This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian) (format=pdflatex 2012.5.14)  18 DEC 2012 13:21
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**\nonstopmode \input{"/home/bartek/work/code/bnfinder/doc/methods.tex"}
(/home/bartek/work/code/bnfinder/doc/methods.tex

! LaTeX Error: Missing \begin{document}.

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l.1  I
      n the present section we give a brief exposition of the algorithm impl...

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If that doesn't work, type  X <return>  to quit.

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\citation{dojer06}
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\citation{dojer10}
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! Undefined control sequence.
l.6 \subsection
               {Polynomial-time exact algorithm}
The control sequence at the end of the top line
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! LaTeX Error: Missing \begin{document}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.6 \subsection{P
                 olynomial-time exact algorithm}
You're in trouble here.  Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.

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! LaTeX Error: Missing \begin{document}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.8  A
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You're in trouble here.  Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.

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l.11   \item a directed acyclic graph $\G
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spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.11   \item a directed acyclic graph $\G=(\X
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The control sequence at the end of the top line
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misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.11   \item a directed acyclic graph $\G=(\X,\E
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spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

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Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no - in font nullfont!
Missing character: There is no ) in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!

Overfull \hbox (7.7778pt too wide) in paragraph at lines 11--12
\OT1/cmr/m/n/10 =
 []


Overfull \hbox (12.22221pt too wide) in paragraph at lines 11--12
\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 )$
 []

Missing character: There is no a in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
! Undefined control sequence.
l.12 ...a$ of conditional distributions $P(X_i|\Pa
                                                  _i)$, where
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no , in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!

Overfull \hbox (4.97223pt too wide) in paragraph at lines 12--13
\OML/cmm/m/it/10 ^^R$
 []


Overfull \hbox (33.30792pt too wide) in paragraph at lines 12--13
\OML/cmm/m/it/10 P\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 X[]\OMS/cmsy/m/n/10 j[]\OT1
/cmr/m/n/10 )$
 []

! Undefined control sequence.
l.13    $$\Pa
             _i=\{Y\in\X|(Y,X_i)\in\E\}$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.13    $$\Pa_i=\{Y\in\X
                        |(Y,X_i)\in\E\}$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.13    $$\Pa_i=\{Y\in\X|(Y,X_i)\in\E
                                     \}$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


Overfull \hbox (89.33195pt too wide) detected at line 13
[] \OT1/cmr/m/n/10 = \OMS/cmsy/m/n/10 f\OML/cmm/m/it/10 Y \OMS/cmsy/m/n/10 2 j\
OT1/cmr/m/n/10 (\OML/cmm/m/it/10 Y; X[]\OT1/cmr/m/n/10 ) \OMS/cmsy/m/n/10 2g
 []

Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no j in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
! Undefined control sequence.
<recently read> \X 
                   
l.15  The joint distribution of $\X
                                   $ is given by
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no y in font nullfont!
! Undefined control sequence.
l.17  P(\X
          )=\prod_{i=1}^n P(X_i|\Pa_i)
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.17  P(\X)=\prod_{i=1}^n P(X_i|\Pa
                                   _i)
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


Overfull \hbox (76.84894pt too wide) detected at line 18
[]\OML/cmm/m/it/10 P\OT1/cmr/m/n/10 () = [] \OML/cmm/m/it/10 P\OT1/cmr/m/n/10 (
\OML/cmm/m/it/10 X[]\OMS/cmsy/m/n/10 j[]\OT1/cmr/m/n/10 )
 []

Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no B in font nullfont!
Missing character: There is no N in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no : in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
! Undefined control sequence.
<recently read> \X 
                   
l.21  given a multiset of $\X
                             $-instances $\D=\{\x_1,\ldots,\x_N\}$ find a ne...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no - in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
! Undefined control sequence.
<recently read> \D 
                   
l.21  given a multiset of $\X$-instances $\D
                                            =\{\x_1,\ldots,\x_N\}$ find a ne...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.21  given a multiset of $\X$-instances $\D=\{\x
                                                 _1,\ldots,\x_N\}$ find a ne...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.21 ...set of $\X$-instances $\D=\{\x_1,\ldots,\x
                                                  _N\}$ find a network graph...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no h in font nullfont!
! Undefined control sequence.
<recently read> \G 
                   
l.21 ..._1,\ldots,\x_N\}$ find a network graph $\G
                                                  $ that best matches $\D$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
! Undefined control sequence.
<recently read> \D 
                   
l.21 ...a network graph $\G$ that best matches $\D
                                                  $.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no . in font nullfont!
Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no z in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no a in font nullfont!
! Undefined control sequence.
l.22 ...y means of a \emph{scoring function} $S(\G
                                                  :\D)$ having positive valu...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.22 ...eans of a \emph{scoring function} $S(\G:\D
                                                  )$ having positive values ...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no h in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no z in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no h in font nullfont!
! Undefined control sequence.
<recently read> \G 
                   
l.23 ...nt is to find a directed acyclic graph $\G
                                                  $ with the set of vertices...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no w in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
! Undefined control sequence.
<recently read> \X 
                   
l.23 ...ic graph $\G$ with the set of vertices $\X
                                                  $ minimizing $S(\G:\D)$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no m in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no z in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
! Undefined control sequence.
l.23 ... the set of vertices $\X$ minimizing $S(\G
                                                  :\D)$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.23 ...e set of vertices $\X$ minimizing $S(\G:\D
                                                  )$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no . in font nullfont!

Overfull \hbox (20.0pt too wide) in paragraph at lines 20--24
[]
 []


Overfull \hbox (7.7778pt too wide) in paragraph at lines 20--24
\OT1/cmr/m/n/10 =
 []


Overfull \hbox (44.29295pt too wide) in paragraph at lines 20--24
\OMS/cmsy/m/n/10 f[]\OML/cmm/m/it/10 ; [] ;[] \OMS/cmsy/m/n/10 g$
 []


Overfull \hbox (21.08316pt too wide) in paragraph at lines 20--24
\OT1/cmr/m/it/10 scor-
 []


Overfull \hbox (13.2888pt too wide) in paragraph at lines 20--24
\OT1/cmr/m/it/10 ing
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Overfull \hbox (22.23318pt too wide) in paragraph at lines 20--24
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\citation{friedman98}
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LaTeX Warning: Citation `friedman98' on page  undefined on input line 27.

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Missing character: There is no h in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no B in font nullfont!
Missing character: There is no N in font nullfont!
Missing character: There is no F in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no j in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no x in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no I in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no B in font nullfont!
Missing character: There is no N in font nullfont!
Missing character: There is no F in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no I in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no q in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
! Undefined control sequence.
l.41  The first one states that $S(\G
                                     :\D)$ decomposes into a sum over the se...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.41  The first one states that $S(\G:\D
                                        )$ decomposes into a sum over the se...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no . in font nullfont!

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! LaTeX Error: Environment ass undefined.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.43 \begin{ass}
                [additivity]\label{as1}
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

Missing character: There is no [ in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no ] in font nullfont!
! Undefined control sequence.
l.44  $S(\G
           :\D) = \sum_{i=1}^n s(X_i,\Pa_i:\D|_{\{X_i\}\cup\Pa_i})$, where $...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.44  $S(\G:\D
              ) = \sum_{i=1}^n s(X_i,\Pa_i:\D|_{\{X_i\}\cup\Pa_i})$, where $...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.44  $S(\G:\D) = \sum_{i=1}^n s(X_i,\Pa
                                        _i:\D|_{\{X_i\}\cup\Pa_i})$, where $...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.44  $S(\G:\D) = \sum_{i=1}^n s(X_i,\Pa_i:\D
                                             |_{\{X_i\}\cup\Pa_i})$, where $...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.44 ...um_{i=1}^n s(X_i,\Pa_i:\D|_{\{X_i\}\cup\Pa
                                                  _i})$, where $\D|_{\Y}$ de...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no , in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
! Undefined control sequence.
<recently read> \D 
                   
l.44 ...,\Pa_i:\D|_{\{X_i\}\cup\Pa_i})$, where $\D
                                                  |_{\Y}$ denotes the restri...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.44 ...i:\D|_{\{X_i\}\cup\Pa_i})$, where $\D|_{\Y
                                                  }$ denotes the restriction...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
! Undefined control sequence.
<recently read> \D 
                   
l.44 ... $\D|_{\Y}$ denotes the restriction of $\D
                                                  $ to the values of the mem...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
! Undefined control sequence.
<recently read> \Y 
                   
l.44 ...f $\D$ to the values of the members of $\Y
                                                  \subseteq\X$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.44 ...he values of the members of $\Y\subseteq\X
                                                  $.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no . in font nullfont!

! LaTeX Error: \begin{document} ended by \end{ass}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.45 \end{ass}
              
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.


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[][]
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\OML/cmm/m/it/10 S\OT1/cmr/m/n/10 (:
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\OT1/cmr/m/n/10 ) =
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 :
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\OMS/cmsy/m/n/10 j[]\OT1/cmr/m/n/10 )$
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\OMS/cmsy/m/n/10 j[]$
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\OMS/cmsy/m/n/10 ^^R$
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Missing character: There is no W in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no x in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
! Undefined control sequence.
<recently read> \Pa 
                    
l.48  Thus the point is to find $\Pa
                                    _i$ minimizing $s(X_i,\Pa_i:\D|_{\{X_i\}...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no m in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no z in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
! Undefined control sequence.
l.48 ...t is to find $\Pa_i$ minimizing $s(X_i,\Pa
                                                  _i:\D|_{\{X_i\}\cup\Pa_i})...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.48 ...to find $\Pa_i$ minimizing $s(X_i,\Pa_i:\D
                                                  |_{\{X_i\}\cup\Pa_i})$ for...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.48 ...inimizing $s(X_i,\Pa_i:\D|_{\{X_i\}\cup\Pa
                                                  _i})$ for each $i$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no . in font nullfont!

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[]
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Overfull \hbox (3.32928pt too wide) in paragraph at lines 47--49
[]$
 []


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\OML/cmm/m/it/10 s\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 X[];[] \OT1/cmr/m/n/10 :
 []


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\OMS/cmsy/m/n/10 j[]\OT1/cmr/m/n/10 )$
 []


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\OML/cmm/m/it/10 i$ 
 []

Missing character: There is no L in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no x in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
! Undefined control sequence.
<recently read> \D 
                   
l.50  Let us fix a dataset $\D
                              $ and a random variable $X$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no W in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no y in font nullfont!
! Undefined control sequence.
<recently read> \X 
                   
l.51  We denote by $\X
                      '$ the set of potential parents of $X$ (possibly small...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no ( in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
! Undefined control sequence.
<recently read> \X 
                   
l.51 ... parents of $X$ (possibly smaller than $\X
                                                  $ due to given constraints...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no d in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no ) in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no T in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
! Undefined control sequence.
l.52 ...y the notation we continue to write $s(\Pa
                                                  )$ for $s(X,\Pa:\D|_{\{X\}...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
! Undefined control sequence.
l.52 ...we continue to write $s(\Pa)$ for $s(X,\Pa
                                                  :\D|_{\{X\}\cup\Pa})$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.52 ...continue to write $s(\Pa)$ for $s(X,\Pa:\D
                                                  |_{\{X\}\cup\Pa})$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.52 ...te $s(\Pa)$ for $s(X,\Pa:\D|_{\{X\}\cup\Pa
                                                  })$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no . in font nullfont!

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[]
 []


Overfull \hbox (9.06943pt too wide) in paragraph at lines 50--53
\OML/cmm/m/it/10 X$
 []


Overfull \hbox (2.80556pt too wide) in paragraph at lines 50--53
[]$
 []


Overfull \hbox (9.06943pt too wide) in paragraph at lines 50--53
\OML/cmm/m/it/10 X$
 []


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\OML/cmm/m/it/10 s\OT1/cmr/m/n/10 ()$
 []


Overfull \hbox (24.31247pt too wide) in paragraph at lines 50--53
\OML/cmm/m/it/10 s\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 X; \OT1/cmr/m/n/10 :
 []


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\OMS/cmsy/m/n/10 j[]\OT1/cmr/m/n/10 )$ 
 []

Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no x in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no 2 in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no : in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no z in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no x in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no x in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no . in font nullfont!

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[]
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Overfull \hbox (5.12846pt too wide) in paragraph at lines 54--55
\OML/cmm/m/it/10 g$
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Overfull \hbox (5.20486pt too wide) in paragraph at lines 54--55
\OML/cmm/m/it/10 d$
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! LaTeX Error: Environment ass undefined.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.56 \begin{ass}
                [splitting]\label{as2}
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

Missing character: There is no [ in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no ] in font nullfont!
! Undefined control sequence.
l.57  $s(\Pa
            )=g(\Pa)+d(\Pa)$ for some functions $g,d:\mathcal{P}(\X)\to\math...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.57  $s(\Pa)=g(\Pa
                   )+d(\Pa)$ for some functions $g,d:\mathcal{P}(\X)\to\math...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.57  $s(\Pa)=g(\Pa)+d(\Pa
                          )$ for some functions $g,d:\mathcal{P}(\X)\to\math...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
! Undefined control sequence.
l.57 ...a)$ for some functions $g,d:\mathcal{P}(\X
                                                  )\to\mathbb{R}^+$ satisfyi...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.57 ...e functions $g,d:\mathcal{P}(\X)\to\mathbb
                                                  {R}^+$ satisfying $\Pa\sub...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
! Undefined control sequence.
<recently read> \Pa 
                    
l.57 ...cal{P}(\X)\to\mathbb{R}^+$ satisfying $\Pa
                                                  \subseteq\Pa'\Longrightarr...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.57 ...o\mathbb{R}^+$ satisfying $\Pa\subseteq\Pa
                                                  '\Longrightarrow g(\Pa)\le...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.57 ...ing $\Pa\subseteq\Pa'\Longrightarrow g(\Pa
                                                  )\le g(\Pa')$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.57 ...ubseteq\Pa'\Longrightarrow g(\Pa)\le g(\Pa
                                                  ')$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no . in font nullfont!

