilistic networks allow for specifying more than one transition function per variable/gene. Each of these functions has a probability to be chosen, where the probabilities of all functions for one variable sum up to 1. Transitions are performed synchronously by choosing one transition function for each gene according to their probabilities and applying them to the current state.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000573"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/boolnet</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">BoolNet</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000574 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000574">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000201"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/boolnet</isImplementedIn>
        <rdfs:label xml:lang="en">species transition probabilities</rdfs:label>
        <skos:definition xml:lang="en">Probability of each species to be chosen for the next state transition.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000574"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/boolnet</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">BoolNet</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000575 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000575">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000039"/>
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000352"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000246"/>
                <owl:someValuesFrom>
                    <owl:Class>
                        <owl:intersectionOf rdf:parseType="Collection">
                            <rdf:Description rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000039"/>
                            <owl:Class>
                                <owl:unionOf rdf:parseType="Collection">
                                    <rdf:Description rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000064"/>
                                    <rdf:Description rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000088"/>
                                    <rdf:Description rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000281"/>
                                </owl:unionOf>
                            </owl:Class>
                        </owl:intersectionOf>
                    </owl:Class>
                </owl:someValuesFrom>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-11-06</dc:created>
        <dc:creator xml:lang="en">BD</dc:creator>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/gillespy2</isImplementedIn>
        <rdfs:label xml:lang="en">Hybrid tau-leaping method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://github.com/StochSS/GillesPy2</rdfs:seeAlso>
        <skos:definition xml:lang="en">A continuously coupled hybrid deterministic/stochastic simulation algorithm for biochemical networks. Biochemical species are classified as continuous, discrete, or switch. Tau-leaping is used to simulate stochastic species, and LSODA or another ODE integration method is used to simulate continuous species. Switch species are dynamically classified as either continuous or discrete at each timestep depending on a user defined error tolerance.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000575"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/gillespy2</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">GillesPy2</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000575"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://github.com/StochSS/GillesPy2</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Drawert B et al. GillesPy2</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000576 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000576">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000593"/>
        <rdfs:subClassOf>
            <owl:Restriction>
                <owl:onProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000259"/>
                <owl:someValuesFrom rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000577"/>
            </owl:Restriction>
        </rdfs:subClassOf>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/cobratoolbox</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/optflux</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/raven</isImplementedIn>
        <rdfs:label xml:lang="en">Quadratic MOMA</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1073/pnas.232349399</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">MOMA</skos:altLabel>
        <skos:altLabel xml:lang="en">Minimization of Metabolic Adjustment</skos:altLabel>
        <skos:altLabel xml:lang="en">Quadratic Minimization of Metabolic Adjustment</skos:altLabel>
        <skos:definition xml:lang="en">Minimization Of Metabolic Adjustment (MOMA) is an extension of FBA for the prediction of flux distributions in gene knockouts. MOMA employs quadratic programming to identify the closest point (in terms of its Euclidean distance) in the permissible flux space of the knockout to the wild-type flux vector by solving the optimization problem

Min sum((fluxAi - fluxBi)^2) + sum(fluxAi)^(fluxMinimizationWeight) + sum(fluxBi)^(fluxMinimizationWeight)</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000576"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/cobratoolbox</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">COBRA Toolbox</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000576"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/optflux</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">Optflux</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000576"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/raven</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">RAVEN</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000576"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1073/pnas.232349399</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Segre, D., Vitkup, D., &amp; Church, G. M. (2002). Analysis of optimality in natural and perturbed metabolic networks. Proceedings of the National Academy of Sciences, 99(23), 15112-15117.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000576"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Quadratic Minimization of Metabolic Adjustment</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000577 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000577">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000201"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <rdfs:label xml:lang="en">flux minimization weight</rdfs:label>
