101 lines
3.9 KiB
TeX
101 lines
3.9 KiB
TeX
\documentclass[a4paper,12pt,pdftex]{exam}
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\newcommand{\ptitle}{Orientation tuning}
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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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In the visual cortex V1 orientation sensitive neurons respond to bars
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in dependence on their orientation. In this project we explore the
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question:
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How is the orientation of a bar encoded by the activity of a
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population of orientation sensitive neurons?
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\begin{questions}
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\question Orientation tuning of the neurons
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In an electrophysiological experiment, 6 neurons have been recorded
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simultaneously. First, the tuning of these neurons was characterized
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by presenting them bars in a range of 12 orientation angles. Each
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orientation was presented 50 times. Each of the \texttt{unit*.mat}
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files contains the responses of one of the neurons. In there,
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\texttt{angles} is a vector with the orientation angles of the bars
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in degrees. \texttt{spikes} is a cell array that contains the
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vectors of spike times for each angle and presentation. The spike
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times are given in seconds. The stimulation with the bar starts a
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time $t_0=0$ and ends at time $t_1=200$\,ms.
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\begin{parts}
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\part Illustrate the spiking activity of the V1 cells in response
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to different orientation angles of the bars by means of spike
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raster plots (of a single unit).
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\part Plot the firing rate of each of the 6 neurons as a function
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of the orientation angle of the bar. As the firing rate compute
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the number of spikes in the time interval $0<t<200$\,ms divided by
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200\,ms. The resulting curves are the tuning curves $r(\varphi)$
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of the neurons.
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\part Fit the function \[ r(\varphi) = g \cdot
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(1+\cos(2(\varphi-\varphi_0)))/2 + a \] to the measured tuning
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curves in order to estimated the orientation angle at which the
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neurons respond strongest. In this function $\varphi_0$ is the
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position of the peak, $g$ is a gain factor that sets the
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modulation depth of the firing rate, and $a$ is an offset.
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Why is there a factor two in the argument of the cosine?
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\end{parts}
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\question Inferring stimulus orientation from neural activity
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In the second part of the experiment the population activity of the
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6 neurons was measured in response to arbitrarily oriented bars. The
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responses of the 6 neurons to 50 presentation of a bar are stored in
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the \texttt{spikes} variables of the \texttt{population*.mat} files.
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The \texttt{angle} variable holds the angle of the presented bar.
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\begin{parts}
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\part How can the orientation angle of the presented bar be read
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out from one trial of the population activity of the 6 neurons?
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One possible method is the so called ``population vector'' where
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unit vectors pointing into the direction of the maximum response
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of each neuron are weighted by their firing rate. The stimulus
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orientation is then the direction of the averaged vectors.
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%Think of another (simpler) method how the orientation of the bar
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%may be approximately read out from the population.
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An alternative read out is maximum likelihood (see script).
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Load one of the \texttt{population*.mat} files, illustrate the
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data, and estimate the orientation angle of the bar from single
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trial data by the two different methods.
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\part Compare, illustrate and discuss the performance of the two
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decoding methods by using all of the recorded responses (all
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\texttt{population*.mat} files). How exactly is the orientation of
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the bar encoded? How robust is the estimate of the orientation
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from trial to trial?
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\part Can you think of yet another strategy to estimate the
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orientation of the bar from the activity of the neurons?
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\end{parts}
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\end{questions}
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\end{document}
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gains and angles of the 6 neurons:
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gain=10.7 phase=5
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gain=18.0 phase=38
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gain=11.3 phase=71
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gain=14.1 phase=108
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gain=19.0 phase=138
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gain=16.4 phase=174
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