121 lines
5.0 KiB
TeX
121 lines
5.0 KiB
TeX
\documentclass[a4paper,12pt,pdftex]{exam}
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\newcommand{\ptitle}{Stimulus discrimination}
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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 An important property of sensory systems is their ability
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to discriminate similar stimuli. For example, discrimination of two
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colors, light intensities, pitch of two tones, sound intensities,
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etc. Here we look at the level of a single neuron. What does it
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mean in terms of the neuron's $f$-$I$ curve (firing rate versus
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stimulus intensity) that two similar stimuli can be discriminated
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given the spike train responses that have been evoked by the two
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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
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two different sound intensities, $I_1$ and $I_2$, and the spiking
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activity of an auditory afferent). The neuron responds to a stimulus
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with a number of spikes. You (an upstream neuron) can count the
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number of spikes of this response within an observation time of
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duration $T=100$\,ms. For perfect discrimination, the number of
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spikes evoked by the stronger stimulus within $T$ is always larger
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than for the smaller stimulus. The situation is more complicated,
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because the number of spikes evoked by one stimulus is not fixed but
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varies, such that the number of spikes evoked by the stronger
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stimulus could happen to be lower than the number of spikes evoked
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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
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on the 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:
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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
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for a duration of \texttt{tmax} seconds. The intensity of the
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stimulus is 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
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what the \texttt{lifboltzmannspikes()} function returns. In addition
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you can record from different neurons with different properties
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by setting the \texttt{gain} parameter to different values.
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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.
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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 $T$ (use $T=100$\,ms) of the spike responses to the two
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different stimuli. Do the two histograms overlap? What does this
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mean for the 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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\part Think about a measure based on the spike-count histograms
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that quantifies how well the two stimuli can be distinguished
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based on the spike counts. Plot the dependence of this measure as
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a function of the gain of the neuron.
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For which gains can the two stimuli perfectly discriminated?
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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 a given $T$ 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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\end{parts}
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\end{questions}
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\end{document}
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