125 lines
5.3 KiB
TeX
125 lines
5.3 KiB
TeX
\documentclass[a4paper,12pt,pdftex]{exam}
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\newcommand{\ptitle}{Stimulus discrimination: gain}
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\input{../header.tex}
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\firstpagefooter{Supervisor: Jan Benda}{}{email: jan.benda@uni-tuebingen.de}
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\begin{document}
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\input{../instructions.tex}
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An important property of sensory systems is their ability to
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discriminate similar stimuli. For example, discrimination of two
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colors, light intensities, pitch of two tones, sound intensities, etc.
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Here we look at the level of a single neuron. What does it mean in
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terms of the neuron's $f$-$I$ curve (firing rate versus stimulus
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intensity) that two similar stimuli can be discriminated given the
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spike train responses that have been evoked by the two stimuli?
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You are recording the activity of a neuron in response to two
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different stimuli $I_1$ and $I_2$ (think of them, for example, of two
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different sound intensities, $I_1$ and $I_2$, and the spiking activity
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of an auditory afferent). The neuron responds to a stimulus with a
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number of spikes. You (an upstream neuron) can count the number of
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spikes of this response within an observation time of duration
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$T=100$\,ms. For perfect discrimination, the number of spikes evoked
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by the stronger stimulus within $T$ is always larger than for the
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smaller stimulus. The situation is more complicated, because the
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number of spikes evoked by one stimulus is not fixed but varies, such
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that the number of spikes evoked by the stronger stimulus could happen
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to be lower than the number of spikes evoked by the smaller stimulus.
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The central questions of this project are:
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\begin{itemize}
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\item How can an upstream neuron discriminate two stimuli based on the
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spike counts $n$?
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\item How does this depend on the gain of the neuron?
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\end{itemize}
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The neuron is implemented in the file \texttt{lifboltzmannspikes.m}.
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Call it with the following parameters:\vspace{-5ex}
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\begin{lstlisting}
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trials = 10;
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tmax = 50.0;
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gain = 0.1;
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input = 10.0;
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spikes = lifboltzmanspikes(trials, input, tmax, gain);
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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 for
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a duration of \texttt{tmax} seconds. The intensity of the stimulus is
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set via the \texttt{input} variable.
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Think of calling the \texttt{lifboltzmannspikes()} function as a
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simple way of doing an electrophysiological experiment. You are
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presenting a stimulus with an 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 what
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the \texttt{lifboltzmannspikes()} function returns. In addition you
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can record from different neurons with different properties by setting
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the \texttt{gain} parameter to different values.
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\begin{questions}
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\question Spike counts of the responses
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\begin{parts}
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\part Measure the tuning curve of the neuron with respect to the
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input. That is, compute the mean firing rate (number of spikes
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within the recording time \texttt{tmax} divided by \texttt{tmax}
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and averaged over trials) as a function of the input
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strength. Find an appropriate range of input values.
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Plot the tuning curve for four different neurons that differ in
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their \texttt{gain} property. Use 0.1, 0.2, 0.5 and 1 as values
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for the \texttt{gain} parameter. Why is this parameter called 'gain'?
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\part Show two raster plots for the responses to two different
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stimuli with $I_1=10$ and $I_2=11$. Set the gain of the neuron to
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0.1. Use an appropriate time window and an appropriate number of
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trials for illustrating the spike raster.
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Just by looking at the raster plots, can you discriminate the two
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stimuli? That is, do you see differences between the two
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responses?
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\part Generate properly normalized histograms of the spike counts
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within windows of duration $T$ (use $T=100$\,ms) of the spike
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responses to the two different stimuli.
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Do the two histograms overlap? What does this mean for the
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discriminability of the two stimuli?
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How do the histograms of the spike counts depend on the gain of
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the neuron? Plot them for the four different values of the gain
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used in (a).
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\end{parts}
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\question Discriminability of the responses
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\begin{parts}
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\part \label{discrmeasure} Think about a measure based on the
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spike-count histograms that quantifies how well the two stimuli
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can be distinguished based on the spike counts.
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\underline{Hint:} A possible readout is to set a threshold
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$n_{thresh}$ for the observed spike count. Any response smaller
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than the threshold assumes that the stimulus was $I_1$, any
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response larger than the threshold assumes that the stimulus was
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$I_2$. For the given window $T$ find the threshold $n_{thresh}$ that
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results in the best discrimination performance. How can you
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quantify ``best discrimination'' performance?
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\part \label{gaindiscr} For which gains can the two stimuli perfectly discriminated?
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Plot the dependence of this measure as a function of the gain of
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the neuron.
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\part Another way to quantify the discriminability of the spike
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counts in response to the two stimuli is to apply an appropriate
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statistical test and check for significant differences. How does
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this compare to your findings from (\ref{gaindiscr})?
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\end{parts}
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\end{questions}
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\end{document}
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