102 lines
4.0 KiB
TeX
102 lines
4.0 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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\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 constant input current $I$?
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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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How can intrinsic noise be usefull for encoding stimuli?
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The neuron is implemented in the file \texttt{lifspikes.m}. Call it
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with the following parameters:\\[-7ex]
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\begin{lstlisting}
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trials = 10;
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tmax = 50.0;
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current = 10.0; % the constant input current I
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Dnoise = 1.0; % noise strength
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spikes = lifspikes(trials, current, 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 current is set
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via the \texttt{current} variable, the strength of the intrinsic
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noise via \texttt{Dnoise}. If \texttt{current} is a single number,
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then an input current of that intensity is simulated for
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\texttt{tmax} seconds. Alternatively, \texttt{current} can be a
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vector containing an input current that changes in time. In this
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case, \texttt{tmax} is ignored, and you have to provide a value
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for the input current for every 0.0001\,seconds.
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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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current 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 for example $D_{noise} = 10^{-3}$,
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$10^{-2}$, and $10^{-1}$.
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How does the intrinsic noise influence the response curve?
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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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How do the responses differ?
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\part Let's now use as an input to the neuron a 1\,s long sine
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wave $I(t) = I_0 + A \sin(2\pi f t)$ with offset current $I_0$,
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amplitude $A$, and frequency $f$. Set $I_0=5$, $A=4$, and
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$f=5$\,Hz.
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Do you get a response of the noiseless ($D_{noise}=0$) neuron?
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What happens if you increase the noise strength?
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What happens at really large noise strengths?
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Generate some example plots that illustrate your findings.
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Explain the encoding of the sine wave based on your findings
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regarding the $f$-$I$ curves.
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\end{parts}
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\end{questions}
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\end{document}
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