84 lines
3.3 KiB
TeX
84 lines
3.3 KiB
TeX
\documentclass[a4paper,12pt,pdftex]{exam}
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\newcommand{\ptitle}{Adaptation and interspike-interval correlations}
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\input{../header.tex}
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\firstpagefooter{Supervisor: Jan Benda}{phone: 29 74573}%
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{email: jan.benda@uni-tuebingen.de}
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\begin{document}
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\input{../instructions.tex}
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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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The neuron is a neuron with an adaptation current. It is
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implemented in the file \texttt{lifadaptspikes.m}. Call it with the
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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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\begin{parts}
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\part Show a spike-raster plot and a time-resolved firing rate of
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the neuron for an input current of 50 for three different
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adaptation time constants \texttt{adapttau} (10\,m, 100\,ms,
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1\,s). How do the neural responses look like and how do they
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depend on the adaptation time constant?
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\uplevel{For all the following analysis we only use the spike
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times of the steady-state response, i.e. we skip all spikes
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occuring before at least three times the adaptation time
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constant.}
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\part \label{ficurve} Measure the intensity-response curve of the
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neuron, that is the mean firing rate as a function of the input
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for a range of inputs from 0 to 120.
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\part Additionally compute the correlations between each
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interspike interval $T_i$ and the next one $T_{i+1}$ (serial
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interspike interval correlation at lag 1) for the same range of
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inputs as in (\ref{ficurve}). Plot the correlation as a function
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of the input.
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\part How does the intensity-response curve and the
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interspike-interval correlations depend on the adaptation time
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constant \texttt{adapttau}? Use several values between 10\,ms and
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1\,s for \texttt{adapttau} (logarithmically distributed).
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\part Determine the firing rate at which the minimum interspike
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interval correlation occurs. How does the minimum correlation and
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this firing rate (or the inverse of it, the mean interspike
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interval) depend on the adaptation time constant
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\texttt{adapttau}? Is this dependence siginificant? If yes, can
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you explain this dependence?
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\part How do all the results change if the level of the intrinsic
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noise \texttt{Dnoise} is modified? Use values of 1e-4, 1e-3,
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1e-2, 1e-1, and 1 for \texttt{Dnoise}.
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\end{parts}
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\end{questions}
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\end{document}
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