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Fabian Sinz
2014-11-03 11:28:54 +01:00
parent 11564e16a1
commit 57f727ecf4
22 changed files with 210 additions and 132 deletions
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32
projects/project_isipdffit/isipdffit.tex
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@@ -1,4 +1,4 @@
\documentclass[addpoints,10pt]{exam}
\documentclass[addpoints,11pt]{exam}
\usepackage{url}
\usepackage{color}
\usepackage{hyperref}
@@ -9,7 +9,7 @@
\firstpageheader{Scientific Computing}{Project Assignment}{11/05/2014
-- 11/06/2014}
%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
\firstpagefooter{}{}{}
\firstpagefooter{}{}{{\bf Supervisor:} Jan Benda}
\runningfooter{}{}{}
\pointsinmargin
\bracketedpoints
@@ -31,7 +31,7 @@
% captionpos=t,
xleftmargin=2em,
xrightmargin=1em,
% aboveskip=10pt,
% aboveskip=11pt,
%title=\lstname,
% title={\protect\filename@parse{\lstname}\protect\filename@base.\protect\filename@ext}
}
@@ -72,7 +72,8 @@
p_\mathrm{ig}(T) = \frac{1}{\sqrt{4 \pi D T^{3}}} \exp \left[ - \frac{(T - \mu)^{2} }{4 D T \mu^{2}} \right]
\end{equation}
where $\mu$ is the mean interspike interval and
$D=\textrm{var}(T)/(2\mu^3)$ is the so called diffusion coefficient.
% $D=\textrm{var}(T)/(2\mu^3)$
$D$ is the so called diffusion coefficient.
The third one was derived for neurons driven with colored noise:
\begin{equation}\label{pcn}
@@ -91,32 +92,31 @@
\end{equation}
with $\delta=\mu/\tau$.
\begin{parts}
\part The two neurons are implemented in the files \texttt{pifouspikes.m}
The two neurons are implemented in the files \texttt{pifouspikes.m}
and \texttt{lifouspikes.m}.
Call them with the following parameters:
\begin{lstlisting}
trials = 10;
tmax = 50.0;
input = 10.0; % the input I
Dnoise = 1.0; % noise strength
outau = 1.0; % correlation time of the noise in seconds
trials = 10;
tmax = 50.0;
input = 10.0; % the input I
Dnoise = 1.0; % noise strength
outau = 1.0; % correlation time of the noise in seconds
spikes = pifouspikes( trials, input, tmax, Dnoise, outau );
spikes = pifouspikes( trials, input, tmax, Dnoise, outau );
\end{lstlisting}
The returned \texttt{spikes} is a cell array with \texttt{trials} elements, each being a vector
of spike times (in seconds) computed for a duration of \texttt{tmax} seconds.
The input is set via the \texttt{input} variable.
\part Find for both model neurons the inputs $I_i$ required to make the fire with a mean rate
of 10, 20, 50, and 100\,Hz.
\begin{parts}
\part For both model neurons find the inputs $I_i$ required to
make them fire with a mean rate of 10, 20, 50, and 100\,Hz.
\part Compute interspike interval distributions of the two model neurons for these inputs $I_i$.
\part Compare the interspike interval distributions with the exponential
distribution eq.~(\ref{exppdf}) and the inverse Gaussian
eq.~(\ref{invgauss}) by measuring their parameters from the
interspike intervals. How well do theu describe the real
interspike intervals. How well do they describe the real
distributions for the different conditions?
\part Also fit eq.~(\ref{pcn}) to the data. Here you need to apply a non-linear fit algorithm.