        <skos:definition xml:lang="en">The degree to which minimization of the sum of fluxes should be taken into account in Minimization of Metabolic Adjustment (MOMA) which solvers the optimization problem
 
Min sum((fluxAi - fluxBi)^2) + sum(fluxAi)^(fluxMinimizationWeight) + sum(fluxBi)^(fluxMinimizationWeight)</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000578 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000578">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000243"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <rdfs:label xml:lang="en">nested algorithm</rdfs:label>
        <skos:altLabel xml:lang="en">nested method</skos:altLabel>
        <skos:altLabel xml:lang="en">subalgorithm</skos:altLabel>
        <skos:definition xml:lang="en">A nested algorithm of an algorithm</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000578"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">nested method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000578"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">subalgorithm</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000579 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000579">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000593"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/cobratoolbox</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/optflux</isImplementedIn>
        <rdfs:label xml:lang="en">Linear MOMA</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1038/ng.846</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Linear Minimization of Metabolic Adjustment</skos:altLabel>
        <skos:definition xml:lang="en">Linear Minimization Of Metabolic Adjustment (MOMA) is an extension of FBA for the prediction of flux distributions in gene knockouts. Linear MOMA employs linear programming to identify the closest point (in terms of its L1 norm) in the permissible flux space of the knockout to the wild-type flux vector by solving the optimization problem

Min sum(|fluxAi - fluxBi|)</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000579"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/cobratoolbox</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">COBRA Toolbox</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000579"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/optflux</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">Optflux</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000579"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1038/ng.846</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Szappanos, B., Kovács, K., Szamecz, B., Honti, F., Costanzo, M., Baryshnikova, A., ... &amp; Andrews, B. J. (2011). An integrated approach to characterize genetic interaction networks in yeast metabolism. Nature genetics, 43(7), 656-662.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000579"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Linear Minimization of Metabolic Adjustment</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000580 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000580">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000407"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/cobratoolbox</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/optflux</isImplementedIn>
        <rdfs:label xml:lang="en">ROOM</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1073/pnas.0406346102</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Regulatory on/off minimization of metabolic flux changes</skos:altLabel>
        <skos:definition xml:lang="en">Constraint-based algorithm for predicting the metabolic steady state after gene knockouts which aims to minimize the number of significant flux changes (hence on/off) with respect to the wild type.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000580"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/cobratoolbox</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">COBRA Toolbox</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000580"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/optflux</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">Optflux</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000580"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1073/pnas.0406346102</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Shlomi, T., Berkman, O., &amp; Ruppin, E. (2005). Regulatory on/off minimization of metabolic flux changes after genetic perturbations. Proceedings of the national academy of sciences, 102(21), 7695-7700.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000580"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Regulatory on/off minimization of metabolic flux changes</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000581 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000581">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000029"/>
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000450"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/maboss</isImplementedIn>
        <rdfs:label xml:lang="en">BKMC</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1186/1752-0509-6-116</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Boolean Kinetic Monte-Carlo</skos:altLabel>
        <skos:definition xml:lang="en">The Boolean Kinetic Monte Carlo method (BKMC) is a natural generalization of the asynchronous Boolean simulation method, with a direct probabilistic interpretation. In the BKMC framework, the dynamics is parameterized by a biological time and the order of update is noisy, which is less strict than priority classes introduced in GINsin. A BKMC model is specified by logical rules as in regular Boolean models but with a more precise information: a numerical rate is added for each transition of each node.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000581"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/maboss</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">MaBoSS</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000581"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1186/1752-0509-6-116</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Stoll, G., Viara, E., Barillot, E., &amp; Calzone, L. (2012). Continuous time Boolean modeling for biological signaling: application of Gillespie algorithm. BMC systems biology, 6(1), 1-18.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000581"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Boolean Kinetic Monte-Carlo</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000582 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000582">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000056"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/ecell4</isImplementedIn>
