91 lines
3.3 KiB
TeX
91 lines
3.3 KiB
TeX
\documentclass[a4paper,12pt,pdftex]{exam}
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\newcommand{\ptitle}{Neural tuning and noise}
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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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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 $I$?
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How does the intensity-response curve of a neuron depend on the
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level of 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}
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elements, each being a vector of spike times (in seconds) computed
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for a duration of \texttt{tmax} seconds. The input is set via the
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\texttt{input} variable, the noise strength via \texttt{Dnoise}.
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Think of calling the \texttt{lifspikes()} function as a simple way
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of doing an electrophysiological experiment. You are presenting a
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stimulus with a constant intensity $I$ that you set. The neuron
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responds to this stimulus, and you record this response. After
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detecting the timepoints of the spikes in your recordings you get
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what the \texttt{lifspikes()} function returns. In addition you
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can record from different neurons with different noise properties
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by setting the \texttt{Dnoise} parameter to different values.
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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 neuron's $f$-$I$ curve, i.e. the mean firing rate (number
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of spikes within the recording time \texttt{tmax} divided by
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\texttt{tmax} and averaged over trials) as a function of the input
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for inputs ranging from 0 to 20.
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How are different stimulus intensities encoded by the firing rate
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of this neuron?
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\part Compute the $f$-$I$ curves of neurons with various noise
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strengths \texttt{Dnoise}. Use $D_{noise} = 1e-3$, $1e-2$, and
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$1e-1$.
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How does the intrinsic noise influence the response curve?
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How is the encoding of stimuli influenced by increasing intrinsic
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noise?
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What are possible sources of this intrinsic noise?
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\part Show spike raster plots and interspike interval histograms
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of the responses for some interesting values of the input and the
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noise strength. For example, you might want to compare the
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responses of the four different neurons to the same input, or by
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the same resulting mean firing rate.
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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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\part Based o your results, discuss how intrinsic noise might
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improve and how it might deteriote the encoding of different
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stimulus intensities.
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\end{parts}
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\end{questions}
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\end{document}
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