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\begin{document}
\begin{LARGE}


%% (2)introduction
\clearpage
{\bf
\noindent
Introduction:\\

\begin{itemize}
\item We apply 
   \begin{itemize}
   \item ECs to neural network model of Associative Memory.
   \end{itemize}
\item We study
   \begin{itemize}
   \item
 behaviors of the model under simple evolutionary processes.
   \end{itemize}
\item[]
\item We observe here
\begin{itemize}
   \item trajectries of the neuron states during evolution,
   \end{itemize}
\item using
\begin{itemize}
   \item a GA that gives perturbations on a fixed weight matrix.
   \end{itemize}
\end{itemize}
}

%% (4)associative memory with Hopfield model
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{\bf
\noindent
The Hopfield Model of Associative Memory:\\
\begin{itemize}
\item stores information by distributing it among neurons;
\item recalls the information from dynamically relaxed state;
\item[]
\item has a capability to tolerate noisy and/or partial input\\in recalling the information (content addressabibity);
\item[]
\item has a limited storage capacity.
\item The capacity is traded-off against basin of attraction.\\
\end{itemize}
}


%% (6)conceptual algorithm
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%%{\bf The Breeder Genetic Algorithm Implementation:}
{\bf The GA Implementation:}
\begin{itemize}
\setlength{\itemsep}{0pt}
\item[]{\bf begin}
   \begin{itemize}
   \item[]{\bf initialize} 256 chromosomes
   \item[]{\bf while} termination criterion not fulfilled {\bf do}
      \begin{itemize}
      \item[]{\bf evaluate} fitness of each individual
      \item[](by the degree to how many patterns are memorized as fixed points)
%%      \item[]{\bf select} the best $T$\% individuals
      \item[]{\bf repeat} until the worst 60\% of the  population are replaced {\bf do} 
         \begin{itemize}
         \item[]{\bf select} two individuals {\it randomly} from the best 40\%
         \item[]{\bf recombine} them with ``discrete crossover'' to produce one offspring
         \item[]{\bf mutate} the offspring
         \end{itemize}
%%    \item[]{\bf od}
      \end{itemize}
   \item[]{\bf return} a set of $w_{ij}$'s
%% \item[]{\bf od}
   \end{itemize}
%%\item[]{\bf end}
\end{itemize}


\clearpage
\begin{figure}[hbtp]
 \begin{center}
   \epsfile{file=fitness.eps,width=21cm,height=14cm}
 \end{center}
\end{figure}

\clearpage
\begin{figure}[hbtp]
 \begin{center}
   \epsfile{file=trajectory-0210.eps,width=7cm,height=5cm}
   \epsfile{file=trajectory-0240.eps,width=7cm,height=5cm}
   \epsfile{file=trajectory-0300.eps,width=7cm,height=5cm}
 \end{center}
\end{figure}

\clearpage
\begin{figure}[hbtp]
 \begin{center}
   \epsfile{file=basin-slide.eps,width=21cm,height=14cm}
 \end{center}
\end{figure}

%% its realization
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{\bf
\noindent
The Associative Memory can be realized with:\\
\begin{itemize}
\item neural network model \\ \hspace*{1.9in}(leyered/recurrent/self-organized)\\
\item immune system model\\
\item etc
\end{itemize}
}

%% (9)GA implementation
\clearpage
\begin{figure}[hbtp]
 \begin{center}
   \epsfile{file=overview.eps,width=21cm,height=14cm}
 \end{center}
\end{figure}


%% (13) future work
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{\bf
\noindent
$\Box$ Conclusions:\\
\begin{itemize}
\item The GA can create fixed point attractors exactly at the location of given patterns starting with Zero matrix;
   \begin{itemize}
   \item (It can be visualized with trajectories of neuron states)
   \end{itemize}
\item But the basin of attractions are very small;
   \begin{itemize}
   \item Due to remaining sprious attractors?
   \end{itemize}
\item[]
\item Can locate all the optima?
   \begin{itemize}
   \item The number and distribution of solutions;
   \end{itemize}
\item[]
\item These studies shed new light on the analysis of the Hopfield model of associative memory.
\end{itemize}
}



\end{LARGE}
\end{document}