        <rdfs:label xml:lang="en">Spatiocyte method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1038/npre.2009.3845.1</rdfs:seeAlso>
        <skos:definition xml:lang="en">Lattice-based stochastic particle simulation method for biochemical reaction and diffusion processes.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000582"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/ecell4</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">E-Cell 4</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000582"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1038/npre.2009.3845.1</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Arjunan, S., &amp; Tomita, M. (2009). A new multicompartmental reaction-diffusion modeling method links transient membrane attachment of E. coli MinE to E-ring formation. Nature Precedings, 1-1.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000583 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000583">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000594"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/jsim</isImplementedIn>
        <rdfs:label xml:lang="en">minimum order</rdfs:label>
        <skos:definition xml:lang="en">Minimum order of method.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000583"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/jsim</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">JSim</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000584 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000584">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000594"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/jsim</isImplementedIn>
        <rdfs:label xml:lang="en">initial order</rdfs:label>
        <skos:definition xml:lang="en">Initial order of method.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000584"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/jsim</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">JSim</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000585 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000585">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000369"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/jsim</isImplementedIn>
        <rdfs:label xml:lang="en">TOMS731</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1145/178365.178391</rdfs:seeAlso>
        <skos:definition xml:lang="en">Moving-grid interface for systems of one-dimensional time-dependent partial differential equations.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000585"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/jsim</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">JSim</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000585"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1145/178365.178391</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Blom, J. G., &amp; Zegeling, P. A. (1994). Algorithm 731: a moving-grid interface for systems of one-dimensional time-dependent partial differential equations. ACM Transactions on Mathematical Software (TOMS), 20(2), 194-214.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000586 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000586">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000027"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/sbscl</isImplementedIn>
        <rdfs:label xml:lang="en">Gibson-Bruck next reaction algorithm with indexed priority queue</rdfs:label>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000586"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/sbscl</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">SBSCL</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000587 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000587">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000064"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/biouml</isImplementedIn>
        <rdfs:label xml:lang="en">IMEX</rdfs:label>
        <skos:altLabel xml:lang="en">Implicit-Explicit Runge-Kutta method</skos:altLabel>
        <skos:definition xml:lang="en">Method for solving stiff and imaginary ODE problems</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000587"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/biouml</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">BioUML</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000587"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Implicit-Explicit Runge-Kutta method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000588 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000588">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000407"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <rdfs:label xml:lang="en">flux sampling</rdfs:label>
        <skos:definition xml:lang="en">Method for sampling fluxes from the null space of a flux balance analysis model</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000589 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000589">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000588"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/cobratoolbox</isImplementedIn>
        <rdfs:label xml:lang="en">ACB flux sampling method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1038/s41596-018-0098-2</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Artificial centering boundary flux sampling method</skos:altLabel>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000589"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/cobratoolbox</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">COBRA Toolbox</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000589"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1038/s41596-018-0098-2</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Heirendt, L., Arreckx, S., Pfau, T., Mendoza, S. N., Richelle, A., Heinken, A., ... &amp; Magnusdóttir, S. (2019). Creation and analysis of biochemical constraint-based models using the COBRA Toolbox v. 3.0. Nature protocols, 14(3), 639-702.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000589"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Artificial centering boundary flux sampling method</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000590 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000590">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000588"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/cobrapy</isImplementedIn>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/cobratoolbox</isImplementedIn>