! LaTeX Error: \begin{document} ended by \end{ass}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.58 \end{ass}
              
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.


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[][]
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\OML/cmm/m/it/10 s\OT1/cmr/m/n/10 () =
 []


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\OML/cmm/m/it/10 g\OT1/cmr/m/n/10 () +
 []


Overfull \hbox (12.98267pt too wide) in paragraph at lines 56--59
\OML/cmm/m/it/10 d\OT1/cmr/m/n/10 ()$
 []


Overfull \hbox (20.33324pt too wide) in paragraph at lines 56--59
\OML/cmm/m/it/10 g; d \OT1/cmr/m/n/10 :
 []


Overfull \hbox (28.33333pt too wide) in paragraph at lines 56--59
\OMS/cmsy/m/n/10 P\OT1/cmr/m/n/10 () \OMS/cmsy/m/n/10 !
 []


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\OML/cmm/m/it/10 R[]$
 []


Overfull \hbox (26.69455pt too wide) in paragraph at lines 56--59
\OMS/cmsy/m/n/10 ^^R[][][])
 []


Overfull \hbox (23.46178pt too wide) in paragraph at lines 56--59
\OML/cmm/m/it/10 g\OT1/cmr/m/n/10 () \OMS/cmsy/m/n/10 ^^T
 []


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\OML/cmm/m/it/10 g\OT1/cmr/m/n/10 ([])$
 []

Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no q in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no . in font nullfont!

Overfull \hbox (20.0pt too wide) in paragraph at lines 60--61
[]
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Overfull \hbox (5.12846pt too wide) in paragraph at lines 60--61
\OML/cmm/m/it/10 g$ 
 []


! LaTeX Error: Environment alg undefined.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.62 \begin{alg}
                \label{a1}~
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.


Overfull \hbox (20.0pt too wide) in paragraph at lines 62--63
[] 
 []

! Undefined control sequence.
<recently read> \Pa 
                    
l.66 \item $\Pa
               :=\emptyset$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no h in font nullfont!
! Undefined control sequence.
<recently read> \PP 
                    
l.67 \item for each $\PP
                        \subseteq\X'$ chosen according to $g(\PP)$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.67 \item for each $\PP\subseteq\X
                                   '$ chosen according to $g(\PP)$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no c in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
! Undefined control sequence.
l.67 ...PP\subseteq\X'$ chosen according to $g(\PP
                                                  )$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no i in font nullfont!
Missing character: There is no f in font nullfont!
! Undefined control sequence.
l.69 \item if $s(\PP
                    )<s(\Pa)$ then $\Pa:=\PP$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.69 \item if $s(\PP)<s(\Pa
                           )$ then $\Pa:=\PP$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
! Undefined control sequence.
<recently read> \Pa 
                    
l.69 \item if $s(\PP)<s(\Pa)$ then $\Pa
                                       :=\PP$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.69 \item if $s(\PP)<s(\Pa)$ then $\Pa:=\PP
                                            $
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no i in font nullfont!
Missing character: There is no f in font nullfont!
! Undefined control sequence.
l.70 \item if $g(\PP
                    )\ge s(\Pa)$ then return $\Pa$; stop
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.70 \item if $g(\PP)\ge s(\Pa
                              )$ then return $\Pa$; stop
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no n in font nullfont!
! Undefined control sequence.
<recently read> \Pa 
                    
l.70 \item if $g(\PP)\ge s(\Pa)$ then return $\Pa
                                                 $; stop
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no ; in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no p in font nullfont!

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! LaTeX Error: \begin{document} ended by \end{alg}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.76 \end{alg}
              
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

Missing character: There is no I in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no m in font nullfont!
! Undefined control sequence.
<argument> choosing according to $g(\PP 
                                        )$
l.78 ...ithm \emph{choosing according to $g(\PP)$}
                                                   means choosing increasing...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no . in font nullfont!

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Overfull \hbox (27.0887pt too wide) in paragraph at lines 78--79
\OT1/cmr/m/it/10 choos-
 []


Overfull \hbox (13.2888pt too wide) in paragraph at lines 78--79
\OT1/cmr/m/it/10 ing
 []


Overfull \hbox (13.28879pt too wide) in paragraph at lines 78--79
\OT1/cmr/m/it/10 ac-
 []


Overfull \hbox (21.59425pt too wide) in paragraph at lines 78--79
\OT1/cmr/m/it/10 cord-
 []


Overfull \hbox (13.2888pt too wide) in paragraph at lines 78--79
\OT1/cmr/m/it/10 ing
 []


Overfull \hbox (8.43327pt too wide) in paragraph at lines 78--79
\OT1/cmr/m/it/10 to
 []


Overfull \hbox (12.90627pt too wide) in paragraph at lines 78--79
\OML/cmm/m/it/10 g\OT1/cmr/m/n/10 ()$
 []


Overfull \hbox (5.12846pt too wide) in paragraph at lines 78--79
\OML/cmm/m/it/10 g$
 []


! LaTeX Error: Environment theorem undefined.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.80  \begin{theorem}
                     
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

Missing character: There is no S in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no A in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
! Undefined control sequence.
<write> ...ning: Reference `as1' on page \thepage 
                                                  \space undefined\on@line .
l.81 ...g function satisfies Assumptions \ref{as1}
                                                  -\ref{as2}. Then Algorithm...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


LaTeX Warning: Reference `as1' on page  undefined on input line 81.

Missing character: There is no - in font nullfont!
! Undefined control sequence.
<write> ...ning: Reference `as2' on page \thepage 
                                                  \space undefined\on@line .
l.81 ... satisfies Assumptions \ref{as1}-\ref{as2}
                                                  . Then Algorithm \ref{a1} ...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


LaTeX Warning: Reference `as2' on page  undefined on input line 81.

Missing character: There is no . in font nullfont!
Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no A in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no m in font nullfont!
! Undefined control sequence.
<write> ...rning: Reference `a1' on page \thepage 
                                                  \space undefined\on@line .
l.81 ...ef{as1}-\ref{as2}. Then Algorithm \ref{a1}
                                                   applied to each random va...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


LaTeX Warning: Reference `a1' on page  undefined on input line 81.

Missing character: There is no a in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no . in font nullfont!

! LaTeX Error: \begin{document} ended by \end{theorem}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.82  \end{theorem}
                   
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.


Overfull \hbox (20.0pt too wide) in paragraph at lines 81--83
[]
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Overfull \hbox (21.7221pt too wide) in paragraph at lines 81--83
[][]
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Overfull \hbox (10.86105pt too wide) in paragraph at lines 81--83
[]
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Missing character: There is no A in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
! Undefined control sequence.
<recently read> \PP 
                    
l.84 ...rithm is that finding a proper subset $\PP
                                                  \subseteq\X'$ involves com...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.84 ...at finding a proper subset $\PP\subseteq\X
                                                  '$ involves computing $g(\...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
! Undefined control sequence.
l.84 ...\PP\subseteq\X'$ involves computing $g(\PP
                                                  ')$ for all $\subseteq$-su...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no - in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
! Undefined control sequence.
<recently read> \PP 
                    
l.84 ...\PP')$ for all $\subseteq$-successors $\PP
                                                  '$ of previously chosen su...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no I in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no . in font nullfont!

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[]
 []


Overfull \hbox (10.58336pt too wide) in paragraph at lines 84--86
\OMS/cmsy/m/n/10 ^^R[]$
 []


Overfull \hbox (15.71182pt too wide) in paragraph at lines 84--86
\OML/cmm/m/it/10 g\OT1/cmr/m/n/10 ([])$
 []


Overfull \hbox (7.7778pt too wide) in paragraph at lines 84--86
\OMS/cmsy/m/n/10 ^^R$
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Overfull \hbox (2.80556pt too wide) in paragraph at lines 84--86
[]$
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! LaTeX Error: Environment ass undefined.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.87 \begin{ass}
                [uniformity]\label{as3}
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

Missing character: There is no [ in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no ] in font nullfont!
! Undefined control sequence.
l.88  $|\Pa
           |=|\Pa'|\Longrightarrow g(\Pa)=g(\Pa')$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.88  $|\Pa|=|\Pa
                 '|\Longrightarrow g(\Pa)=g(\Pa')$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.88  $|\Pa|=|\Pa'|\Longrightarrow g(\Pa
                                        )=g(\Pa')$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.88  $|\Pa|=|\Pa'|\Longrightarrow g(\Pa)=g(\Pa
                                               ')$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no . in font nullfont!

! LaTeX Error: \begin{document} ended by \end{ass}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.89 \end{ass}
              
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.


Overfull \hbox (20.0pt too wide) in paragraph at lines 87--90
[][]
 []


Overfull \hbox (16.11108pt too wide) in paragraph at lines 87--90
\OMS/cmsy/m/n/10 jj \OT1/cmr/m/n/10 =
 []


Overfull \hbox (27.25003pt too wide) in paragraph at lines 87--90
\OMS/cmsy/m/n/10 j[]j [][])
 []


Overfull \hbox (23.46178pt too wide) in paragraph at lines 87--90
\OML/cmm/m/it/10 g\OT1/cmr/m/n/10 () =
 []


Overfull \hbox (15.71182pt too wide) in paragraph at lines 87--90
\OML/cmm/m/it/10 g\OT1/cmr/m/n/10 ([])$
 []

Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
! Undefined control sequence.
<recently read> \g 
                   
l.91 ...above assumption suggests the notation $\g
                                                  (|\Pa|)=g(\Pa)$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.91 ... assumption suggests the notation $\g(|\Pa
                                                  |)=g(\Pa)$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.91 ...ion suggests the notation $\g(|\Pa|)=g(\Pa
                                                  )$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no . in font nullfont!
Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no . in font nullfont!

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[]
 []


Overfull \hbox (23.88889pt too wide) in paragraph at lines 91--93
\OT1/cmr/m/n/10 (\OMS/cmsy/m/n/10 jj\OT1/cmr/m/n/10 ) =
 []


Overfull \hbox (12.90627pt too wide) in paragraph at lines 91--93
\OML/cmm/m/it/10 g\OT1/cmr/m/n/10 ()$
 []


Overfull \hbox (5.12846pt too wide) in paragraph at lines 91--93
\OML/cmm/m/it/10 g$
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Overfull \hbox (5.12846pt too wide) in paragraph at lines 91--93
\OML/cmm/m/it/10 g$ 
 []


! LaTeX Error: Environment alg undefined.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.94 \begin{alg}
                \label{a2}~
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.


Overfull \hbox (20.0pt too wide) in paragraph at lines 94--95
[] 
 []

! Undefined control sequence.
<recently read> \Pa 
                    
l.98 \item $\Pa
               :=\emptyset$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no f in font nullfont!
! Undefined control sequence.
<recently read> \g 
                   
l.101 \item if $\g
                  (p)\ge s(\Pa)$ then return $\Pa$; stop
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.101 \item if $\g(p)\ge s(\Pa
                              )$ then return $\Pa$; stop
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no n in font nullfont!
! Undefined control sequence.
<recently read> \Pa 
                    
l.101 \item if $\g(p)\ge s(\Pa)$ then return $\Pa
                                                 $; stop
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no ; in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no p in font nullfont!
! Undefined control sequence.
<recently read> \PP 
                    
l.102 \item $\PP
                =arg min_{\{\Y\subseteq\X' : |\Y|=p\}}s(\Y)$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.102 \item $\PP=arg min_{\{\Y
                              \subseteq\X' : |\Y|=p\}}s(\Y)$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.102 \item $\PP=arg min_{\{\Y\subseteq\X
                                         ' : |\Y|=p\}}s(\Y)$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.102 \item $\PP=arg min_{\{\Y\subseteq\X' : |\Y
                                                |=p\}}s(\Y)$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.102 ...arg min_{\{\Y\subseteq\X' : |\Y|=p\}}s(\Y
                                                  )$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no i in font nullfont!
Missing character: There is no f in font nullfont!
! Undefined control sequence.
l.103 \item if $s(\PP
                     )<s(\Pa)$ then $\Pa:=\PP$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.103 \item if $s(\PP)<s(\Pa
                            )$ then $\Pa:=\PP$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
! Undefined control sequence.
<recently read> \Pa 
                    
l.103 \item if $s(\PP)<s(\Pa)$ then $\Pa
                                        :=\PP$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.103 \item if $s(\PP)<s(\Pa)$ then $\Pa:=\PP
                                             $
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


Overfull \hbox (7372.74998pt too wide) in paragraph at lines 96--108
 [] 
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! LaTeX Error: \begin{document} ended by \end{alg}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.109 \end{alg}
               
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.


! LaTeX Error: Environment theorem undefined.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.111  \begin{theorem}
                      
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

Missing character: There is no S in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no A in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
! Undefined control sequence.
<write> ...ning: Reference `as1' on page \thepage 
                                                  \space undefined\on@line .
l.112 ... function satisfies Assumptions \ref{as1}
                                                  -\ref{as3}. Then Algorithm...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


LaTeX Warning: Reference `as1' on page  undefined on input line 112.

