97 lines
2.8 KiB
TeX
97 lines
2.8 KiB
TeX
\documentclass[addpoints,11pt]{exam}
|
|
\usepackage{url}
|
|
\usepackage{color}
|
|
\usepackage{hyperref}
|
|
|
|
\pagestyle{headandfoot}
|
|
\runningheadrule
|
|
\firstpageheadrule
|
|
\firstpageheader{Scientific Computing}{Project Assignment}{11/02/2014
|
|
-- 11/05/2014}
|
|
%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
|
|
\firstpagefooter{}{}{{\bf Supervisor:} Jan Benda}
|
|
\runningfooter{}{}{}
|
|
\pointsinmargin
|
|
\bracketedpoints
|
|
|
|
%\printanswers
|
|
%\shadedsolutions
|
|
|
|
%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
\usepackage{listings}
|
|
\lstset{
|
|
basicstyle=\ttfamily,
|
|
numbers=left,
|
|
showstringspaces=false,
|
|
language=Matlab,
|
|
breaklines=true,
|
|
breakautoindent=true,
|
|
columns=flexible,
|
|
frame=single,
|
|
% captionpos=t,
|
|
xleftmargin=2em,
|
|
xrightmargin=1em,
|
|
% aboveskip=11pt,
|
|
%title=\lstname,
|
|
% title={\protect\filename@parse{\lstname}\protect\filename@base.\protect\filename@ext}
|
|
}
|
|
|
|
|
|
\begin{document}
|
|
%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
|
|
\sffamily
|
|
% \begin{flushright}
|
|
% \gradetable[h][questions]
|
|
% \end{flushright}
|
|
|
|
\begin{center}
|
|
\input{../disclaimer.tex}
|
|
\end{center}
|
|
|
|
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
|
\begin{questions}
|
|
\question You are recording the activity of a neuron in response to
|
|
constant stimuli of intensity $I$ (think of that, for example,
|
|
as a current $I$ injected via a patch-electrode into the neuron).
|
|
|
|
Measure the tuning curve (also called the intensity-response curve) of the
|
|
neuron. That is, what is the firing rate of the neuron's response
|
|
as a function of the input $I$. How does this depend on the level of
|
|
the intrinsic noise of the neuron?
|
|
|
|
The neuron is implemented in the file \texttt{lifspikes.m}. Call it
|
|
with the following parameters:
|
|
\begin{lstlisting}
|
|
trials = 10;
|
|
tmax = 50.0;
|
|
input = 10.0; % the input I
|
|
Dnoise = 1.0; % noise strength
|
|
|
|
spikes = lifspikes( trials, input, tmax, Dnoise );
|
|
\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, the noise strength via \texttt{Dnoise}.
|
|
|
|
\begin{parts}
|
|
\part First set the noise \texttt{Dnoise=0} (no noise). Compute and plot the firing rate
|
|
as a function of the input for inputs ranging from 0 to 20.
|
|
|
|
\part Do the same for various noise strength \texttt{Dnoise}. Use $D_{noise} = 1e-3$,
|
|
1e-2, and 1e-1. How does the intrinsic noise influence the response curve?
|
|
|
|
\part Show some interspike interval histograms for some
|
|
interesting values of the input and the noise strength.
|
|
|
|
\part How does the coefficient of variation $CV_{isi}$ (standard
|
|
deviation divided by mean) of the interspike intervalls depend on
|
|
the input and the noise level?
|
|
|
|
|
|
\end{parts}
|
|
|
|
\end{questions}
|
|
|
|
\end{document}
|