        <rdfs:label xml:lang="en">ACHR flux sampling method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1287/opre.46.1.84</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Artificial Centering Hit-and-Run flux sampling method</skos:altLabel>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000590"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/cobrapy</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">COBRApy</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000590"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/cobratoolbox</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">COBRA Toolbox</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000590"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1287/opre.46.1.84</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Kaufman, D. E., &amp; Smith, R. L. (1998). Direction choice for accelerated convergence in hit-and-run sampling. Operations Research, 46(1), 84-95.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000591 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000591">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000437"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/cobratoolbox</isImplementedIn>
        <rdfs:label xml:lang="en">mdFBA</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1186/gb-2010-11-4-r43</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">metabolic dilution flux balance analysis</skos:altLabel>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000591"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/cobratoolbox</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">COBRA Toolbox</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000591"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1186/gb-2010-11-4-r43</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Benyamini, T., Folger, O., Ruppin, E., &amp; Shlomi, T. (2010). Flux balance analysis accounting for metabolite dilution. Genome biology, 11(4), R43.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000592 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000592">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000595"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/cobratoolbox</isImplementedIn>
        <rdfs:label xml:lang="en">dynamic rFBA</rdfs:label>
        <rdfs:seeAlso xml:lang="en">https://identifiers.org/doi/10.1006/jtbi.2001.2405</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">dynamic regulatory flux balance analysis</skos:altLabel>
        <skos:altLabel xml:lang="en">rFBA</skos:altLabel>
        <skos:altLabel xml:lang="en">regulatory flux balance analysis</skos:altLabel>
        <skos:definition xml:lang="en">Method for predicting the dynamics of metabolic fluxes under patterns of the regulation of gene expression</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000592"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/cobratoolbox</owl:annotatedTarget>
        <rdfs:comment xml:lang="end">COBRA Toolbox</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000592"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget xml:lang="en">https://identifiers.org/doi/10.1006/jtbi.2001.2405</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Covert, M. W., Schilling, C. H., &amp; Palsson, B. (2001). Regulation of gene expression in flux balance models of metabolism. Journal of theoretical biology, 213(1), 73-88.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000592"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">dynamic regulatory flux balance analysis</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000593 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000593">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000407"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <rdfs:label xml:lang="en">MOMA</rdfs:label>
        <skos:altLabel xml:lang="en">Minimization of Metabolic Adjustment</skos:altLabel>
        <skos:definition xml:lang="en">Minimization Of Metabolic Adjustment (MOMA) is an extension of FBA for the prediction of flux distributions in gene knockouts. MOMA identifies the closest point in the permissible flux space of the knockout to the wild-type flux vector by solving an optimization problem.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000593"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Minimization of Metabolic Adjustment</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000594 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000594">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000243"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <rdfs:label xml:lang="en">order</rdfs:label>
        <skos:definition xml:lang="en">Order of method</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000595 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000595">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000437"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <rdfs:label xml:lang="en">rFBA</rdfs:label>
        <skos:altLabel xml:lang="en">regulatory flux balance analysis</skos:altLabel>
        <skos:definition xml:lang="en">Method for predicting metabolic fluxes under patterns of the regulation of gene expression</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000595"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">regulatory flux balance analysis</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000596 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000596">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000595"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <rdfs:label xml:lang="en">srFBA</rdfs:label>
        <rdfs:seeAlso xml:lang="en">https://identifiers.org/doi/10.1038/msb4100141</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">SR-FBA</skos:altLabel>
        <skos:altLabel xml:lang="en">steady-state regulatory flux balance analysis</skos:altLabel>
        <skos:definition xml:lang="en">Method for predicting steady-state metabolic fluxes under patterns of the regulation of gene expression</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000596"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget xml:lang="en">https://identifiers.org/doi/10.1038/msb4100141</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Shlomi, T., Eisenberg, Y., Sharan, R., &amp; Ruppin, E. (2007). A genome‐scale computational study of the interplay between transcriptional regulation and metabolism. Molecular systems biology, 3(1), 101.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000596"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">SR-FBA</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000597 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000597">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000242"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2020-10-29</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <rdfs:label xml:lang="en">tolerance</rdfs:label>