Missing character: There is no - in font nullfont!
! Undefined control sequence.
<write> ...ning: Reference `as3' on page \thepage 
                                                  \space undefined\on@line .
l.112 ...satisfies Assumptions \ref{as1}-\ref{as3}
                                                  . Then Algorithm \ref{a2} ...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


LaTeX Warning: Reference `as3' on page  undefined on input line 112.

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Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
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Missing character: There is no l in font nullfont!
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! Undefined control sequence.
<write> ...rning: Reference `a2' on page \thepage 
                                                  \space undefined\on@line .
l.112 ...f{as1}-\ref{as3}. Then Algorithm \ref{a2}
                                                   applied to each random va...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


LaTeX Warning: Reference `a2' on page  undefined on input line 112.

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! LaTeX Error: \begin{document} ended by \end{theorem}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.113  \end{theorem}
                    
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.


Overfull \hbox (20.0pt too wide) in paragraph at lines 112--114
[]
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Overfull \hbox (21.7221pt too wide) in paragraph at lines 112--114
[][]
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Overfull \hbox (10.86105pt too wide) in paragraph at lines 112--114
[]
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! Undefined control sequence.
l.115 \subsection
                 {Minimal Description Length}
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no M in font nullfont!
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Overfull \hbox (20.0pt too wide) in paragraph at lines 115--116
[]
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\citation{lam94}
! Undefined control sequence.
<write> ...: Citation `\@citeb ' on page \thepage 
                                                  \space undefined\on@line .
l.117 ...ates from information theory \cite{lam94}
                                                  .
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


LaTeX Warning: Citation `lam94' on page  undefined on input line 117.

Missing character: There is no ] in font nullfont!
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! Undefined control sequence.
<recently read> \N 
                   
l.118  A network $\N
                    $ is viewed here as a model of compression of a dataset ...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
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! Undefined control sequence.
<recently read> \D 
                   
l.118 ...s a model of compression of a dataset $\D
                                                  $.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no . in font nullfont!
Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no o in font nullfont!
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\citation{neapolitan03}
! Undefined control sequence.
<write> ...: Citation `\@citeb ' on page \thepage 
                                                  \space undefined\on@line .
l.121  (see \cite{neapolitan03}
                               ),
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


LaTeX Warning: Citation `neapolitan03' on page  undefined on input line 121.

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Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no . in font nullfont!

Overfull \hbox (20.0pt too wide) in paragraph at lines 117--124
[]
 []


Overfull \hbox (5.43053pt too wide) in paragraph at lines 117--124
[]
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Overfull \hbox (5.43053pt too wide) in paragraph at lines 117--124
[]
 []

Missing character: There is no L in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no x in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
! Undefined control sequence.
<recently read> \D 
                   
l.125  Let us fix a dataset $\D
                               =\{\x_1,\ldots,\x_N\}$ and a random variable ...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.125  Let us fix a dataset $\D=\{\x
                                    _1,\ldots,\x_N\}$ and a random variable ...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.125  Let us fix a dataset $\D=\{\x_1,\ldots,\x
                                                _N\}$ and a random variable ...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no R in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
! Undefined control sequence.
l.126  Recall the decomposition $s(\Pa
                                      )=g(\Pa)+d(\Pa)$ of the local score fo...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.126  Recall the decomposition $s(\Pa)=g(\Pa
                                             )+d(\Pa)$ of the local score fo...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.126 ...ll the decomposition $s(\Pa)=g(\Pa)+d(\Pa
                                                  )$ of the local score for ...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no I in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no M in font nullfont!
Missing character: There is no D in font nullfont!
Missing character: There is no L in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
! Undefined control sequence.
l.127  In the MDL score $g(\Pa
                              )$ stands for the length of the description of...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no ( in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
! Undefined control sequence.
l.127 ...and the conditional distribution $P(X|\Pa
                                                  )$) and $d(\Pa)$ is the le...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no ) in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
! Undefined control sequence.
l.127 ...ional distribution $P(X|\Pa)$) and $d(\Pa
                                                  )$ is the length of the co...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no - in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
! Undefined control sequence.
<recently read> \D 
                   
l.127 ...e compressed version of $X$-values in $\D
                                                  $.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no . in font nullfont!

Overfull \hbox (20.0pt too wide) in paragraph at lines 125--128
[]
 []


Overfull \hbox (7.7778pt too wide) in paragraph at lines 125--128
\OT1/cmr/m/n/10 =
 []


Overfull \hbox (44.29295pt too wide) in paragraph at lines 125--128
\OMS/cmsy/m/n/10 f[]\OML/cmm/m/it/10 ; [] ;[] \OMS/cmsy/m/n/10 g$
 []


Overfull \hbox (9.06943pt too wide) in paragraph at lines 125--128
\OML/cmm/m/it/10 X$
 []


Overfull \hbox (23.02081pt too wide) in paragraph at lines 125--128
\OML/cmm/m/it/10 s\OT1/cmr/m/n/10 () =
 []


Overfull \hbox (20.68407pt too wide) in paragraph at lines 125--128
\OML/cmm/m/it/10 g\OT1/cmr/m/n/10 () +
 []


Overfull \hbox (12.98267pt too wide) in paragraph at lines 125--128
\OML/cmm/m/it/10 d\OT1/cmr/m/n/10 ()$
 []


Overfull \hbox (9.06943pt too wide) in paragraph at lines 125--128
\OML/cmm/m/it/10 X$
 []


Overfull \hbox (12.90627pt too wide) in paragraph at lines 125--128
\OML/cmm/m/it/10 g\OT1/cmr/m/n/10 ()$
 []


Overfull \hbox (9.06943pt too wide) in paragraph at lines 125--128
\OML/cmm/m/it/10 X$
 []


Overfull \hbox (27.43405pt too wide) in paragraph at lines 125--128
\OML/cmm/m/it/10 P\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 X\OMS/cmsy/m/n/10 j\OT1/cmr
/m/n/10 )$
 []


Overfull \hbox (12.98267pt too wide) in paragraph at lines 125--128
\OML/cmm/m/it/10 d\OT1/cmr/m/n/10 ()$
 []


Overfull \hbox (9.06943pt too wide) in paragraph at lines 125--128
\OML/cmm/m/it/10 X$
 []

Missing character: There is no L in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
! Undefined control sequence.
<recently read> \V 
                   
l.129 ..._Y$ denote the cardinality of the set $\V
                                                  _Y$ of possible values of ...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
! Undefined control sequence.
l.129 ...ble values of the random variable $Y\in\X
                                                  $.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no . in font nullfont!
Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!

Overfull \hbox (20.0pt too wide) in paragraph at lines 129--131
[]
 []


Overfull \hbox (12.129pt too wide) in paragraph at lines 129--131
\OML/cmm/m/it/10 k[]$
 []


Overfull \hbox (6.92296pt too wide) in paragraph at lines 129--131
[]$
 []


Overfull \hbox (17.47218pt too wide) in paragraph at lines 129--131
\OML/cmm/m/it/10 Y \OMS/cmsy/m/n/10 2$
 []

! Undefined control sequence.
l.131  $$g(\Pa
              )=|\Pa|\log n+\frac{\log N}{2}(k_X-1)\prod_{Y\in\Pa}k_Y$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.131  $$g(\Pa)=|\Pa
                    |\log n+\frac{\log N}{2}(k_X-1)\prod_{Y\in\Pa}k_Y$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.131 ...g n+\frac{\log N}{2}(k_X-1)\prod_{Y\in\Pa
                                                  }k_Y$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


Overfull \hbox (149.53725pt too wide) detected at line 131
\OML/cmm/m/it/10 g\OT1/cmr/m/n/10 () = \OMS/cmsy/m/n/10 jj [] \OML/cmm/m/it/10 
n \OT1/cmr/m/n/10 + [](\OML/cmm/m/it/10 k[] \OMS/cmsy/m/n/10 ^^@ \OT1/cmr/m/n/1
0 1) [] \OML/cmm/m/it/10 k[]
 []


! LaTeX Error: The font size command \normalsize is not defined:
               there is probably something wrong with the class file.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.131 ...rac{\log N}{2}(k_X-1)\prod_{Y\in\Pa}k_Y$$
                                                  
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

[1{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}
! Undefined control sequence.
<write> \newlabel{joinprob}{{1}{\thepage 
                                         }}
l.131 ...rac{\log N}{2}(k_X-1)\prod_{Y\in\Pa}k_Y$$
                                                  
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

\newlabel{joinprob}{{1}{}}
! Undefined control sequence.
<write> \newlabel{as1}{{}{\thepage 
                                   }}
l.131 ...rac{\log N}{2}(k_X-1)\prod_{Y\in\Pa}k_Y$$
                                                  
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

\newlabel{as1}{{}{}}
! Undefined control sequence.
<write> \newlabel{as2}{{}{\thepage 
                                   }}
l.131 ...rac{\log N}{2}(k_X-1)\prod_{Y\in\Pa}k_Y$$
                                                  
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

\newlabel{as2}{{}{}}
! Undefined control sequence.
<write> \newlabel{a1}{{}{\thepage 
                                  }}
l.131 ...rac{\log N}{2}(k_X-1)\prod_{Y\in\Pa}k_Y$$
                                                  
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

\newlabel{a1}{{}{}}
! Undefined control sequence.
<write> \newlabel{as3}{{}{\thepage 
                                   }}
l.131 ...rac{\log N}{2}(k_X-1)\prod_{Y\in\Pa}k_Y$$
                                                  
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

\newlabel{as3}{{}{}}
! Undefined control sequence.
<write> \newlabel{a2}{{}{\thepage 
                                  }}
l.131 ...rac{\log N}{2}(k_X-1)\prod_{Y\in\Pa}k_Y$$
                                                  
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

\newlabel{a2}{{}{}}
]
Missing character: There is no w in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no A in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!

! Undefined control sequence.
<write> ...ning: Reference `as2' on page \thepage 
                                                  \space undefined\on@line .
l.133  This formula satisfies Assumption \ref{as2}
                                                   but fails to satisfy Assu...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


LaTeX Warning: Reference `as2' on page  undefined on input line 133.

Missing character: There is no b in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no A in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
! Undefined control sequence.
<write> ...ning: Reference `as3' on page \thepage 
                                                  \space undefined\on@line .
l.133 ...but fails to satisfy Assumption \ref{as3}
                                                  .
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


LaTeX Warning: Reference `as3' on page  undefined on input line 133.

Missing character: There is no . in font nullfont!
Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no A in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no m in font nullfont!
! Undefined control sequence.
<write> ...rning: Reference `a1' on page \thepage 
                                                  \space undefined\on@line .
l.134  Therefore Algorithm \ref{a1}
                                    can be used to learn an optimal network,...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


LaTeX Warning: Reference `a1' on page  undefined on input line 134.

Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no A in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no m in font nullfont!
! Undefined control sequence.
<write> ...rning: Reference `a2' on page \thepage 
                                                  \space undefined\on@line .
l.134 ...n optimal network, but Algorithm \ref{a2}
                                                   cannot.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


LaTeX Warning: Reference `a2' on page  undefined on input line 134.

Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no . in font nullfont!

Overfull \hbox (21.19424pt too wide) in paragraph at lines 131--135
 $[]$
 []


Overfull \hbox (10.86105pt too wide) in paragraph at lines 131--135
[]
 []


Overfull \hbox (10.86105pt too wide) in paragraph at lines 131--135
[]
 []


Overfull \hbox (10.86105pt too wide) in paragraph at lines 131--135
[]
 []


Overfull \hbox (10.86105pt too wide) in paragraph at lines 131--135
[]
 []

Missing character: There is no H in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
! Undefined control sequence.
<recently read> \V 
                   
l.137 ...dom variables have the same value set $\V
                                                  $ of cardinality $k$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no I in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no a in font nullfont!

Overfull \hbox (20.0pt too wide) in paragraph at lines 136--139
[]
 []


Overfull \hbox (5.52084pt too wide) in paragraph at lines 136--139
\OML/cmm/m/it/10 k$
 []

! Undefined control sequence.
l.139  $$g(\Pa
              )=|\Pa|\log n+\frac{\log N}{2}(k-1)k^{|\Pa|}$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.139  $$g(\Pa)=|\Pa
                    |\log n+\frac{\log N}{2}(k-1)k^{|\Pa|}$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.139 ...=|\Pa|\log n+\frac{\log N}{2}(k-1)k^{|\Pa
                                                  |}$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


Overfull \hbox (124.78073pt too wide) detected at line 139
\OML/cmm/m/it/10 g\OT1/cmr/m/n/10 () = \OMS/cmsy/m/n/10 jj [] \OML/cmm/m/it/10 
n \OT1/cmr/m/n/10 + [](\OML/cmm/m/it/10 k \OMS/cmsy/m/n/10 ^^@ \OT1/cmr/m/n/10 
1)\OML/cmm/m/it/10 k[]
 []

Missing character: There is no w in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no A in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
! Undefined control sequence.
<write> ...ning: Reference `as3' on page \thepage 
                                                  \space undefined\on@line .
l.140  which satisfies Assumption \ref{as3}
                                           .
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


LaTeX Warning: Reference `as3' on page  undefined on input line 140.

Missing character: There is no . in font nullfont!
Missing character: There is no F in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no . in font nullfont!

Overfull \hbox (10.86105pt too wide) in paragraph at lines 139--142
   []
 []

Missing character: There is no C in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no : in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no - in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
! Undefined control sequence.
<recently read> \Pa 
                    
l.143 ...coding the $X$-values, the values of $\Pa
                                                  $-instances are assumed to...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no - in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no y in font nullfont!

