\documentclass[a4paper,12pt,pdftex]{exam}

\newcommand{\ptitle}{Orientation tuning}
\input{../header.tex}
\firstpagefooter{Supervisor: Jan Benda}{}%
{email: jan.benda@uni-tuebingen.de}

\begin{document}

\input{../instructions.tex}

In the visual cortex V1 orientation sensitive neurons respond to bars
in dependence on their orientation. In this project we explore the
question:

How is the orientation of a bar encoded by the activity of a
population of orientation sensitive neurons?

\begin{questions}
  \question Orientation tuning of the neurons

  In an electrophysiological experiment, 6 neurons have been recorded
  simultaneously. First, the tuning of these neurons was characterized
  by presenting them bars in a range of 12 orientation angles. Each
  orientation was presented 50 times. Each of the \texttt{unit*.mat}
  files contains the responses of one of the neurons. In there,
  \texttt{angles} is a vector with the orientation angles of the bars
  in degrees. \texttt{spikes} is a cell array that contains the
  vectors of spike times for each angle and presentation. The spike
  times are given in seconds. The stimulation with the bar starts a
  time $t_0=0$ and ends at time $t_1=200$\,ms.

  \begin{parts}
    \part Illustrate the spiking activity of the V1 cells in response
    to different orientation angles of the bars by means of spike
    raster plots (of a single unit).

    \part Plot the firing rate of each of the 6 neurons as a function
    of the orientation angle of the bar. As the firing rate compute
    the number of spikes in the time interval $0<t<200$\,ms divided by
    200\,ms. The resulting curves are the tuning curves $r(\varphi)$
    of the neurons.

    \part Fit the function \[ r(\varphi) = g \cdot
    (1+\cos(2(\varphi-\varphi_0)))/2 + a \] to the measured tuning
    curves in order to estimated the orientation angle at which the
    neurons respond strongest. In this function $\varphi_0$ is the
    position of the peak, $g$ is a gain factor that sets the
    modulation depth of the firing rate, and $a$ is an offset.

    Why is there a factor two in the argument of the cosine?
  \end{parts}

  \question Inferring stimulus orientation from neural activity  

  In the second part of the experiment the population activity of the
  6 neurons was measured in response to arbitrarily oriented bars. The
  responses of the 6 neurons to 50 presentation of a bar are stored in
  the \texttt{spikes} variables of the \texttt{population*.mat} files.
  The \texttt{angle} variable holds the angle of the presented bar.

  \begin{parts}
    \part How can the orientation angle of the presented bar be read
    out from one trial of the population activity of the 6 neurons?
    One possible method is the so called ``population vector'' where
    unit vectors pointing into the direction of the maximum response
    of each neuron are weighted by their firing rate. The stimulus
    orientation is then the direction of the averaged vectors.

    %Think of another (simpler) method how the orientation of the bar
    %may be approximately read out from the population.
    An alternative read out is maximum likelihood (see script).

    Load one of the \texttt{population*.mat} files, illustrate the
    data, and estimate the orientation angle of the bar from single
    trial data by the two different methods.

    \part Compare, illustrate and discuss the performance of the two
    decoding methods by using all of the recorded responses (all
    \texttt{population*.mat} files). How exactly is the orientation of
    the bar encoded? How robust is the estimate of the orientation
    from trial to trial?

    \part Can you think of yet another strategy to estimate the
    orientation of the bar from the activity of the neurons?
  \end{parts}
\end{questions}

\end{document}


gains and angles of the 6 neurons:

gain=10.7 phase=5
gain=18.0 phase=38
gain=11.3 phase=71
gain=14.1 phase=108
gain=19.0 phase=138
gain=16.4 phase=174


