110 lines
3.6 KiB
TeX
110 lines
3.6 KiB
TeX
\documentclass[addpoints,10pt]{exam}
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\usepackage{url}
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\usepackage{color}
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\usepackage{hyperref}
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\pagestyle{headandfoot}
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\runningheadrule
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\firstpageheadrule
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\firstpageheader{Scientific Computing}{Project Assignment}{11/05/2014
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-- 11/06/2014}
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%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
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\firstpagefooter{}{}{}
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\runningfooter{}{}{}
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\pointsinmargin
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\bracketedpoints
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%\printanswers
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%\shadedsolutions
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%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage{listings}
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\lstset{
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basicstyle=\ttfamily,
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numbers=left,
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showstringspaces=false,
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language=Matlab,
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breaklines=true,
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breakautoindent=true,
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columns=flexible,
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frame=single,
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% captionpos=t,
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xleftmargin=2em,
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xrightmargin=1em,
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% aboveskip=10pt,
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%title=\lstname,
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% title={\protect\filename@parse{\lstname}\protect\filename@base.\protect\filename@ext}
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}
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\begin{document}
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%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
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\sffamily
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% \begin{flushright}
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% \gradetable[h][questions]
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% \end{flushright}
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\begin{center}
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\input{../disclaimer.tex}
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\end{center}
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%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{questions}
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\question You are recording the activity of a neuron in response to
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constant stimuli of intensity $I$ (think of that, for example,
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of sound waves with intensities $I$). The neuron has an adaptatation
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current that adapts the firing rate with a slow time constant down.
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Explore the dependence of interspike interval correlations on the firing rate,
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adaptation time constant and noise level.
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\begin{parts}
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\part The neuron is a neuron with an adaptation current.
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It is implemented in the file \texttt{lifadaptspikes.m}. Call it
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with the following parameters:
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\begin{lstlisting}
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trials = 10;
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tmax = 50.0;
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input = 10.0; % the input I
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Dnoise = 1e-2; % noise strength
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adapttau = 0.1; % adaptation time constant in seconds
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adaptincr = 0.5; % adaptation strength
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spikes = lifadaptspikes( trials, input, tmax, Dnoise, adapttau, adaptincr );
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\end{lstlisting}
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The returned \texttt{spikes} is a cell array with \texttt{trials} elements, each being a vector
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of spike times (in seconds) computed for a duration of \texttt{tmax} seconds.
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The input is set via the \texttt{input} variable, the noise strength via \texttt{Dnoise},
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and the adaptation time constant via \texttt{adapttau}.
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\part Measure the intensity-response curve of the neuron, that is the mean firing rate
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as a function of the input for a range of inputs from 0 to 120.
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\part Compute the correlations between each interspike interval $T_i$ and the next one $T_{i+1}$
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(serial interspike interval correlation at lag 1). Plot this correlation as a function of the
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firing rate by varying the input as in (a).
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\part How does this dependence change for different values of the adaptation
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time constant \texttt{adapttau}? Use values between 10\,ms and
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1\,s for \texttt{adapttau}.
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\part Determine the firing rate at which the minimum interspike interval correlation
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occurs. How does the minimum correlation and this firing rate
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depend on the adaptation time constant \texttt{adapttau}?
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\part How do the results change if the level of the intrinsic noise \texttt{Dnoise} is modified?
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Use values of 1e-4, 1e-3, 1e-2, 1e-1, and 1 for \texttt{Dnoise}.
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\uplevel{If you still have time you can continue with the following question:}
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\part How do the interspike interval distributions look like for the different noise levels
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at some example values for the input and the adaptation time constant?
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\end{parts}
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\end{questions}
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\end{document}
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