Overfull \hbox (20.0pt too wide) in paragraph at lines 143--145
[]
 []


Overfull \hbox (9.06943pt too wide) in paragraph at lines 143--145
\OML/cmm/m/it/10 X$
 []

! Undefined control sequence.
l.145  $$d(\Pa
              )=N\cdot H(X|\Pa)$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.145  $$d(\Pa)=N\cdot H(X|\Pa
                              )$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


Overfull \hbox (66.96863pt too wide) detected at line 145
\OML/cmm/m/it/10 d\OT1/cmr/m/n/10 () = \OML/cmm/m/it/10 N \OMS/cmsy/m/n/10 ^^A 
\OML/cmm/m/it/10 H\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 X\OMS/cmsy/m/n/10 j\OT1/cmr
/m/n/10 )
 []

Missing character: There is no w in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
! Undefined control sequence.
l.146  where $H(X|\Pa
                     )=-\sum_{v\in\V}\sum_{\vp\in\V^{\Pa}}P(v,\vp)\log P(v|\...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.146  where $H(X|\Pa)=-\sum_{v\in\V
                                    }\sum_{\vp\in\V^{\Pa}}P(v,\vp)\log P(v|\...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.146  where $H(X|\Pa)=-\sum_{v\in\V}\sum_{\vp
                                              \in\V^{\Pa}}P(v,\vp)\log P(v|\...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.146 ...re $H(X|\Pa)=-\sum_{v\in\V}\sum_{\vp\in\V
                                                  ^{\Pa}}P(v,\vp)\log P(v|\v...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.146 ...(X|\Pa)=-\sum_{v\in\V}\sum_{\vp\in\V^{\Pa
                                                  }}P(v,\vp)\log P(v|\vp)$ i...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.146 ...\sum_{v\in\V}\sum_{\vp\in\V^{\Pa}}P(v,\vp
                                                  )\log P(v|\vp)$ is the con...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.146 ...\sum_{\vp\in\V^{\Pa}}P(v,\vp)\log P(v|\vp
                                                  )$ is the conditional entr...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
! Undefined control sequence.
<recently read> \Pa 
                    
l.146 ...the conditional entropy of $X$ given $\Pa
                                                  $ (the distributions are e...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no ( in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
! Undefined control sequence.
<recently read> \D 
                   
l.146 ...(the distributions are estimated from $\D
                                                  $).
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no ) in font nullfont!
Missing character: There is no . in font nullfont!

Overfull \hbox (39.3055pt too wide) in paragraph at lines 145--147
 $\OML/cmm/m/it/10 H\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 X\OMS/cmsy/m/n/10 j\OT1/c
mr/m/n/10 ) =
 []


Overfull \hbox (115.47568pt too wide) in paragraph at lines 145--147
\OMS/cmsy/m/n/10 ^^@ [][] [][] \OML/cmm/m/it/10 P\OT1/cmr/m/n/10 (\OML/cmm/m/it
/10 v; \OT1/cmr/m/n/10 ) [] \OML/cmm/m/it/10 P\OT1/cmr/m/n/10 (\OML/cmm/m/it/10
 v\OMS/cmsy/m/n/10 j\OT1/cmr/m/n/10 )$
 []


Overfull \hbox (9.06943pt too wide) in paragraph at lines 145--147
\OML/cmm/m/it/10 X$
 []

Missing character: There is no S in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no A in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no m in font nullfont!
! Undefined control sequence.
<write> ...rning: Reference `a2' on page \thepage 
                                                  \space undefined\on@line .
l.148 ...section are satisfied, Algorithm \ref{a2}
                                                   may be applied to learn t...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


LaTeX Warning: Reference `a2' on page  undefined on input line 148.

Missing character: There is no m in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no L in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no x in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no . in font nullfont!

Overfull \hbox (20.0pt too wide) in paragraph at lines 148--150
[]
 []


Overfull \hbox (10.86105pt too wide) in paragraph at lines 148--150
[]
 []


! LaTeX Error: Environment theorem undefined.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.151  \begin{theorem}
                      
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no - in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no x in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no A in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no m in font nullfont!
! Undefined control sequence.
<write> ...rning: Reference `a2' on page \thepage 
                                                  \space undefined\on@line .
l.152 ...ase time complexity of Algorithm \ref{a2}
                                                   for the MDL score is $\OO...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


LaTeX Warning: Reference `a2' on page  undefined on input line 152.

Missing character: There is no f in font nullfont!
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! Undefined control sequence.
<recently read> \OO 
                    
l.152 ...orithm \ref{a2} for the MDL score is $\OO
                                                  (n^{\log_k N}N\log_k N)$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

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! LaTeX Error: \begin{document} ended by \end{theorem}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.153  \end{theorem}
                    
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.


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\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 n[]N [][] N\OT1/cmr/m/n/10 )$
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! Undefined control sequence.
l.155 \subsection
                 {Bayesian-Dirichlet equivalence}
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
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\citation{cooper92}
! Undefined control sequence.
<write> ...: Citation `\@citeb ' on page \thepage 
                                                  \space undefined\on@line .
l.157 ... from Bayesian statistics \cite{cooper92}
                                                  .
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


LaTeX Warning: Citation `cooper92' on page  undefined on input line 157.

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! Undefined control sequence.
<recently read> \D 
                   
l.158  Given a dataset $\D
                          $ the optimal network structure $\G$ maximizes the...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

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! Undefined control sequence.
<recently read> \G 
                   
l.158 ...et $\D$ the optimal network structure $\G
                                                  $ maximizes the \emph{post...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

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! Undefined control sequence.
l.158 ...{posterior} conditional probability $P(\G
                                                  |\D)$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
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! Undefined control sequence.
l.158 ...sterior} conditional probability $P(\G|\D
                                                  )$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

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\OML/cmm/m/it/10 P\OT1/cmr/m/n/10 (\OMS/cmsy/m/n/10 j\OT1/cmr/m/n/10 )$
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! Undefined control sequence.
l.160  $$P(\G
             |\D)\propto P(\G)P(\D|\G)=P(\G)\int P(\D|\G,\theta)P(\theta|\G)...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.160  $$P(\G|\D
                )\propto P(\G)P(\D|\G)=P(\G)\int P(\D|\G,\theta)P(\theta|\G)...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.160  $$P(\G|\D)\propto P(\G
                             )P(\D|\G)=P(\G)\int P(\D|\G,\theta)P(\theta|\G)...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.160  $$P(\G|\D)\propto P(\G)P(\D
                                  |\G)=P(\G)\int P(\D|\G,\theta)P(\theta|\G)...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.160  $$P(\G|\D)\propto P(\G)P(\D|\G
                                     )=P(\G)\int P(\D|\G,\theta)P(\theta|\G)...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.160  $$P(\G|\D)\propto P(\G)P(\D|\G)=P(\G
                                           )\int P(\D|\G,\theta)P(\theta|\G)...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.160 ...G|\D)\propto P(\G)P(\D|\G)=P(\G)\int P(\D
                                                  |\G,\theta)P(\theta|\G)d\t...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.160 ...D)\propto P(\G)P(\D|\G)=P(\G)\int P(\D|\G
                                                  ,\theta)P(\theta|\G)d\theta$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.160 ...|\G)=P(\G)\int P(\D|\G,\theta)P(\theta|\G
                                                  )d\theta$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


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\OML/cmm/m/it/10 P\OT1/cmr/m/n/10 (\OMS/cmsy/m/n/10 j\OT1/cmr/m/n/10 ) \OMS/cms
y/m/n/10 / \OML/cmm/m/it/10 P\OT1/cmr/m/n/10 ()\OML/cmm/m/it/10 P\OT1/cmr/m/n/1
0 (\OMS/cmsy/m/n/10 j\OT1/cmr/m/n/10 ) = \OML/cmm/m/it/10 P\OT1/cmr/m/n/10 () [
] \OML/cmm/m/it/10 P\OT1/cmr/m/n/10 (\OMS/cmsy/m/n/10 j\OML/cmm/m/it/10 ; ^^R\O
T1/cmr/m/n/10 )\OML/cmm/m/it/10 P\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 ^^R\OMS/cmsy
/m/n/10 j\OT1/cmr/m/n/10 )\OML/cmm/m/it/10 d^^R
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! Undefined control sequence.
l.161  where $P(\G
                  )$ and $P(\theta|\G)$ are \emph{prior} probability distrib...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

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! Undefined control sequence.
l.161  where $P(\G)$ and $P(\theta|\G
                                     )$ are \emph{prior} probability distrib...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

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! Undefined control sequence.
l.161 ...ions' parameters, respectively, and $P(\D
                                                  |\G,\theta)$ is evaluated ...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.161 ...s' parameters, respectively, and $P(\D|\G
                                                  ,\theta)$ is evaluated due...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

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Missing character: There is no u in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
! Undefined control sequence.
l.161 ...\D|\G,\theta)$ is evaluated due to \eqref
                                                  {joinprob}.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no j in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no . in font nullfont!

Overfull \hbox (15.58684pt too wide) in paragraph at lines 160--162
 $\OML/cmm/m/it/10 P\OT1/cmr/m/n/10 ()$
 []


Overfull \hbox (23.33685pt too wide) in paragraph at lines 160--162
\OML/cmm/m/it/10 P\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 ^^R\OMS/cmsy/m/n/10 j\OT1/c
mr/m/n/10 )$
 []


Overfull \hbox (21.72208pt too wide) in paragraph at lines 160--162
\OT1/cmr/m/it/10 prior
 []


Overfull \hbox (27.78127pt too wide) in paragraph at lines 160--162
\OML/cmm/m/it/10 P\OT1/cmr/m/n/10 (\OMS/cmsy/m/n/10 j\OML/cmm/m/it/10 ; ^^R\OT1
/cmr/m/n/10 )$
 []

Missing character: There is no H in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no [ in font nullfont!
\citation{heckerman95}
! Undefined control sequence.
<write> ...: Citation `\@citeb ' on page \thepage 
                                                  \space undefined\on@line .
l.163  Heckerman et al. \cite{heckerman95}
                                          , following Cooper and Herskovits ...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


LaTeX Warning: Citation `heckerman95' on page  undefined on input line 163.

Missing character: There is no ] in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no C in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no H in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no [ in font nullfont!
\citation{cooper92}
! Undefined control sequence.
<write> ...: Citation `\@citeb ' on page \thepage 
                                                  \space undefined\on@line .
l.163 ...ing Cooper and Herskovits \cite{cooper92}
                                                  , identified a set of inde...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


LaTeX Warning: Citation `cooper92' on page  undefined on input line 163.

Missing character: There is no ] in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
! Undefined control sequence.
<recently read> \X 
                   
l.163 ...the above formula into a product over $\X
                                                  $.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no . in font nullfont!
Missing character: There is no U in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
! Undefined control sequence.
l.164 ...ilar one regarding decomposition of $P(\G
                                                  )$, the scoring criterion
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no , in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!

Overfull \hbox (20.0pt too wide) in paragraph at lines 163--165
[]
 []


Overfull \hbox (5.43053pt too wide) in paragraph at lines 163--165
[]
 []


Overfull \hbox (5.43053pt too wide) in paragraph at lines 163--165
[]
 []


Overfull \hbox (15.58684pt too wide) in paragraph at lines 163--165
\OML/cmm/m/it/10 P\OT1/cmr/m/n/10 ()$
 []

! Undefined control sequence.
l.165  $$S(\G
             :\D)=-\log P(\G)-\log P(\D|\G)$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.165  $$S(\G:\D
                )=-\log P(\G)-\log P(\D|\G)$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.165  $$S(\G:\D)=-\log P(\G
                            )-\log P(\D|\G)$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.165  $$S(\G:\D)=-\log P(\G)-\log P(\D
                                       |\G)$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.165  $$S(\G:\D)=-\log P(\G)-\log P(\D|\G
                                          )$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


Overfull \hbox (110.93744pt too wide) detected at line 165
\OML/cmm/m/it/10 S\OT1/cmr/m/n/10 (:) = \OMS/cmsy/m/n/10 ^^@ [] \OML/cmm/m/it/1
0 P\OT1/cmr/m/n/10 () \OMS/cmsy/m/n/10 ^^@ [] \OML/cmm/m/it/10 P\OT1/cmr/m/n/10
 (\OMS/cmsy/m/n/10 j\OT1/cmr/m/n/10 )
 []

Missing character: There is no o in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no A in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
! Undefined control sequence.
<write> ...ning: Reference `as1' on page \thepage 
                                                  \space undefined\on@line .
l.166 ...above term satisfies Assumption \ref{as1}
                                                  .
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


LaTeX Warning: Reference `as1' on page  undefined on input line 166.

Missing character: There is no . in font nullfont!
Missing character: There is no M in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
! Undefined control sequence.
l.167  Moreover, the decomposition $s(\Pa
                                         )=g(\Pa)+d(\Pa)$ of the local score...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.167  Moreover, the decomposition $s(\Pa)=g(\Pa
                                                )+d(\Pa)$ of the local score...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.167 ...r, the decomposition $s(\Pa)=g(\Pa)+d(\Pa
                                                  )$ of the local scores app...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
! Undefined control sequence.
l.167 ...ents $g$ and $d$ derived from $-\log P(\G
                                                  )$ and $-\log P(\D|\G)$, r...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
! Undefined control sequence.
l.167 ...erived from $-\log P(\G)$ and $-\log P(\D
                                                  |\G)$, respectively.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.167 ...ved from $-\log P(\G)$ and $-\log P(\D|\G
                                                  )$, respectively.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no , in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no . in font nullfont!