        <skos:definition xml:lang="en">Numeric value specifying the desired tolerance the user wants to achieve. A smaller value means that the prediction is calculated more accurately.</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000598 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000598">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000352"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2021-01-13</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <dc:creator xml:lang="en">MLB</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/vcell</isImplementedIn>
        <rdfs:label xml:lang="en">Hybrid Gibson - Milstein Method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1186/1471-2105-7-93</rdfs:seeAlso>
        <skos:definition xml:lang="en">A hybrid stochastic method partitions the system into subsets of fast and slow reactions and approximates the fast reactions as a continuous Markov process, using a chemical Langevin equation, and accurately describes the slow dynamics using the Gibson algorithm. Fixed time step Milstein is used for approximate numerical solution of CLE.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000598"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/vcell</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">VCell</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000598"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1186/1471-2105-7-93</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">H.Salis, V. Sotiropoulos and Y. Kaznessis,&apos;Multiscale Hy3S: Hybrid stochastic simulation for supercomputers&apos;, BMC Bioinformatics 7:93 (2006).</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000599 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000599">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000352"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2021-01-13</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <dc:creator xml:lang="en">MLB</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/vcell</isImplementedIn>
        <rdfs:label xml:lang="en">Hybrid Gibson - Euler-Maruyama Method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1186/1471-2105-7-93</rdfs:seeAlso>
        <skos:definition xml:lang="en">A hybrid stochastic method partitions the system into subsets of fast and slow reactions and approximates the fast reactions as a continuous Markov process, using a chemical Langevin equation, and accurately describes the slow dynamics using the Gibson algorithm. Fixed time step Milstein is used for approximate numerical solution of CLE.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000599"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/vcell</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">VCell</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000599"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1186/1471-2105-7-93</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">H.Salis, V. Sotiropoulos and Y. Kaznessis,&apos;Multiscale Hy3S: Hybrid stochastic simulation for supercomputers&apos;, BMC Bioinformatics 7:93 (2006).</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000600 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000600">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000352"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2021-01-13</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <dc:creator xml:lang="en">MLB</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/vcell</isImplementedIn>
        <rdfs:label xml:lang="en">Hybrid Adaptive Gibson - Milstein Method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1186/1471-2105-7-93</rdfs:seeAlso>
        <skos:definition xml:lang="en">A hybrid stochastic method partitions the system into subsets of fast and slow reactions and approximates the fast reactions as a continuous Markov process, using a chemical Langevin equation, and accurately describes the slow dynamics using the Gibson algorithm. Fixed time step Milstein is used for approximate numerical solution of CLE.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000600"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/vcell</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">VCell</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000600"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1186/1471-2105-7-93</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">H.Salis, V. Sotiropoulos and Y. Kaznessis,&apos;Multiscale Hy3S: Hybrid stochastic simulation for supercomputers&apos;, BMC Bioinformatics 7:93 (2006).</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000601 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000601">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000244"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2021-01-13</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <dc:creator xml:lang="en">MLB</dc:creator>
        <rdfs:label xml:lang="en">Number of trials</rdfs:label>
        <skos:altLabel xml:lang="en">trials</skos:altLabel>
        <skos:definition xml:lang="en">Number of multiple trials (e.g., of a scatter search method).</skos:definition>
    </owl:Class>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000602 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000602">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000244"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2021-01-13</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <dc:creator xml:lang="en">MLB</dc:creator>
        <rdfs:label xml:lang="en">Minimum species threshold for continuous approximation</rdfs:label>
        <skos:altLabel xml:lang="en">Epsilon</skos:altLabel>
        <skos:definition xml:lang="en">Minimum number of molecules of both reactant and product species required for approximation as a continuous Markov process.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000602"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Epsilon</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000603 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000603">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000244"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2021-01-13</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <dc:creator xml:lang="en">MLB</dc:creator>
        <rdfs:label xml:lang="en">Minimum reaction rate for continuous approximation</rdfs:label>
        <skos:altLabel xml:lang="en">Lambda</skos:altLabel>
