\batchmode
\documentclass{article}
\RequirePackage{ifthen}


\usepackage{epsfig}%
\providecommand{\bra}[1]{\left(#1\right)}%
\providecommand{\pot}[1]{\psi_{#1}}%
\providecommand{\nodes}[1]{S_{#1}}%
\providecommand{\nodescap}[1]{S_\mathrm{\scriptscriptstyle #1}}%
\providecommand{\nodescapprime}[1]{S_\mathrm{\scriptscriptstyle #1}'}%
\providecommand{\statecap}[1]{\vec s_\mathrm{\scriptscriptstyle #1}}%
\providecommand{\statecapprime}[1]{{\vec s\makebox[0pt][l]{$\,'$}}_\mathrm{\scriptscriptstyle #1}}%
\providecommand{\ncap}[1]{n_\mathrm{\scriptscriptstyle #1}}%
\providecommand{\marnodes}{S_\mathrm{\scriptscriptstyle mar}}%
\providecommand{\marnodesprime}{S_\mathrm{\scriptscriptstyle mar}'}%
\providecommand{\sepnodes}{S_\mathrm{\scriptscriptstyle sep}}%
\providecommand{\othnodes}{S_\mathrm{\scriptscriptstyle oth}}%
\providecommand{\encnodes}{S_\mathrm{\scriptscriptstyle enc}}%
\providecommand{\clnodes}{S_\mathrm{\scriptscriptstyle cl}}%
\providecommand{\marstate}{\vec s_\mathrm{\scriptscriptstyle mar}}%
\providecommand{\marstateprime}{{\vec s\makebox[0pt][l]{$\,'$}}_\mathrm{\scriptscriptstyle mar}}%
\providecommand{\sepstate}{\vec s_\mathrm{\scriptscriptstyle sep}}%
\providecommand{\othstate}{\vec s_\mathrm{\scriptscriptstyle oth}}%
\providecommand{\nenc}{n_\mathrm{\scriptscriptstyle enc}}%
\providecommand{\nsep}{n_\mathrm{\scriptscriptstyle sep}}%
\providecommand{\prob}[1]{p\left(#1\right)}%
\providecommand{\qrob}[1]{q\left(#1\right)}%
\providecommand{\ubound}[1]{p_+\left(#1\right)}%
\providecommand{\lbound}[1]{p_-\left(#1\right)}%
\providecommand{\norm}[1]{\left\|#1\right\|}%
\providecommand{\trinorm}[1]{\left\{#1\right\}}%
\providecommand{\hide}[1]{}%
\providecommand{\equationref}[1]{Equation~\ref{#1}}%
\providecommand{\sectionref}[1]{Section~\ref{#1}}%
\providecommand{\figureref}[1]{Figure~\ref{#1}}

\usepackage[dvips]{color}


\pagecolor[gray]{.7}

\usepackage[]{inputenc}



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\providecommand{\selectlanguage}[1]{}%
\makeatletter \tracingstats = 1 


\begin{document}
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% !!! IMAGES START HERE !!!