Overfull \hbox (22.36111pt too wide) in paragraph at lines 165--168
   $\OMS/cmsy/m/n/10 ^^@ []$
 []


Overfull \hbox (10.86105pt too wide) in paragraph at lines 165--168
[]
 []


Overfull \hbox (23.02081pt too wide) in paragraph at lines 165--168
\OML/cmm/m/it/10 s\OT1/cmr/m/n/10 () =
 []


Overfull \hbox (20.68407pt too wide) in paragraph at lines 165--168
\OML/cmm/m/it/10 g\OT1/cmr/m/n/10 () +
 []


Overfull \hbox (12.98267pt too wide) in paragraph at lines 165--168
\OML/cmm/m/it/10 d\OT1/cmr/m/n/10 ()$
 []


Overfull \hbox (5.12846pt too wide) in paragraph at lines 165--168
\OML/cmm/m/it/10 g$
 []


Overfull \hbox (5.20486pt too wide) in paragraph at lines 165--168
\OML/cmm/m/it/10 d$
 []


Overfull \hbox (39.61458pt too wide) in paragraph at lines 165--168
\OMS/cmsy/m/n/10 ^^@ [] \OML/cmm/m/it/10 P\OT1/cmr/m/n/10 ()$
 []


Overfull \hbox (42.39236pt too wide) in paragraph at lines 165--168
\OMS/cmsy/m/n/10 ^^@ [] \OML/cmm/m/it/10 P\OT1/cmr/m/n/10 (\OMS/cmsy/m/n/10 j\O
T1/cmr/m/n/10 )$
 []

Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
! Undefined control sequence.
l.174  The distribution $P((\X
                              ,\E))\propto\prod_{e\in\E}\alpha_{e}$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.174  The distribution $P((\X,\E
                                 ))\propto\prod_{e\in\E}\alpha_{e}$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.174 ...tribution $P((\X,\E))\propto\prod_{e\in\E
                                                  }\alpha_{e}$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no w in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no B in font nullfont!
Missing character: There is no N in font nullfont!
Missing character: There is no F in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!

Overfull \hbox (20.0pt too wide) in paragraph at lines 174--179
[]
 []


Overfull \hbox (38.36456pt too wide) in paragraph at lines 174--179
\OML/cmm/m/it/10 P\OT1/cmr/m/n/10 ((\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 )) \OMS/
cmsy/m/n/10 /
 []


Overfull \hbox (31.48524pt too wide) in paragraph at lines 174--179
[][] \OML/cmm/m/it/10 []$
 []


Overfull \hbox (15.55553pt too wide) in paragraph at lines 174--179
\OT1/cmr/m/n/10 0 \OML/cmm/m/it/10 <
 []


Overfull \hbox (21.24664pt too wide) in paragraph at lines 174--179
\OML/cmm/m/it/10 [] <
 []


Overfull \hbox (5.00002pt too wide) in paragraph at lines 174--179
\OT1/cmr/m/n/10 1$
 []


Overfull \hbox (38.31096pt too wide) in paragraph at lines 174--179
\OML/cmm/m/it/10 [] \OT1/cmr/m/n/10 =
 []


Overfull \hbox (22.12903pt too wide) in paragraph at lines 174--179
\OT1/cmr/m/n/10 1\OML/cmm/m/it/10 =k[]$
 []

! Undefined control sequence.
l.179  $$g(\Pa
              )=\sum_{Y\in\Pa}\log k_Y$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.179  $$g(\Pa)=\sum_{Y\in\Pa
                             }\log k_Y$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


Overfull \hbox (69.0629pt too wide) detected at line 179
\OML/cmm/m/it/10 g\OT1/cmr/m/n/10 () = [] [] \OML/cmm/m/it/10 k[]
 []

Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no A in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
! Undefined control sequence.
<write> ...ning: Reference `as2' on page \thepage 
                                                  \space undefined\on@line .
l.180  satisfying Assumptions \ref{as2}
                                       .
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


LaTeX Warning: Reference `as2' on page  undefined on input line 180.

Missing character: There is no . in font nullfont!
Missing character: There is no I in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
! Undefined control sequence.
<recently read> \V 
                   
l.182  have the same value set $\V
                                  $ of cardinality $k$,
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!

Overfull \hbox (10.86105pt too wide) in paragraph at lines 179--184
  []
 []


Overfull \hbox (5.52084pt too wide) in paragraph at lines 179--184
\OML/cmm/m/it/10 k$
 []

! Undefined control sequence.
l.184  $$g(\Pa
              )=|\Pa|\log k$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.184  $$g(\Pa)=|\Pa
                    |\log k$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


Overfull \hbox (53.56584pt too wide) detected at line 184
\OML/cmm/m/it/10 g\OT1/cmr/m/n/10 () = \OMS/cmsy/m/n/10 jj [] \OML/cmm/m/it/10 
k
 []

Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no A in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
! Undefined control sequence.
<write> ...ning: Reference `as3' on page \thepage 
                                                  \space undefined\on@line .
l.185  satisfying also Assumption \ref{as3}
                                           .
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


LaTeX Warning: Reference `as3' on page  undefined on input line 185.

Missing character: There is no . in font nullfont!
Missing character: There is no F in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no . in font nullfont!

Overfull \hbox (10.86105pt too wide) in paragraph at lines 184--187
   []
 []

Missing character: There is no H in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no A in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
! Undefined control sequence.
<write> ...ning: Reference `as2' on page \thepage 
                                                  \space undefined\on@line .
l.189  which satisfy neither Assumption \ref{as2}
                                                  nor \ref{as3},
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


LaTeX Warning: Reference `as2' on page  undefined on input line 189.

Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
! Undefined control sequence.
<write> ...ning: Reference `as3' on page \thepage 
                                                  \space undefined\on@line .
l.189 ...either Assumption \ref{as2} nor \ref{as3}
                                                  ,
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


LaTeX Warning: Reference `as3' on page  undefined on input line 189.

Missing character: There is no , in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no . in font nullfont!
! Undefined control sequence.
l.190  e.g.  $P(\G
                  )\propto\alpha^{\Delta(\G,\G_0)}$,
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.190  e.g.  $P(\G)\propto\alpha^{\Delta(\G
                                           ,\G_0)}$,
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.190  e.g.  $P(\G)\propto\alpha^{\Delta(\G,\G
                                              _0)}$,
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no , in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
! Undefined control sequence.
l.191  where $\Delta(\G
                       ,\G_0)$ is the cardinality of the symmetric difference
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.191  where $\Delta(\G,\G
                          _0)$ is the cardinality of the symmetric difference
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
! Undefined control sequence.
<recently read> \G 
                   
l.192  between the sets of edges in $\G
                                       $ and in the prior network $\G_0$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no k in font nullfont!
! Undefined control sequence.
<recently read> \G 
                   
l.192 ...dges in $\G$ and in the prior network $\G
                                                  _0$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no . in font nullfont!

Overfull \hbox (20.0pt too wide) in paragraph at lines 188--193
[]
 []


Overfull \hbox (10.86105pt too wide) in paragraph at lines 188--193
[]
 []


Overfull \hbox (10.86105pt too wide) in paragraph at lines 188--193
[]
 []


Overfull \hbox (26.14235pt too wide) in paragraph at lines 188--193
\OML/cmm/m/it/10 P\OT1/cmr/m/n/10 () \OMS/cmsy/m/n/10 /
 []


Overfull \hbox (26.03137pt too wide) in paragraph at lines 188--193
\OML/cmm/m/it/10 []$
 []


Overfull \hbox (25.0417pt too wide) in paragraph at lines 188--193
\OT1/cmr/m/n/10 ^^A(\OML/cmm/m/it/10 ;[] \OT1/cmr/m/n/10 )$
 []


Overfull \hbox (4.48613pt too wide) in paragraph at lines 188--193
[]$ 
 []

Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no ' in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no I in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no s in font nullfont!

Overfull \hbox (20.0pt too wide) in paragraph at lines 194--196
[]
 []


Overfull \hbox (31.18866pt too wide) in paragraph at lines 194--196
\OT1/cmr/m/it/10 Dirich-
 []


Overfull \hbox (10.47769pt too wide) in paragraph at lines 194--196
\OT1/cmr/m/it/10 let
 []


Overfull \hbox (15.84435pt too wide) in paragraph at lines 194--196
\OT1/cmr/m/it/10 dis-
 []


Overfull \hbox (14.18321pt too wide) in paragraph at lines 194--196
\OT1/cmr/m/it/10 tri-
 []


Overfull \hbox (13.54434pt too wide) in paragraph at lines 194--196
\OT1/cmr/m/it/10 bu-
 []


Overfull \hbox (17.12212pt too wide) in paragraph at lines 194--196
\OT1/cmr/m/it/10 tion
 []

! Undefined control sequence.
l.196  $$d(\Pa
              )=\log\left(\prod_{\vp\in\V^{|\Pa|}}
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.196  $$d(\Pa)=\log\left(\prod_{\vp
                                    \in\V^{|\Pa|}}
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.196  $$d(\Pa)=\log\left(\prod_{\vp\in\V
                                         ^{|\Pa|}}
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.196  $$d(\Pa)=\log\left(\prod_{\vp\in\V^{|\Pa
                                               |}}
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
<argument> \Gamma (\sum _{v\in \V 
                                  }(H_{v,\vp }+N_{v,\vp }))
l.197 ...v,\vp}))}{\Gamma(\sum_{v\in\V}H_{v,\vp})}
                                                  
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
<argument> \Gamma (\sum _{v\in \V }(H_{v,\vp 
                                             }+N_{v,\vp }))
l.197 ...v,\vp}))}{\Gamma(\sum_{v\in\V}H_{v,\vp})}
                                                  
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
<argument> ...sum _{v\in \V }(H_{v,\vp }+N_{v,\vp 
                                                  }))
l.197 ...v,\vp}))}{\Gamma(\sum_{v\in\V}H_{v,\vp})}
                                                  
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
<argument> \Gamma (\sum _{v\in \V 
                                  }H_{v,\vp })
l.197 ...v,\vp}))}{\Gamma(\sum_{v\in\V}H_{v,\vp})}
                                                  
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
<argument> \Gamma (\sum _{v\in \V }H_{v,\vp 
                                            })
l.197 ...v,\vp}))}{\Gamma(\sum_{v\in\V}H_{v,\vp})}
                                                  
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.198   \prod_{v\in\V
                     }\frac{\Gamma(H_{v,\vp})}{\Gamma(H_{v,\vp}+N_{v,\vp})}\...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
<argument> \Gamma (H_{v,\vp 
                            })
l.198 ...(H_{v,\vp})}{\Gamma(H_{v,\vp}+N_{v,\vp})}
                                                  \right)$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
<argument> \Gamma (H_{v,\vp 
                            }+N_{v,\vp })
l.198 ...(H_{v,\vp})}{\Gamma(H_{v,\vp}+N_{v,\vp})}
                                                  \right)$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
<argument> \Gamma (H_{v,\vp }+N_{v,\vp 
                                       })
l.198 ...(H_{v,\vp})}{\Gamma(H_{v,\vp}+N_{v,\vp})}
                                                  \right)$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


Overfull \hbox (235.92728pt too wide) detected at line 198
\OML/cmm/m/it/10 d\OT1/cmr/m/n/10 () = [] []
 []

Missing character: There is no w in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no , in font nullfont!
! Undefined control sequence.
l.199 ...$ is the \emph{Gamma} function, $N_{v,\vp
                                                  }$ denotes the number of s...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
! Undefined control sequence.
<recently read> \D 
                   
l.199 ...vp}$ denotes the number of samples in $\D
                                                  $ with $X=v$ and $\Pa=\vp$...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no w in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
! Undefined control sequence.
<recently read> \Pa 
                    
l.199 ...er of samples in $\D$ with $X=v$ and $\Pa
                                                  =\vp$, and $H_{v,\vp}$ is ...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.199 ...f samples in $\D$ with $X=v$ and $\Pa=\vp
                                                  $, and $H_{v,\vp}$ is the ...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no , in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
! Undefined control sequence.
l.199 ...$ with $X=v$ and $\Pa=\vp$, and $H_{v,\vp
                                                  }$ is the corresponding \e...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no D in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no . in font nullfont!

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\OT1/cmr/m/it/10 Gamma
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\OT1/cmr/m/it/10 e-
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Missing character: There is no S in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no s in font nullfont!