        <skos:definition xml:lang="en">Minimum reaction rate required for approximation as a continuous Markov process.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000603"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Lambda</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000604 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000604">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000209"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2021-01-13</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <dc:creator xml:lang="en">MLB</dc:creator>
        <rdfs:label xml:lang="en">MSR Tolerance</rdfs:label>
        <skos:altLabel xml:lang="en">Multiple slow reactions tolerance</skos:altLabel>
        <skos:definition xml:lang="en">Maximum allowed effect of executing multiple slow reactions per numerical integration of the SDEs.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000604"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Multiple slow reactions tolerance</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000605 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000605">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000209"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2021-01-13</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <dc:creator xml:lang="en">MLB</dc:creator>
        <rdfs:label xml:lang="en">SDE Tolerance</rdfs:label>
        <skos:altLabel xml:lang="en">Maximum allowed value of the drift and diffusion errors.</skos:altLabel>
        <skos:definition xml:lang="en">Stochastic differential equation tolerance</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000605"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Maximum allowed value of the drift and diffusion errors.</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000606 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000606">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000241"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2021-01-25</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/ibiosim</isImplementedIn>
        <rdfs:label xml:lang="en">Hierarchical Stochastic Simulation Algorithm</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.3389/fbioe.2014.00055</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">hSSA</skos:altLabel>
        <skos:definition xml:lang="en">Fast, memory-efficient method for stochastic simulation of hierarchically organized models, such as a model of a cellular population where each cell in the population is represented by the same species and reactions.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000606"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/ibiosim</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">iBioSim</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000606"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.3389/fbioe.2014.00055</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Watanabe, L. H., &amp; Myers, C. J. (2014). Hierarchical stochastic simulation algorithm for SBML models of genetic circuits. Frontiers in bioengineering and biotechnology, 2, 55.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000606"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">hSSA</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000607 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000607">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000086"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2021-01-25</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/ibiosim</isImplementedIn>
        <rdfs:label xml:lang="en">Hierarchical Fehlberg method</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.3389/fbioe.2014.00055</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Hierarchical ODE integration method</skos:altLabel>
        <skos:altLabel xml:lang="en">Hierarchical ordinary differential equation integration method</skos:altLabel>
        <skos:altLabel xml:lang="en">hODE</skos:altLabel>
        <skos:definition xml:lang="en">Method for continuous simulation of hierarchically organized models, such as a model of a cellular population where each cell in the population is represented by the same species and reactions.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000607"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/ibiosim</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">iBioSim</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000607"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.3389/fbioe.2014.00055</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Watanabe, L. H., &amp; Myers, C. J. (2014). Hierarchical stochastic simulation algorithm for SBML models of genetic circuits. Frontiers in bioengineering and biotechnology, 2, 55.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000607"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">hODE</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000608 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000608">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000437"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2021-01-25</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/ibiosim</isImplementedIn>
        <rdfs:label xml:lang="en">Hierarchical flux balance analysis</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.3389/fbioe.2014.00055</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">Hierarchical FBA</skos:altLabel>
        <skos:altLabel xml:lang="en">hFBA</skos:altLabel>
        <skos:definition xml:lang="en">Method for constraint-based simulation of hierarchically organized models, such as a model of a cellular population where each cell in the population is represented by the same species and reactions.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000608"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/ibiosim</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">iBioSim</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000608"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.3389/fbioe.2014.00055</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Watanabe, L. H., &amp; Myers, C. J. (2014). Hierarchical stochastic simulation algorithm for SBML models of genetic circuits. Frontiers in bioengineering and biotechnology, 2, 55.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000608"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">Hierarchical FBA</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000608"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">hFBA</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000609 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000609">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000302"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2021-01-25</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/ibiosim</isImplementedIn>
