121 lines
3.9 KiB
TeX
121 lines
3.9 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}{11/05/2014
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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{}{}{{\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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two different stimuli $I_1$ and $I_2$ (think of them, for example,
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of two sound waves with different intensities $I_1$ and
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$I_2$). Within an observation time of duration $W$ the neuron
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responds stochastically with $n_i$ spikes.
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How well can an upstream neuron discriminate the two
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stimuli based on the spike counts $n_i$? How does this depend on the
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duration $W$ of the observation time? How is this related to the fano factor
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(the ratio between the variance and the mean of the spike counts)?
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The neuron is implemented in the file \texttt{lifadaptspikes.m}.
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Call it 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 = 65.0;
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Dnoise = 0.1;
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adapttau = 0.2;
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adaptincr = 0.5;
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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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For the two inputs $I_1$ and $I_2$ use
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\begin{lstlisting}
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input = 65.0; % I_1
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input = 75.0; % I_2
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\end{lstlisting}
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\begin{parts}
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\part
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Show two raster plots for the responses to the two different stimuli.
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\part Generate histograms of the spike counts within $W$ of the
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responses to the two different stimuli. How do they depend on the observation time $W$
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(use values between 1\,ms and 1\,s)?
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\part Think about a measure based on the spike count histograms that quantifies how well
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the two stimuli can be distinguished based on the spike
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counts. Plot the dependence of this measure as a function of the observation time $W$.
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For which observation times can the two stimuli perfectly discriminated?
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\underline{Hint:} A possible readout is to set a threshold $n_{thresh}$ for
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the observed spike count. Any response smaller than the threshold
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assumes that the stimulus was $I_1$, any response larger than the
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threshold assumes that the stimulus was $I_2$. What is the
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probability that the stimulus was indeed $I_1$ or $I_2$,
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respectively? For a given $W$ find the threshold $n_{thresh}$ that
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results in the best discrimination performance.
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\part Also plot the Fano factor as a function of $W$. How is it related to the discriminability?
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\uplevel{If you still have time you can continue with the following question:}
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\part You may change the two stimuli $I_1$ and $I_2$ and the intrinsic noise of the neuron via
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\texttt{Dnoise} (change it in factors of ten, higher values will make the responses more variable)
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and repeat your analysis.
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\end{parts}
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\end{questions}
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\end{document}
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