! LaTeX Error: Environment multline* undefined.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.202  \begin{multline*}
                        d(\Pa)=\log\left(\prod_{\vp\in\V^{|\Pa|}}
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

Missing character: There is no d in font nullfont!
Missing character: There is no ( in font nullfont!
! Undefined control sequence.
l.202  \begin{multline*}d(\Pa
                             )=\log\left(\prod_{\vp\in\V^{|\Pa|}}
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no ) in font nullfont!
Missing character: There is no = in font nullfont!
! Missing $ inserted.
<inserted text> 
                $
l.202  \begin{multline*}d(\Pa)=\log
                                   \left(\prod_{\vp\in\V^{|\Pa|}}
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Undefined control sequence.
l.202 ...gin{multline*}d(\Pa)=\log\left(\prod_{\vp
                                                  \in\V^{|\Pa|}}
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.202 ...ultline*}d(\Pa)=\log\left(\prod_{\vp\in\V
                                                  ^{|\Pa|}}
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.202 ...e*}d(\Pa)=\log\left(\prod_{\vp\in\V^{|\Pa
                                                  |}}
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
<argument> (k-1+\sum _{v\in \V 
                               }N_{v,\vp })!
l.203 ...ac{(k-1+\sum_{v\in\V}N_{v,\vp})!}{(k-1)!}
                                                  
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
<argument> (k-1+\sum _{v\in \V }N_{v,\vp 
                                         })!
l.203 ...ac{(k-1+\sum_{v\in\V}N_{v,\vp})!}{(k-1)!}
                                                  
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.204   \prod_{v\in\V
                     }\frac{1}{N_{v,\vp}!}\right)=\\
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
<argument> N_{v,\vp 
                    }!
l.204   \prod_{v\in\V}\frac{1}{N_{v,\vp}!}
                                          \right)=\\
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.205   =\sum_{\vp
                  \in\V^{|\Pa|}}\left(
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.205   =\sum_{\vp\in\V
                       ^{|\Pa|}}\left(
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.205   =\sum_{\vp\in\V^{|\Pa
                             |}}\left(
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.206  \log({\textstyle k-1+\underset
                                     {v\in\V}{\sum}N_{v,\vp}})!-\log(k-1)!
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.206  \log({\textstyle k-1+\underset{v\in\V
                                            }{\sum}N_{v,\vp}})!-\log(k-1)!
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.206 ...style k-1+\underset{v\in\V}{\sum}N_{v,\vp
                                                  }})!-\log(k-1)!
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.207   -\sum_{v\in\V
                     }\log{N_{v,\vp}!}\right)
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.207   -\sum_{v\in\V}\log{N_{v,\vp
                                   }!}\right)
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


! LaTeX Error: \begin{document} ended by \end{multline*}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.208  \end{multline*}
                      
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Missing $ inserted.
<inserted text> 
                $
l.208  \end{multline*}
                      
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

Missing character: There is no w in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
! Undefined control sequence.
l.209  where $k=|\V
                   |$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no . in font nullfont!
Missing character: There is no F in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no ( in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no C in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no H in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no [ in font nullfont!
\citation{cooper92}
! Undefined control sequence.
<write> ...: Citation `\@citeb ' on page \thepage 
                                                  \space undefined\on@line .
l.210 ...ing Cooper and Herskovits \cite{cooper92}
                                                  ).
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


LaTeX Warning: Citation `cooper92' on page  undefined on input line 210.

Missing character: There is no ] in font nullfont!
Missing character: There is no ) in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no . in font nullfont!

Overfull \hbox (20.0pt too wide) in paragraph at lines 201--212
[]
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Overfull \hbox (5.00002pt too wide) in paragraph at lines 201--212
\OT1/cmr/m/n/10 1$
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Overfull \hbox (168.00204pt too wide) in paragraph at lines 201--212
[] [] \OT1/cmr/m/n/10 =
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\OT1/cmr/m/n/10 =
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Overfull \hbox (256.70937pt too wide) in paragraph at lines 201--212
[][] []$
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Overfull \hbox (16.07635pt too wide) in paragraph at lines 201--212
\OML/cmm/m/it/10 k \OT1/cmr/m/n/10 =
 []


Overfull \hbox (5.55557pt too wide) in paragraph at lines 201--212
\OMS/cmsy/m/n/10 jj$
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Overfull \hbox (5.43053pt too wide) in paragraph at lines 201--212
[]
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Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no . in font nullfont!

Overfull \hbox (20.0pt too wide) in paragraph at lines 213--214
[]
 []


Overfull \hbox (5.12846pt too wide) in paragraph at lines 213--214
\OML/cmm/m/it/10 g$
 []


Overfull \hbox (5.20486pt too wide) in paragraph at lines 213--214
\OML/cmm/m/it/10 d$ 
 []


! LaTeX Error: Environment proposition undefined.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.215  \begin{proposition}
                          
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

Missing character: There is no D in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
! Undefined control sequence.
l.216  Define $d_{min}=\sum_{v\in\V
                                   }\left(\log(k-1+N_v)!-\log(k-1)!-\log N_v...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no , in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
! Undefined control sequence.
<recently read> \D 
                   
l.216 ...N_v$ denotes the number of samples in $\D
                                                  $ with $X=v$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no w in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
! Undefined control sequence.
l.217  Then $d(\Pa
                  )\ge d_{min}$ for each $\Pa\in\X$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no h in font nullfont!
! Undefined control sequence.
<recently read> \Pa 
                    
l.217  Then $d(\Pa)\ge d_{min}$ for each $\Pa
                                             \in\X$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.217  Then $d(\Pa)\ge d_{min}$ for each $\Pa\in\X
                                                  $.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no . in font nullfont!

! LaTeX Error: \begin{document} ended by \end{proposition}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.218  \end{proposition}
                        
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.


Overfull \hbox (20.0pt too wide) in paragraph at lines 216--219
[]
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Overfull \hbox (31.1291pt too wide) in paragraph at lines 216--219
\OML/cmm/m/it/10 d[] \OT1/cmr/m/n/10 =
 []


Overfull \hbox (202.16997pt too wide) in paragraph at lines 216--219
[][] []$
 []


Overfull \hbox (12.7859pt too wide) in paragraph at lines 216--219
\OML/cmm/m/it/10 N[]$
 []


Overfull \hbox (19.62494pt too wide) in paragraph at lines 216--219
\OML/cmm/m/it/10 X \OT1/cmr/m/n/10 =
 []


Overfull \hbox (5.20601pt too wide) in paragraph at lines 216--219
\OML/cmm/m/it/10 v$
 []


Overfull \hbox (23.53818pt too wide) in paragraph at lines 216--219
\OML/cmm/m/it/10 d\OT1/cmr/m/n/10 () \OMS/cmsy/m/n/10 ^^U
 []


Overfull \hbox (20.5736pt too wide) in paragraph at lines 216--219
\OML/cmm/m/it/10 d[]$
 []


Overfull \hbox (6.66669pt too wide) in paragraph at lines 216--219
\OMS/cmsy/m/n/10 2$
 []

Missing character: There is no B in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no y in font nullfont!
! Undefined control sequence.
l.220 ...sition of the local score given by $s(\Pa
                                                  )=g'(\Pa)+d'(\Pa)$ with th...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.220 ...f the local score given by $s(\Pa)=g'(\Pa
                                                  )+d'(\Pa)$ with the compon...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.220 ...cal score given by $s(\Pa)=g'(\Pa)+d'(\Pa
                                                  )$ with the components $g'...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no w in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
! Undefined control sequence.
l.220 ...\Pa)+d'(\Pa)$ with the components $g'(\Pa
                                                  )=g(\Pa)+d_{min}$ and $d'(...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.220 ...(\Pa)$ with the components $g'(\Pa)=g(\Pa
                                                  )+d_{min}$ and $d'(\Pa)=d(...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
! Undefined control sequence.
l.220 ...ents $g'(\Pa)=g(\Pa)+d_{min}$ and $d'(\Pa
                                                  )=d(\Pa)-d_{min}$ satisfie...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.220 ...'(\Pa)=g(\Pa)+d_{min}$ and $d'(\Pa)=d(\Pa
                                                  )-d_{min}$ satisfies all t...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no q in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no A in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no m in font nullfont!
! Undefined control sequence.
<write> ...rning: Reference `a2' on page \thepage 
                                                  \space undefined\on@line .
l.220 ...ssumptions required by Algorithm \ref{a2}
                                                  .
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


LaTeX Warning: Reference `a2' on page  undefined on input line 220.

Missing character: There is no . in font nullfont!
Missing character: There is no L in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no x in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no . in font nullfont!

Overfull \hbox (20.0pt too wide) in paragraph at lines 220--222
[]
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Overfull \hbox (23.02081pt too wide) in paragraph at lines 220--222
\OML/cmm/m/it/10 s\OT1/cmr/m/n/10 () =
 []


Overfull \hbox (23.48962pt too wide) in paragraph at lines 220--222
\OML/cmm/m/it/10 g[]\OT1/cmr/m/n/10 () +
 []


Overfull \hbox (15.78822pt too wide) in paragraph at lines 220--222
\OML/cmm/m/it/10 d[]\OT1/cmr/m/n/10 ()$
 []


Overfull \hbox (26.26733pt too wide) in paragraph at lines 220--222
\OML/cmm/m/it/10 g[]\OT1/cmr/m/n/10 () =
 []


Overfull \hbox (20.68407pt too wide) in paragraph at lines 220--222
\OML/cmm/m/it/10 g\OT1/cmr/m/n/10 () +
 []


Overfull \hbox (20.5736pt too wide) in paragraph at lines 220--222
\OML/cmm/m/it/10 d[]$
 []


Overfull \hbox (26.34373pt too wide) in paragraph at lines 220--222
\OML/cmm/m/it/10 d[]\OT1/cmr/m/n/10 () =
 []


Overfull \hbox (20.76047pt too wide) in paragraph at lines 220--222
\OML/cmm/m/it/10 d\OT1/cmr/m/n/10 () \OMS/cmsy/m/n/10 ^^@
 []


Overfull \hbox (20.5736pt too wide) in paragraph at lines 220--222
\OML/cmm/m/it/10 d[]$
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Overfull \hbox (10.86105pt too wide) in paragraph at lines 220--222
[]
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! LaTeX Error: Environment theorem undefined.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.223  \begin{theorem}
                      
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no - in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no x in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no A in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no m in font nullfont!
! Undefined control sequence.
<write> ...rning: Reference `a2' on page \thepage 
                                                  \space undefined\on@line .
l.224 ...ase time complexity of Algorithm \ref{a2}
                                                   for the BDe score with th...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


LaTeX Warning: Reference `a2' on page  undefined on input line 224.

Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no B in font nullfont!
Missing character: There is no D in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no y in font nullfont!
! Undefined control sequence.
l.224 ...sition of the local score given by $s(\Pa
                                                  )=g'(\Pa)+d'(\Pa)$ is $\OO...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.224 ...f the local score given by $s(\Pa)=g'(\Pa
                                                  )+d'(\Pa)$ is $\OO(n^{N\lo...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.224 ...cal score given by $s(\Pa)=g'(\Pa)+d'(\Pa
                                                  )$ is $\OO(n^{N\log_{\alph...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
! Undefined control sequence.
<recently read> \OO 
                    
l.224 ...given by $s(\Pa)=g'(\Pa)+d'(\Pa)$ is $\OO
                                                  (n^{N\log_{\alpha^{-1}}k}N...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no . in font nullfont!

! LaTeX Error: \begin{document} ended by \end{theorem}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.225  \end{theorem}
                    
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.


Overfull \hbox (20.0pt too wide) in paragraph at lines 224--226
[]
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Overfull \hbox (10.86105pt too wide) in paragraph at lines 224--226
[]
 []


Overfull \hbox (23.02081pt too wide) in paragraph at lines 224--226
\OML/cmm/m/it/10 s\OT1/cmr/m/n/10 () =
 []


Overfull \hbox (23.48962pt too wide) in paragraph at lines 224--226
\OML/cmm/m/it/10 g[]\OT1/cmr/m/n/10 () +
 []


Overfull \hbox (15.78822pt too wide) in paragraph at lines 224--226
\OML/cmm/m/it/10 d[]\OT1/cmr/m/n/10 ()$
 []


Overfull \hbox (103.64667pt too wide) in paragraph at lines 224--226
\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 n[]N[] [][] k\OT1/cmr/m/n/10 )$
 []

! Undefined control sequence.
l.228 \subsection
                 {Mutual information test}
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no M in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no i in font nullfont!
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Overfull \hbox (20.0pt too wide) in paragraph at lines 228--229
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\citation{deCampos}
! Undefined control sequence.
<write> ...: Citation `\@citeb ' on page \thepage 
                                                  \space undefined\on@line .
l.230 ...sed on information theory \cite{deCampos}
                                                  . Briefly speaking, this m...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
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and I'll forget about whatever was undefined.


LaTeX Warning: Citation `deCampos' on page  undefined on input line 230.

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Overfull \hbox (5.43053pt too wide) in paragraph at lines 230--231
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Missing character: There is no k in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no L in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
LaTeX Font Info:    Try loading font information for OMS+cmr on input line 233.

(/usr/share/texmf-texlive/tex/latex/base/omscmr.fd
File: omscmr.fd 1999/05/25 v2.5h Standard LaTeX font definitions
)
LaTeX Font Info:    Font shape `OMS/cmr/m/n' in size <10> not available
(Font)              Font shape `OMS/cmsy/m/n' tried instead on input line 233.
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no L in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no ' in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!

! Undefined control sequence.
<recently read> \Pa 
                    
l.235 as $\Pa
             _i = \{X_{i1},...,X_{is_i}\}$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no . in font nullfont!
Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no M in font nullfont!
Missing character: There is no I in font nullfont!
Missing character: There is no T in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no [ in font nullfont!
\citation{globMIT}
! Undefined control sequence.
<write> ...: Citation `\@citeb ' on page \thepage 
                                                  \space undefined\on@line .
l.236 ...core is defined as follows \cite{globMIT}
                                                  :
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


LaTeX Warning: Citation `globMIT' on page  undefined on input line 236.

Missing character: There is no ] in font nullfont!
Missing character: There is no : in font nullfont!

