110 lines
3.5 KiB
TeX
110 lines
3.5 KiB
TeX
\documentclass[addpoints,11pt]{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}{11/02/2014
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-- 11/05/2014}
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%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
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\firstpagefooter{}{}{{\bf Supervisor:} Jan Benda}
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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=11pt,
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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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as a current $I$ injected via a patch-electrode into the neuron).
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Measure the tuning curve (also called the intensity-response curve) of the
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neuron. That is, what is the mean firing rate of the neuron's response
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as a function of the input $I$. How does this depend on the level of
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the intrinsic noise of the neuron?
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The neuron is implemented in the file \texttt{lifspikes.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 = 1.0; % noise strength
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spikes = lifspikes( trials, input, tmax, Dnoise );
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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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Think of calling the \texttt{lifspikes()} function as a
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simple way of doing an electrophysiological experiment. You are
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presenting a stimulus with a constant intensity $I$ that you set. The
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neuron responds to this stimulus, and you record this
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response. After detecting the timepoints of the spikes in your
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recordings you get what the \texttt{lifspikes()} function
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returns. The advantage over real data is, that you have the
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possibility to simply modify the properties of the neuron via the
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\texttt{Dnoise} parameter.
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\begin{parts}
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\part First set the noise \texttt{Dnoise=0} (no noise). Compute
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and plot the mean firing rate (number of spikes within the
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recording time \texttt{tmax} divided by \texttt{tmax} and averaged
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over trials) as a function of the input for inputs ranging from 0
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to 20.
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\part Do the same for various noise strength \texttt{Dnoise}. Use $D_{noise} = 1e-3$,
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1e-2, and 1e-1. How does the intrinsic noise influence the response curve?
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\part Show some interspike interval histograms for some
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interesting values of the input and the noise strength.
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\part How does the coefficient of variation $CV_{isi}$ (standard
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deviation divided by mean) of the interspike intervalls depend on
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the input and the noise level?
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\end{parts}
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\end{questions}
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\end{document}
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