% LaTeX file for generating the Model Description Table in Fig. 5 of
%
%  Nordlie E, Gewaltig M-O, Plesser HE (2009) 
%  Towards Reproducible Descriptions of Neuronal Network Models.
%  PLoS Comput Biol 5(8): e1000456. 
%
%  Paper URL : http://dx.doi.org/10.1371/journal.pcbi.1000456
%  Figure URL: http://dx.doi.org/10.1371/journal.pcbi.1000456.g005
%
% This file is released under a
%
%   Creative Commons Attribution, non-commercial, share-alike licence
%   http://creativecommons.org/licenses/by-nc-sa/3.0/de/deed.en
%
% with the following specifications:
%
%  1. When publishing tables generated from this LaTeX file and modified
%     versions of it, you must cite the paper by Nordlie et al given above.
%
%  2. The non-commercial clause applies only to the distribution of THIS FILE
%     and LaTeX source code files derived from it. You may commercially publish
%     documents generated using this file and derivatived versions of this file.
%
% Contact: Hans Ekkehard Plesser, UMB (hans.ekkehard.plesser at umb.no)

\documentclass{article}

\usepackage[margin=1in]{geometry} % get enough space on page

\usepackage{tabularx}  % automatically adjusts column width in tables
\usepackage{multirow}  % allows entries spanning several rows  
\usepackage{colortbl}  % allows coloring tables

\usepackage[fleqn]{amsmath}   % displayed equations flush left
\setlength{\mathindent}{0em}

% use Helvetica for text, Pazo math fonts
\usepackage{mathpazo}
\usepackage[scaled=.95]{helvet}
\renewcommand\familydefault{\sfdefault}

\renewcommand\arraystretch{1.2}  % slightly more space in tables

\pagestyle{empty}  % no header of footer

% \hdr{ncols}{label}{title}
%
% Typeset header bar across table with ncols columns 
% with label at left margin and centered title
%
\newcommand{\hdr}[3]{%
  \multicolumn{#1}{|l|}{%
    \color{white}\cellcolor[gray]{0.0}%
    \textbf{\makebox[0pt]{#2}\hspace{0.5\linewidth}\makebox[0pt][c]{#3}}%
  }%
}


\begin{document}

% - A ------------------------------------------------------------------------------

\noindent
\begin{tabularx}{\linewidth}{|l|X|}\hline
%
\hdr{2}{A}{Model Summary}\\\hline
\textbf{Populations}     & Three: excitatory, inhibitory, external input \\\hline
\textbf{Topology}        & --- \\\hline
\textbf{Connectivity}    & Random convergent connections \\\hline
\textbf{Neuron model}    & Leaky integrate-and-fire, fixed voltage
                           threshold, fixed absolute refractory time (voltage clamp) \\\hline
\textbf{Channel models}  & --- \\\hline
\textbf{Synapse model}   & $\delta$-current inputs (discontinuous
                           voltage jumps) \\\hline
\textbf{Plasticity}      & ---\\\hline
\textbf{Input}           & Independent fixed-rate Poisson spike trains to all
                           neurons \\\hline
\textbf{Measurements}    & Spike activity \\\hline
\end{tabularx}

\vspace{2ex}

% - B -----------------------------------------------------------------------------

\noindent\begin{tabularx}{\linewidth}{|l|l|X|}\hline
\hdr{3}{B}{Populations}\\\hline
  \textbf{Name}   & \textbf{Elements} & \textbf{Size} \\\hline
    E             & Iaf neuron        & $N_{\text{E}} = 4N_{\text{I}}$  \\\hline
    I             & Iaf neuron        & $N_{\text{I}}$ \\\hline
    E$_{\text{ext}}$ & Poisson generator & $C_E(N_{\text{E}}+N_{\text{I}})$ \\\hline
\end{tabularx}

\vspace{2ex}

% - C ------------------------------------------------------------------------------

\noindent\begin{tabularx}{\linewidth}{|l|l|l|X|}\hline
\hdr{4}{C}{Connectivity}\\\hline
\textbf{Name} & \textbf{Source} & \textbf{Target} & \textbf{Pattern} \\\hline
  EE & E & E & 
  Random convergent $C_{\text{E}}\rightarrow 1$, weight $J$, delay $D$ \\\hline
  IE & E & I & 
  Random convergent $C_{\text{E}}\rightarrow 1$, weight $J$, delay $D$ \\\hline
  EI & I & E & 
  Random convergent $C_{\text{I}}\rightarrow 1$, weight $-gJ$, delay $D$ \\\hline
  II & I & I & 
  Random convergent $C_{\text{I}}\rightarrow 1$, weight $-gJ$, delay $D$ \\\hline
  Ext& E$_{\text{ext}}$ & E $\cup$ I & 
  Non-overlapping $C_{\text{E}}\rightarrow 1$, weight $J$, delay $D$ \\\hline
\end{tabularx}

\vspace{2ex}

% - D ------------------------------------------------------------------------------

\noindent\begin{tabularx}{\linewidth}{|p{0.15\linewidth}|X|}\hline
\hdr{2}{D}{Neuron and Synapse Model}\\\hline
\textbf{Name} & Iaf neuron \\\hline
\textbf{Type} & Leaky integrate-and-fire, $\delta$-current input\\\hline
\raisebox{-4.5ex}{\parbox{\linewidth}{\textbf{Subthreshold dynamics}}} &
\rule{1em}{0em}\vspace*{-3.5ex}
    \begin{equation*}
      \begin{array}{r@{\;=\;}lll}
      \tau \dot{V}(t) & -V(t) + R I(t) &\text{if} & t > t^*+\tau_{\text{rp}} \\
      V(t) & V_{\text{r}} & \text{else} \\[2ex]
      I(t) & \multicolumn{3}{l}{\frac{\tau}{R} \sum_{\tilde{t}} w
        \delta(t-(\tilde{t}+\Delta))}
      \end{array}
    \end{equation*} 
\vspace*{-2.5ex}\rule{1em}{0em}
 \\\hline
\multirow{3}{*}{\textbf{Spiking}} & 
   If $V(t-)<\theta \wedge V(t+)\geq \theta$
\vspace*{-1ex}
\begin{enumerate}\setlength{\itemsep}{-0.5ex}
\item set $t^* = t$
\item emit spike with time-stamp $t^*$
\end{enumerate}
\vspace*{-4ex}\rule{1em}{0em}
\\\hline
\end{tabularx}

\vspace{2ex}

% - E ------------------------------------------------------------------------------

\noindent\begin{tabularx}{\linewidth}{|l|X|}\hline
\hdr{2}{E}{Input}\\\hline
\textbf{Type} & \textbf{Description} \\\hline
{Poisson generators} & Fixed rate $\nu_{\text{ext}}$, $C_{\text{E}}$
generators per neuron, each generator projects to one neuron\\\hline
\end{tabularx}

\vspace{2ex}

% - F -----------------------------------------------------------------------------

\noindent\begin{tabularx}{\linewidth}{|X|}\hline
\hdr{1}{F}{Measurements}\\\hline
Spike activity as raster plots, rates and ``global frequencies'', no details given
\\\hline
\end{tabularx}

% ---------------------------------------------------------------------------------

\end{document}