\stepcounter{section}
\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline876}%
$\psi_{i}\left(S_{i}\right)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline878}%
$S_{i}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline880}%
$S$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath88}%
\begin{displaymath}
p\left(S\right)\propto\prod_i\psi_{i}\left(S_{i}\right)
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline882}%
$S_\mathrm{\scriptscriptstyle mar}$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline886}%
$S_\mathrm{\scriptscriptstyle sep}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline888}%
$S_\mathrm{\scriptscriptstyle oth}$%
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\begin{figure}{\centering\begin{tabular}{cccc}
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a&b&c&d
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{\newpage\clearpage
\lthtmldisplayA{displaymath104}%
\begin{displaymath}
S_\mathrm{\scriptscriptstyle sep}=\bigcup_{S_{i}\cap S_\mathrm{\scriptscriptstyle mar}\neq\emptyset}
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline904}%
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{\newpage\clearpage
\lthtmldisplayA{displaymath111}%
\begin{displaymath}
p\left(\vec s_\mathrm{\scriptscriptstyle mar}\,|\,\vec s_\mathrm{\scriptscriptstyle sep}\right)=\sum_{\vec s_\mathrm{\scriptscriptstyle oth}\in S_\mathrm{\scriptscriptstyle oth}}
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{\newpage\clearpage
\lthtmldisplayA{displaymath116}%
\begin{displaymath}
p\left(\vec s_\mathrm{\scriptscriptstyle mar}\right)=\sum_{\vec s_\mathrm{\scriptscriptstyle sep}\in S_\mathrm{\scriptscriptstyle sep}}\sum_{\vec s_\mathrm{\scriptscriptstyle oth}\in S_\mathrm{\scriptscriptstyle oth}}
	\!\!p\left(\vec s_\mathrm{\scriptscriptstyle mar}\vec s_\mathrm{\scriptscriptstyle oth}\,|\,\vec s_\mathrm{\scriptscriptstyle sep}\right)p\left(\vec s_\mathrm{\scriptscriptstyle sep}\right)
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{\newpage\clearpage
\lthtmldisplayA{displaymath126}%
\begin{displaymath}
p_+\left(\vec s_\mathrm{\scriptscriptstyle mar}\right)=\mathrm{max}_{q\left(\vec s_\mathrm{\scriptscriptstyle sep}\right)}\sum_{\vec s_\mathrm{\scriptscriptstyle sep}\in S_\mathrm{\scriptscriptstyle sep}}
	\sum_{\vec s_\mathrm{\scriptscriptstyle oth}\in S_\mathrm{\scriptscriptstyle oth}}
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{\newpage\clearpage
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{\newpage\clearpage
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\begin{displaymath}
\sum_{\vec s_\mathrm{\scriptscriptstyle sep}\in S_\mathrm{\scriptscriptstyle sep}/S_\mathrm{\scriptscriptstyle mar}'}\!\!\!q\left(\vec s_\mathrm{\scriptscriptstyle sep}\right)=
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{\newpage\clearpage
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{\newpage\clearpage
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{\newpage\clearpage
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{\newpage\clearpage
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\begin{align}
\vec x&=q\left(\vec s_\mathrm{\scriptscriptstyle sep}\right)
\\
\vec c&=\sum_{\vec s_\mathrm{\scriptscriptstyle oth}\in S_\mathrm{\scriptscriptstyle oth}}\!\!p\left(\vec s_\mathrm{\scriptscriptstyle mar}\vec s_\mathrm{\scriptscriptstyle oth}\,|\,\vec s_\mathrm{\scriptscriptstyle sep}\right)
=p\left(\vec s_\mathrm{\scriptscriptstyle mar}\,|\,\vec s_\mathrm{\scriptscriptstyle sep}\right)
\\
A&=\left\{\begin{array}{l}
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	\end{array}\right.\quad
\vec b=\left\{\begin{array}{l}
		p_+\left({\vec s\makebox[0pt][l]{$\,'$}}_\mathrm{\scriptscriptstyle mar}\right)\\
		-p_-\left({\vec s\makebox[0pt][l]{$\,'$}}_\mathrm{\scriptscriptstyle mar}\right)
	\end{array}\right.
\qquad\left(\forall_{S_\mathrm{\scriptscriptstyle mar}'\subseteq S_\mathrm{\scriptscriptstyle sep}}
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\end{align}%
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{\newpage\clearpage
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{\newpage\clearpage
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$\vec b$%
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\lthtmldisplayA{displaymath204}%
\begin{displaymath}
\sum_{\vec s_\mathrm{\scriptscriptstyle sep}}q\left(\vec s_\mathrm{\scriptscriptstyle sep}\right)\le1\qquad\textrm{and}\qquad
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{\newpage\clearpage
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{\newpage\clearpage
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$s_2$%
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{\newpage\clearpage
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{\newpage\clearpage
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{\newpage\clearpage
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{\newpage\clearpage
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{\newpage\clearpage
\lthtmldisplayA{displaymath228}%
\begin{displaymath}
q\left(s_1\!=\!1\right)=\sum_{s_2}q\left(s_1\!=\!1,s_2\right)
=q\left(10\right)+q\left(11\right)\le p_+\left(s_1\!=\!1\right)
\end{displaymath}%
\lthtmldisplayZ
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\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1048}%
$\Omega$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmldisplayA{displaymath242}%
\begin{displaymath}
\Omega\left(N\right)=\left\{S_\mathrm{\scriptscriptstyle sep}\;\vert\;\left\|S_\mathrm{\scriptscriptstyle cl}\right\|\le N\,
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{\newpage\clearpage
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$S_\mathrm{\scriptscriptstyle sep}\cup S_\mathrm{\scriptscriptstyle mar}\cup S_\mathrm{\scriptscriptstyle oth}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1056}%
$s$%
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{\newpage\clearpage
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$N$%
\lthtmlinlinemathZ
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{\newpage\clearpage
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$N=2^5$%
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{\newpage\clearpage
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$N=2^8$%
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{\newpage\clearpage
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$\Omega\left(N\right)$%
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\end{document}
