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

\newcommand{\ptitle}{Serial ISI correlations}
\input{../header.tex}
\firstpagefooter{Supervisor: Jan Benda}{phone: 29 74573}%
{email: jan.benda@uni-tuebingen.de}

\begin{document}

\input{../instructions.tex}


%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%

\begin{questions}
  \question P-unit electroreceptor afferents of the gymnotiform weakly
  electric fish \textit{Apteronotus leptorhynchus} are spontaneously
  active when the fish is not electrically stimulated. 

  How do the firing rates and the serial correlations of the
  interspike intervals vary between different cells?

  In the file \texttt{baselinespikes.mat} you find two variables:
  \texttt{cells} is a cell-array with the names of the recorded cells
  and \texttt{spikes} is a cell array containing the spike times in
  seconds of recorded spontaneous activity for each of these cells.
  \begin{parts}
    \part Load the data! How many cells are contained in the file?

    \part Plot the spike rasters of a few cells.

    For the presentation, choose a few cells based on the results of
    this project.

    By just looking on the spike rasters, what are the differences
    between the cells?

    \part Compute the firing rate of each cell, i.e. number of spikes per time.

    Illustrate the results by means of a histogram and/or box whisker plot.

    \part Compute and plot the serial correlations between interspike intervals up to lag 10.

    What do you observe? In what way are the interspike-interval
    correlations similar betwen the cells? How do they differ?

    \part Implement a permutation test for computing the significance
    at an appropriate significance level of the serial
    correlations. Keep in mind that you test the correlations at 10
    different lags. At which lags are the serial correlations
    statistically significant?

    \part Are the serial correlations somehow dependent on the firing rate?

    Plot the significant correlations against the firing rate. Do you
    observe any dependence?

    Use an appropriate statistical test to support your observation.

  \end{parts}

\end{questions}

\end{document}