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\markright{(Practice -- Neural Networks)}
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\title{{\large (Brest State Technical University 2009 Spring Semester: Course Practice)}\\
Recurrent Neural Network}
\author{Akira Imada\\
(e-mail akira@bstu.by)\\
\hspace{1in}\\
This document is still under construction and was lastly modified on}

\begin{document}
\maketitle

\clearpage
\section{Model and Method}

\begin{figure}[h]
\begin{center}
\includegraphics[width=4.5cm,height=2cm]{plasticity-course.eps}
\end{center}         
\end{figure}

\subsection{Continuous Neuron}
\subsubsection*{Renew of states}
\begin{displaymath}
x_i(t+1) = f(\sum_{j=1}^N w_{ij}(t)x_j(t) + I_i)   \hspace{.3in} (i = 1,2,3\cdots, N)
\end{displaymath}

\subsubsection*{Transfer function -- Sigmoid}
\begin{displaymath}
f(x) = \frac {1 + \tanh(Gx)}{2}
\end{displaymath}

%%\noindent
%%where set $G=10$ for example.


\begin{figure}[h]
\begin{center}
\includegraphics[width=10cm,height=5cm]{sigmoid.eps}
\end{center}         
\end{figure}


\subsubsection*{Update of weights}
\begin{displaymath}
w_{ij} (t+1) = w_{ij}(t) + \eta x_i(t+1) x_j(t)
\end{displaymath}

\begin{center}(where $\eta = 0.01$ here, for example.)\end{center}


\clearpage
\subsection{McCulloh-Pits Neuron}
\subsubsection*{Renew of states}

\begin{displaymath}
s_i (t+1) = {\mbox sgn}( {\sum_{j=0}^{99} {w_{ij}s_j (t)})}
\end{displaymath}

\subsubsection*{Transfer function}

\begin{figure}[h]
\begin{center}
\includegraphics[width=7cm,height=3cm]{sgn.eps}
\end{center}         
\end{figure}


\end{document}