Overfull \hbox (20.0pt too wide) in paragraph at lines 232--237
[]
 []


Overfull \hbox (7.99171pt too wide) in paragraph at lines 232--237
\OMS/cmsy/m/n/10 D$
 []


Overfull \hbox (9.12497pt too wide) in paragraph at lines 232--237
\OML/cmm/m/it/10 N$
 []


Overfull \hbox (6.54169pt too wide) in paragraph at lines 232--237
\OMS/cmsy/m/n/10 G$
 []


Overfull \hbox (19.62494pt too wide) in paragraph at lines 232--237
\OML/cmm/m/it/10 X \OT1/cmr/m/n/10 =
 []


Overfull \hbox (53.72113pt too wide) in paragraph at lines 232--237
\OMS/cmsy/m/n/10 f\OML/cmm/m/it/10 X[]; :::; X[]\OMS/cmsy/m/n/10 g$
 []


Overfull \hbox (6.00235pt too wide) in paragraph at lines 232--237
\OML/cmm/m/it/10 n$
 []


Overfull \hbox (46.17484pt too wide) in paragraph at lines 232--237
\OMS/cmsy/m/n/10 f\OML/cmm/m/it/10 r[]; :::; r[]$\OMS/cmsy/m/n/10 g
 []


Overfull \hbox (11.61401pt too wide) in paragraph at lines 232--237
\OML/cmm/m/it/10 X[]$
 []


Overfull \hbox (6.54169pt too wide) in paragraph at lines 232--237
\OMS/cmsy/m/n/10 G$
 []


Overfull \hbox (53.83224pt too wide) in paragraph at lines 232--237
\OMS/cmsy/m/n/10 f\OML/cmm/m/it/10 r[]; :::; r[]\OMS/cmsy/m/n/10 g$
 []


Overfull \hbox (13.8848pt too wide) in paragraph at lines 232--237
[] \OT1/cmr/m/n/10 =
 []


Overfull \hbox (61.37854pt too wide) in paragraph at lines 232--237
\OMS/cmsy/m/n/10 f\OML/cmm/m/it/10 X[]; :::; X[]\OMS/cmsy/m/n/10 g$
 []


Overfull \hbox (5.43053pt too wide) in paragraph at lines 232--237
[] 
 []

! Undefined control sequence.
l.237 $$\mathcal{S(G:D)} = \sum_{i=0; \Pa
                                         _i \neq \emptyset}^n \{ 2N \cdot I(...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.237 ... \neq \emptyset}^n \{ 2N \cdot I(X_i, \Pa
                                                  _i) - \sum_{j=1}^{s_i} \ch...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


Overfull \hbox (197.96095pt too wide) detected at line 237
[] \OT1/cmr/m/n/10 = []\OMS/cmsy/m/n/10 f\OT1/cmr/m/n/10 2\OML/cmm/m/it/10 N \O
MS/cmsy/m/n/10 ^^A \OML/cmm/m/it/10 I\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 X[];[] \
OT1/cmr/m/n/10 ) \OMS/cmsy/m/n/10 ^^@ [] \OML/cmm/m/it/10 ^^_[]\OMS/cmsy/m/n/10
 g
 []

Missing character: There is no I in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no a in font nullfont!
! Undefined control sequence.
l.239 In this formula $I(X_i, \Pa
                                 _i)$ denotes the mutual information between...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!

Overfull \hbox (20.0pt too wide) in paragraph at lines 239--240
[]
 []


Overfull \hbox (32.34605pt too wide) in paragraph at lines 239--240
\OML/cmm/m/it/10 I\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 X[];[] \OT1/cmr/m/n/10 )$
 []


Overfull \hbox (11.61401pt too wide) in paragraph at lines 239--240
\OML/cmm/m/it/10 X[]$
 []


Overfull \hbox (7.99171pt too wide) in paragraph at lines 239--240
\OMS/cmsy/m/n/10 D$
 []


Overfull \hbox (182.50832pt too wide) detected at line 240
\OML/cmm/m/it/10 I\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 X\OT1/cmr/m/n/10 ; \OML/cmm
/m/it/10 Y\OT1/cmr/m/n/10 ) = [] [] \OML/cmm/m/it/10 p\OT1/cmr/m/n/10 (\OML/cmm
/m/it/10 x; y\OT1/cmr/m/n/10 ) [] []
 []

Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no - in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no q in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no I in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!

Overfull \hbox (35.41783pt too wide) in paragraph at lines 240--242
$\OML/cmm/m/it/10 ^^_[]$
 []


Overfull \hbox (12.77782pt too wide) in paragraph at lines 240--242
\OT1/cmr/m/n/10 1 \OMS/cmsy/m/n/10 ^^@
 []


Overfull \hbox (6.43404pt too wide) in paragraph at lines 240--242
\OML/cmm/m/it/10 $
 []


Overfull \hbox (95.82303pt too wide) detected at line 242
\OML/cmm/m/it/10 p\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 ^^_[]\OT1/cmr/m/n/10 (\OML/
cmm/m/it/10 l[]\OT1/cmr/m/n/10 ) \OMS/cmsy/m/n/10 ^^T \OML/cmm/m/it/10 ^^_[]\OT
1/cmr/m/n/10 ) = \OML/cmm/m/it/10 
 []

Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!

Overfull \hbox (24.07846pt too wide) in paragraph at lines 242--244
\OML/cmm/m/it/10 l[]$
 []

! Misplaced alignment tab character &.
l.245 ...) \prod_{k=1}^{j-1} r_{i \sigma_i (k)}, &
                                                   \text{$j=2..,s_i$}.\\
I can't figure out why you would want to use a tab mark
here. If you just want an ampersand, the remedy is
simple: Just type `I\&' now. But if some right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Undefined control sequence.
l.245 ...d_{k=1}^{j-1} r_{i \sigma_i (k)}, & \text
                                                  {$j=2..,s_i$}.\\
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Missing } inserted.
<inserted text> 
                }
l.245 ...{k=1}^{j-1} r_{i \sigma_i (k)}, & \text{$
                                                  j=2..,s_i$}.\\
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing \endgroup inserted.
<inserted text> 
                \endgroup 
l.245 ...{k=1}^{j-1} r_{i \sigma_i (k)}, & \text{$
                                                  j=2..,s_i$}.\\
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Display math should end with $$.
<to be read again> 
                   j
l.245 ...k=1}^{j-1} r_{i \sigma_i (k)}, & \text{$j
                                                  =2..,s_i$}.\\
The `$' that I just saw supposedly matches a previous `$$'.
So I shall assume that you typed `$$' both times.


Overfull \hbox (170.13902pt too wide) detected at line 245
\OML/cmm/m/it/10 l[] \OT1/cmr/m/n/10 = [] \OML/cmm/m/it/10 r[] \OMS/cmsy/m/n/10
 ^^@ \OT1/cmr/m/n/10 1)(\OML/cmm/m/it/10 r[] \OMS/cmsy/m/n/10 ^^@ \OT1/cmr/m/n/
10 1) [] \OML/cmm/m/it/10 r[]; []
 []

Missing character: There is no j in font nullfont!
Missing character: There is no = in font nullfont!
Missing character: There is no 2 in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no s in font nullfont!
! Missing $ inserted.
<inserted text> 
                $
l.245 ...-1} r_{i \sigma_i (k)}, & \text{$j=2..,s_
                                                  i$}.\\
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Too many }'s.
l.245 ... r_{i \sigma_i (k)}, & \text{$j=2..,s_i$}
                                                  .\\
You've closed more groups than you opened.
Such booboos are generally harmless, so keep going.

Missing character: There is no . in font nullfont!
Missing character: There is no ( in font nullfont!
Missing character: There is no r in font nullfont!
! Missing $ inserted.
<inserted text> 
                $
l.246    (r_
            i-1)(r_{i \sigma_i (j)} -1), & \text{$j=1$}.
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Misplaced alignment tab character &.
l.246    (r_i-1)(r_{i \sigma_i (j)} -1), &
                                           \text{$j=1$}.
I can't figure out why you would want to use a tab mark
here. If you just want an ampersand, the remedy is
simple: Just type `I\&' now. But if some right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Undefined control sequence.
l.246    (r_i-1)(r_{i \sigma_i (j)} -1), & \text
                                                {$j=1$}.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Missing } inserted.
<inserted text> 
                }
l.246    (r_i-1)(r_{i \sigma_i (j)} -1), & \text{$
                                                  j=1$}.
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

Missing character: There is no j in font nullfont!
Missing character: There is no = in font nullfont!
Missing character: There is no 1 in font nullfont!
! Extra }, or forgotten $.
<recently read> }
                 
l.246 ...1)(r_{i \sigma_i (j)} -1), & \text{$j=1$}
                                                  .
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.


! LaTeX Error: \begin{document} ended by \end{cases}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.247  \end{cases}
                  
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Missing $ inserted.
<inserted text> 
                $
l.247  \end{cases}
                  
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Extra \endgroup.
<recently read> \endgroup 
                          
l.247  \end{cases}
                  
Things are pretty mixed up, but I think the worst is over.


Overfull \hbox (3.32928pt too wide) in paragraph at lines 245--248
$[]$ 
 []


Overfull \hbox (11.10709pt too wide) in paragraph at lines 245--248
[] \OMS/cmsy/m/n/10 ^^@
 []


Overfull \hbox (46.16187pt too wide) in paragraph at lines 245--248
\OT1/cmr/m/n/10 1)(\OML/cmm/m/it/10 r[] \OMS/cmsy/m/n/10 ^^@
 []


Overfull \hbox (16.11111pt too wide) in paragraph at lines 245--248
\OT1/cmr/m/n/10 1)\OML/cmm/m/it/10 ; []$$:$ 
 []

! Display math should end with $$.
<to be read again> 
                   \sigma 
l.249 where $\sigma
                   _i = \{\sigma_i (1),...,\sigma_i(s_i)\}$ is any permutati...
The `$' that I just saw supposedly matches a previous `$$'.
So I shall assume that you typed `$$' both times.


Overfull \hbox (27.29173pt too wide) detected at line 249
\OML/cmm/m/it/10 where
 []

! Missing $ inserted.
<inserted text> 
                $
l.249 where $\sigma
                   _i = \{\sigma_i (1),...,\sigma_i(s_i)\}$ is any permutati...
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no x in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
! Undefined control sequence.
<recently read> \Pa 
                    
l.250 $\{1...s_i\}$ of $\Pa
                           _i$ such that, the number of states of the variables
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no . in font nullfont!

Overfull \hbox (19.59892pt too wide) in paragraph at lines 249--252
$\OML/cmm/m/it/10 ^^[[] \OT1/cmr/m/n/10 =
 []


Overfull \hbox (73.88144pt too wide) in paragraph at lines 249--252
\OMS/cmsy/m/n/10 f\OML/cmm/m/it/10 ^^[[]\OT1/cmr/m/n/10 (1)\OML/cmm/m/it/10 ; :
::; ^^[[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 s[]\OT1/cmr/m/n/10 )\OMS/cmsy/m/n/10
 g$
 []


Overfull \hbox (31.35019pt too wide) in paragraph at lines 249--252
\OMS/cmsy/m/n/10 f\OT1/cmr/m/n/10 1\OML/cmm/m/it/10 :::s[]\OMS/cmsy/m/n/10 g$
 []


Overfull \hbox (3.32928pt too wide) in paragraph at lines 249--252
[]$
 []

Missing character: There is no R in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
! Undefined control sequence.
l.253 Recall the decomposition $ S_{MIT}(\Pa
                                            _i) = d_{MIT}(\Pa_i) + g_{MIT}(\...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.253 ...omposition $ S_{MIT}(\Pa_i) = d_{MIT}(\Pa
                                                  _i) + g_{MIT}(\Pa_i) $.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.253 ...IT}(\Pa_i) = d_{MIT}(\Pa_i) + g_{MIT}(\Pa
                                                  _i) $.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no . in font nullfont!
Missing character: There is no I in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no : in font nullfont!

Overfull \hbox (20.0pt too wide) in paragraph at lines 253--255
[]
 []


Overfull \hbox (46.5588pt too wide) in paragraph at lines 253--255
\OML/cmm/m/it/10 S[]\OT1/cmr/m/n/10 ([]) =
 []


Overfull \hbox (42.85402pt too wide) in paragraph at lines 253--255
\OML/cmm/m/it/10 d[]\OT1/cmr/m/n/10 ([]) +
 []


Overfull \hbox (34.64104pt too wide) in paragraph at lines 253--255
\OML/cmm/m/it/10 g[]\OT1/cmr/m/n/10 ([])$
 []

! Undefined control sequence.
l.255 $$ d_{MIT}(\Pa
                    _i) = 2N\cdot I(X_i, \mathbf{X}) - 2N \cdot I(X_i, \Pa_i...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.255 ... I(X_i, \mathbf{X}) - 2N \cdot I(X_i, \Pa
                                                  _i) $$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


Overfull \hbox (160.05pt too wide) detected at line 255
\OML/cmm/m/it/10 d[]\OT1/cmr/m/n/10 ([]) = 2\OML/cmm/m/it/10 N \OMS/cmsy/m/n/10
 ^^A \OML/cmm/m/it/10 I\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 X[]; \OT1/cmr/bx/n/10 
X\OT1/cmr/m/n/10 ) \OMS/cmsy/m/n/10 ^^@ \OT1/cmr/m/n/10 2\OML/cmm/m/it/10 N \OM
S/cmsy/m/n/10 ^^A \OML/cmm/m/it/10 I\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 X[];[] \O
T1/cmr/m/n/10 )
 []

! Undefined control sequence.
l.256 $$ g_{MIT}(\Pa
                    _i) = \sum_{j=1}^{s_i} \chi_{\alpha l_i \sigma_i(j)} $$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


Overfull \hbox (99.50319pt too wide) detected at line 256
\OML/cmm/m/it/10 g[]\OT1/cmr/m/n/10 ([]) = [] \OML/cmm/m/it/10 ^^_[]
 []

Missing character: There is no R in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no j in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no x in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no A in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no 2 in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no H in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no M in font nullfont!
Missing character: There is no I in font nullfont!
Missing character: There is no T in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
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! LaTeX Error: Environment ass undefined.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.263 \begin{ass}
                 [uniformity]\label{as4}
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

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! LaTeX Error: \begin{document} ended by \end{ass}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.265 \end{ass}
               
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.


