\documentclass[10pt]{beamer}

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\usepackage{times}  % fonts are up to you
\usepackage{graphics}
\usepackage{amsmath}
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\renewcommand{\emph}[1]{\textcolor{red}{\em\bf #1}}

% these will be used later in the title page
\title{Fundamentals of Computational Neuroscience 2e}
%\author{Thomas Trappenberg}


\begin{document}

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\begin{frame}
\titlepage

\date{\today}

\begin{center} {Chapter 5: Cortical organizations and simple networks} \end{center}


\end{frame}
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\begin{frame}
\frametitle{\large \large Brain areas}

\begin{center}
\resizebox{10cm}{!}{\includegraphics{figures/Chapter5/brain.pdf}}
\end{center}

\end{frame}
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\begin{frame}
\frametitle{\large \large Hierarchical connectivity}


\begin{center}
\resizebox{6cm}{!}{\includegraphics{figures/Chapter5/module_cortex.pdf}}
\end{center}

\end{frame}
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\begin{frame}
\frametitle{\large \large Layered cortex}

\begin{center}
\resizebox{10cm}{!}{\includegraphics{figures/Chapter5/cortex_layers.pdf}}
\end{center}

\end{frame}
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\begin{frame}
\frametitle{\large \large Layered cortical architecture}

\begin{center}
\resizebox{6cm}{!}{\includegraphics{figures/Chapter5/layers_schematic1.pdf}}
\hspace*{1cm}
\resizebox{3cm}{!}{\includegraphics{figures/Chapter5/layers_schematic2.pdf}}
\end{center}


\end{frame}
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\begin{frame}
\frametitle{\large \large Cortical maps}

\begin{center}
\resizebox{9cm}{!}{\includegraphics{figures/Chapter5/cortex_column.pdf}}
\end{center}


\end{frame}
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\begin{frame}
\frametitle{\large \large Neuronal chains}

\begin{center}
\resizebox{5cm}{!}{\includegraphics{figures/Chapter5/abeles.pdf}}
\end{center}

\end{frame}
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\begin{frame}
\frametitle{\large \large Netlets}
\begin{center}
\resizebox{10cm}{!}{\includegraphics{figures/Chapter5/netlets.pdf}}
\end{center}


\end{frame}
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\begin{frame}
\frametitle{\large \large Random networks with axonal delay}


\begin{center}
\resizebox{10cm}{!}{\includegraphics{figures/Chapter5/izhikevichNet.pdf}}
\end{center}

{\tiny from Izhikevich 2003/2006}

\end{frame}
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\frame[containsverbatim] { \frametitle{\large \large }
\scriptsize
\begin{verbatim}
 1   % Created by Eugene M. Izhikevich, February 25, 2003
 2   % Excitatory neurons   Inhibitory neurons
 3   Ne=800;                Ni=200;
 4   re=rand(Ne,1);         ri=rand(Ni,1);
 5   a=[0.02*ones(Ne,1);    0.02+0.08*ri];
 6   b=[0.2*ones(Ne,1);     0.25-0.05*ri];
 7   c=[-65+15*re.^2;      -65*ones(Ni,1)];
 8   d=[8-6*re.^2;          2*ones(Ni,1)];
 9   S=[0.5*rand(Ne+Ni,Ne),-rand(Ne+Ni,Ni)];
10
11   v=-65*ones(Ne+Ni,1);  % Initial values of v
12   u=b.*v;               % Initial values of u
13   firings=[];           % spike timings
14
15   for t=1:1000          % simulation of 1000 ms
16      I=[5*randn(Ne,1);2*randn(Ni,1)]; % thalamic input
17      fired=find(v>=30); % indices of spikes
18      if ~isempty(fired)
19         firings=[firings; t+0*fired, fired];
20         v(fired)=c(fired);
21         u(fired)=u(fired)+d(fired);
22         I=I+sum(S(:,fired),2);
23      end;
24      v=v+0.5*(0.04*v.^2+5*v+140-u+I);
25      v=v+0.5*(0.04*v.^2+5*v+140-u+I);
26      u=u+a.*(b.*v-u);
27   end;
28   plot(firings(:,1),firings(:,2),'.');
\end{verbatim}
}


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\begin{frame}
\frametitle{\large \large Further Readings} 

\begin{list}{}{\setlength\itemindent{-.3in}  \setlength\rightmargin{.1in} \setlength\itemsep{0.05in}}
\small

\item  Edward L.~White (1989)
\emph{Cortical circuits}, Birkh\"auser

\item  Moshe Abeles (1991)
\emph{Corticonics: Neural circuits of the cerebral cortex}, Cambridge University Press


\end{list} 

\end{frame}

\end{document}