        <rdfs:label xml:lang="en">Embedded Runge-Kutta Prince-Dormand (8,9) method</rdfs:label>
        <skos:altLabel xml:lang="en">RK8PD</skos:altLabel>
        <skos:definition xml:lang="en">An embedded Runge-Kutta integrator of order 8(9).</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000609"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/ibiosim</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">iBioSim</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000609"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2004/02/skos/core#altLabel"/>
        <owl:annotatedTarget xml:lang="en">RK8PD</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000610 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000610">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000241"/>
        <dc:created rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2021-01-25</dc:created>
        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/ibiosim</isImplementedIn>
        <rdfs:label xml:lang="en">Composite-rejection stochastic simulation algorithm</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1063/1.2919546</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">SSA-CR</skos:altLabel>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000610"/>
        <owl:annotatedProperty rdf:resource="http://www.biomodels.net/kisao/KISAO#isImplementedIn"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/biosimulators/ibiosim</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">iBioSim</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000610"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1063/1.2919546</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Slepoy, A., Thompson, A. P., &amp; Plimpton, S. J. (2008). A constant-time kinetic Monte Carlo algorithm for simulation of large biochemical reaction networks. The journal of chemical physics, 128(20), 05B618.</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000611 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000611">
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        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifers.org/biosimulators/ibiosim</isImplementedIn>
        <rdfs:label xml:lang="en">Incremental stochastic simulation algorithm</rdfs:label>
        <rdfs:seeAlso rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1109/ISCAS.2010.5537539</rdfs:seeAlso>
        <skos:altLabel xml:lang="en">iSSA</skos:altLabel>
        <skos:definition xml:lang="en">Performs local averaging over small time-intervals to compute statistics on typical behavior.</skos:definition>
    </owl:Class>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000611"/>
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        <rdfs:comment xml:lang="en">iBioSim</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000611"/>
        <owl:annotatedProperty rdf:resource="http://www.w3.org/2000/01/rdf-schema#seeAlso"/>
        <owl:annotatedTarget rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">https://identifiers.org/doi/10.1109/ISCAS.2010.5537539</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">Winstead, C., Madsen, C., &amp; Myers, C. (2010, May). iSSA: An incremental stochastic simulation algorithm for genetic circuits. In Proceedings of 2010 IEEE International Symposium on Circuits and Systems (pp. 553-556). IEEE.</rdfs:comment>
    </owl:Axiom>
    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000611"/>
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        <owl:annotatedTarget xml:lang="en">iSSA</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </owl:Axiom>
    


    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000612 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000612">
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        <dc:creator xml:lang="en">JRK</dc:creator>
        <isImplementedIn xml:lang="en">https://identifiers.org/biosimulators/ibiosim</isImplementedIn>
        <rdfs:label xml:lang="en">implicit 4th order Runge-Kutta method at Gaussian points</rdfs:label>
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    <owl:Axiom>
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    <owl:Axiom>
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        <owl:annotatedTarget xml:lang="en">RK4IMP</owl:annotatedTarget>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
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    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000613 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000613">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000241"/>
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    <owl:Axiom>
        <owl:annotatedSource rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000613"/>
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        <rdfs:comment xml:lang="en">iBioSim</rdfs:comment>
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    <!-- http://www.biomodels.net/kisao/KISAO#KISAO_0000614 -->

    <owl:Class rdf:about="http://www.biomodels.net/kisao/KISAO#KISAO_0000614">
        <rdfs:subClassOf rdf:resource="http://www.biomodels.net/kisao/KISAO#KISAO_0000243"/>
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        <rdfs:label xml:lang="en">Implementation</rdfs:label>
        <skos:definition xml:lang="en">An implementation of an algorithm. For example, simulation tools can this parameter to differentiate among C, Python, and Java implementations of the same algorithms and allow investigators to select one of these specific implementations through SED-ML.</skos:definition>
    </owl:Class>
    <rdf:Description>
        <rdfs:comment xml:lang="en">EXACT</rdfs:comment>
    </rdf:Description>
    


    <!-- 
    ///////////////////////////////////////////////////////////////////////////////////////
    //
    // Annotations
    //
    ///////////////////////////////////////////////////////////////////////////////////////
     -->

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        <isOrganizational rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean">true</isOrganizational>
    </rdf:Description>
    


    <!-- 
    ///////////////////////////////////////////////////////////////////////////////////////
    //
    // General axioms
    //
    ///////////////////////////////////////////////////////////////////////////////////////
     -->

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