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! LaTeX Error: Environment theorem undefined.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.268  \begin{theorem}
                       \cite{globMITManual}
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

Missing character: There is no [ in font nullfont!
\citation{globMITManual}
! Undefined control sequence.
<write> ...: Citation `\@citeb ' on page \thepage 
                                                  \space undefined\on@line .
l.268  \begin{theorem} \cite{globMITManual}
                                           
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


LaTeX Warning: Citation `globMITManual' on page  undefined on input line 268.

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! Undefined control sequence.
<write> ...rning: Reference `a2' on page \thepage 
                                                  \space undefined\on@line .
l.269 ...ase time complexity of Algorithm \ref{a2}
                                                   for the MIT score under t...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


LaTeX Warning: Reference `a2' on page  undefined on input line 269.

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! LaTeX Error: \begin{document} ended by \end{theorem}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.270  \end{theorem}
                    
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.


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! Undefined control sequence.
l.273 \subsection
                 {Continuous variables}
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

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Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no I in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no z in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no M in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
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Missing character: There is no o in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
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Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
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Missing character: There is no n in font nullfont!
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Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
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Missing character: There is no o in font nullfont!
Missing character: There is no u in font nullfont!
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Missing character: There is no s in font nullfont!
Missing character: There is no . in font nullfont!

Overfull \hbox (20.0pt too wide) in paragraph at lines 275--281
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 []

Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no v in font nullfont!
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Missing character: There is no r in font nullfont!
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Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
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Missing character: There is no x in font nullfont!
Missing character: There is no t in font nullfont!
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Missing character: There is no e in font nullfont!
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Missing character: There is no f in font nullfont!
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Missing character: There is no w in font nullfont!
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Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
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Missing character: There is no a in font nullfont!
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Missing character: There is no d in font nullfont!
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Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
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Missing character: There is no b in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no t in font nullfont!
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Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no M in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no x in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
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Missing character: There is no r in font nullfont!
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Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no b in font nullfont!
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Missing character: There is no e in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
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Missing character: There is no u in font nullfont!
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Missing character: There is no s in font nullfont!
Missing character: There is no ( in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no ) in font nullfont!
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Missing character: There is no f in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no C in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no q in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no : in font nullfont!

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\OML/cmm/m/it/10 X$
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\OT1/cmr/m/it/10 low
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Overfull \hbox (17.88878pt too wide) in paragraph at lines 292--301
\OT1/cmr/m/it/10 high
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Overfull \hbox (11.87498pt too wide) in paragraph at lines 292--301
\OML/cmm/m/it/10 X[]$
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\OML/cmm/m/it/10 X$
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Overfull \hbox (9.06943pt too wide) in paragraph at lines 292--301
\OML/cmm/m/it/10 X$
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! Undefined control sequence.
l.302 P(X|\Pa
             )=
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.303 \sum_{v\in\Vc
                   }\sum_{\vp\in\Vc^{|\Pa|}}P(X|X'=v)P(X'=v|\Pa'=\vp)P(\Pa'=...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.303 \sum_{v\in\Vc}\sum_{\vp
                             \in\Vc^{|\Pa|}}P(X|X'=v)P(X'=v|\Pa'=\vp)P(\Pa'=...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.303 \sum_{v\in\Vc}\sum_{\vp\in\Vc
                                   ^{|\Pa|}}P(X|X'=v)P(X'=v|\Pa'=\vp)P(\Pa'=...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.303 \sum_{v\in\Vc}\sum_{\vp\in\Vc^{|\Pa
                                         |}}P(X|X'=v)P(X'=v|\Pa'=\vp)P(\Pa'=...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.303 ...um_{\vp\in\Vc^{|\Pa|}}P(X|X'=v)P(X'=v|\Pa
                                                  '=\vp)P(\Pa'=\vp|\Pa)
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.303 ...vp\in\Vc^{|\Pa|}}P(X|X'=v)P(X'=v|\Pa'=\vp
                                                  )P(\Pa'=\vp|\Pa)
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.303 ...Vc^{|\Pa|}}P(X|X'=v)P(X'=v|\Pa'=\vp)P(\Pa
                                                  '=\vp|\Pa)
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.303 ...\Pa|}}P(X|X'=v)P(X'=v|\Pa'=\vp)P(\Pa'=\vp
                                                  |\Pa)
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.303 ...}}P(X|X'=v)P(X'=v|\Pa'=\vp)P(\Pa'=\vp|\Pa
                                                  )
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


Overfull \hbox (224.70334pt too wide) detected at line 304
\OML/cmm/m/it/10 P\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 X\OMS/cmsy/m/n/10 j\OT1/cmr
/m/n/10 ) = [] [] \OML/cmm/m/it/10 P\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 X\OMS/cms
y/m/n/10 j\OML/cmm/m/it/10 X[] \OT1/cmr/m/n/10 = \OML/cmm/m/it/10 v\OT1/cmr/m/n
/10 )\OML/cmm/m/it/10 P\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 X[] \OT1/cmr/m/n/10 = 
\OML/cmm/m/it/10 v\OMS/cmsy/m/n/10 j[] \OT1/cmr/m/n/10 =)\OML/cmm/m/it/10 P\OT1
/cmr/m/n/10 ([]= \OMS/cmsy/m/n/10 j\OT1/cmr/m/n/10 )
 []

Missing character: There is no C in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no E in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no ( in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no ) in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no D in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
! Undefined control sequence.
l.321 $P(\Pa
            '|\Pa)=\prod_{Y\in\Pa}P(Y'|Y)$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.321 $P(\Pa'|\Pa
                 )=\prod_{Y\in\Pa}P(Y'|Y)$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.321 $P(\Pa'|\Pa)=\prod_{Y\in\Pa
                                 }P(Y'|Y)$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no . in font nullfont!
Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no G in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no x in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no z in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no y in font nullfont!
! Undefined control sequence.
l.323 ...sian mixtures, parameterized by $P(X'|\Pa
                                                  ')$,
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no , in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no . in font nullfont!

Overfull \hbox (20.0pt too wide) in paragraph at lines 315--326
[]
 []


Overfull \hbox (39.30904pt too wide) in paragraph at lines 315--326
\OML/cmm/m/it/10 P\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 X\OMS/cmsy/m/n/10 j\OML/cmm
/m/it/10 X[]\OT1/cmr/m/n/10 )$
 []


Overfull \hbox (9.06943pt too wide) in paragraph at lines 315--326
\OML/cmm/m/it/10 X$
 []


Overfull \hbox (9.06943pt too wide) in paragraph at lines 315--326
\OML/cmm/m/it/10 X$
 []


Overfull \hbox (8.1777pt too wide) in paragraph at lines 315--326
\OT1/cmr/m/it/10 k-
 []


Overfull \hbox (27.08871pt too wide) in paragraph at lines 315--326
\OT1/cmr/m/it/10 means
 []


Overfull \hbox (16.07635pt too wide) in paragraph at lines 315--326
\OML/cmm/m/it/10 k \OT1/cmr/m/n/10 =
 []


Overfull \hbox (5.00002pt too wide) in paragraph at lines 315--326
\OT1/cmr/m/n/10 2$
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Overfull \hbox (20.0pt too wide) in paragraph at lines 327--335
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Overfull \hbox (20.0pt too wide) in paragraph at lines 337--339
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! LaTeX Error: Environment theorem undefined.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.340  \begin{theorem}
                      
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

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! Undefined control sequence.
<write> ...rning: Reference `a2' on page \thepage 
                                                  \space undefined\on@line .
l.341 ...ase time complexity of Algorithm \ref{a2}
                                                   for the continuous MDL sc...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
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LaTeX Warning: Reference `a2' on page  undefined on input line 341.

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Missing character: There is no L in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
! Undefined control sequence.
<recently read> \OO 
                    
l.341 ...{a2} for the continuous MDL score is $\OO
                                                  (n^{\log N}N^2)$.
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no . in font nullfont!

! LaTeX Error: \begin{document} ended by \end{theorem}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.342  \end{theorem}
                    
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.


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Overfull \hbox (10.86105pt too wide) in paragraph at lines 341--343
[]
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Overfull \hbox (46.6855pt too wide) in paragraph at lines 341--343
\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 n[]N[]\OT1/cmr/m/n/10 )$
 []


! LaTeX Error: Environment theorem undefined.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.344  \begin{theorem}
                      
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no - in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no x in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no A in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no m in font nullfont!
! Undefined control sequence.
<write> ...rning: Reference `a2' on page \thepage 
                                                  \space undefined\on@line .
l.345 ...ase time complexity of Algorithm \ref{a2}
                                                   for the continuous BDe sc...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.


LaTeX Warning: Reference `a2' on page  undefined on input line 345.

Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no B in font nullfont!
Missing character: There is no D in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no y in font nullfont!
! Undefined control sequence.
l.345 ...sition of the local score given by $s(\Pa
                                                  )=g'(\Pa)+d'(\Pa)$ is $\OO...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.345 ...f the local score given by $s(\Pa)=g'(\Pa
                                                  )+d'(\Pa)$ is $\OO((2n)^\f...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.345 ...cal score given by $s(\Pa)=g'(\Pa)+d'(\Pa
                                                  )$ is $\OO((2n)^\frac{N}{\...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
! Undefined control sequence.
<recently read> \OO 
                    
l.345 ...given by $s(\Pa)=g'(\Pa)+d'(\Pa)$ is $\OO
                                                  ((2n)^\frac{N}{\log\alpha^...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no . in font nullfont!

! LaTeX Error: \begin{document} ended by \end{theorem}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.346  \end{theorem}
                    
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.


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[]
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Overfull \hbox (10.86105pt too wide) in paragraph at lines 345--347
[]
 []


Overfull \hbox (23.02081pt too wide) in paragraph at lines 345--347
\OML/cmm/m/it/10 s\OT1/cmr/m/n/10 () =
 []


Overfull \hbox (23.48962pt too wide) in paragraph at lines 345--347
\OML/cmm/m/it/10 g[]\OT1/cmr/m/n/10 () +
 []


Overfull \hbox (15.78822pt too wide) in paragraph at lines 345--347
\OML/cmm/m/it/10 d[]\OT1/cmr/m/n/10 ()$
 []


Overfull \hbox (62.60233pt too wide) in paragraph at lines 345--347
\OT1/cmr/m/n/10 ((2\OML/cmm/m/it/10 n\OT1/cmr/m/n/10 )[]\OML/cmm/m/it/10 N\OT1/
cmr/m/n/10 )$
 []

! Undefined control sequence.
l.348  \subsection
                  {Network density control}
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

Missing character: There is no N in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no l in font nullfont!

Overfull \hbox (20.0pt too wide) in paragraph at lines 348--349
[]
 []

Missing character: There is no R in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no 2 in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no : in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no z in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
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Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no x in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no x in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
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Missing character: There is no i in font nullfont!
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Missing character: There is no b in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no v in font nullfont!
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Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no - in font nullfont!
Missing character: There is no - in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no - in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no - in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no - in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no - in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no . in font nullfont!

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\OML/cmm/m/it/10 g$
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Missing character: There is no B in font nullfont!
Missing character: There is no N in font nullfont!
Missing character: There is no F in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no 3 in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no : in font nullfont!

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Missing character: There is no O in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no - in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no - in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no . in font nullfont!

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Missing character: There is no O in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no - in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no - in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no ( in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no I in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no ) in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no I in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no ( in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no z in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no ) in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no q in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no . in font nullfont!

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Missing character: There is no I in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no - in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no - in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no . in font nullfont!

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Missing character: There is no O in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no - in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no - in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no R in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no j in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no I in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no z in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no ( in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no B in font nullfont!
Missing character: There is no D in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no j in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no ) in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no E in font nullfont!
Missing character: There is no x in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no j in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no q in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no I in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no . in font nullfont!

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Missing character: There is no T in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no I in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no 1 in font nullfont!
Missing character: There is no - in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no x in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no I in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no 1 in font nullfont!
Missing character: There is no - in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no 2 in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no : in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no F in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no B in font nullfont!
Missing character: There is no N in font nullfont!
Missing character: There is no F in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no q in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no I in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no W in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no k in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no q in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no q in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no I in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no O in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no g in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no m in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no . in font nullfont!

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[]
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Missing character: There is no U in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no v in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no b in font nullfont!
Missing character: There is no l in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no a in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no , in font nullfont!
Missing character: There is no t in font nullfont!
Missing character: There is no y in font nullfont!
Missing character: There is no p in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no I in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no o in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no c in font nullfont!
Missing character: There is no u in font nullfont!
Missing character: There is no r in font nullfont!
Missing character: There is no s in font nullfont!
Missing character: There is no w in font nullfont!
Missing character: There is no h in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no n in font nullfont!
Missing character: There is no . in font nullfont!
Missing character: There is no W in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no d in font nullfont!
Missing character: There is no e in font nullfont!
Missing character: There is no f in font nullfont!
Missing character: There is no i in font nullfont!
Missing character: There is no n in font nullfont!
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)
! Emergency stop.
<*> ...bartek/work/code/bnfinder/doc/methods.tex"}
                                                  
*** (job aborted, no legal \end found)

 
Here is how much of TeX's memory you used:
 73 strings out of 495026
 948 string characters out of 1181802
 61141 words of memory out of 3000000
 3342 multiletter control sequences out of 15000+50000
 5081 words of font info for 19 fonts, out of 3000000 for 9000
 48 hyphenation exceptions out of 8191
 21i,11n,26p,680b,266s stack positions out of 5000i,500n,10000p,200000b,50000s
!  ==> Fatal error occurred, no output PDF file produced!
