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

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

\begin{document}

\input{../instructions.tex}

The gymnotiform weakly electric fish \textit{Apteronotus
  leptorhynchus} has an active electrosensory system.  An electric
organ generates an electric field surrounding the
fish. Electroreceptive organs distributed over the whole body of the
fish sense minute perturbations of the electric field caused by
objects close to the fish. P-unit electroreceptor afferents send
information from the electroreceptive organs to the brain. They are
spontaneously active when the fish is not electrically stimulated,
that is when the electroreceptors are only stimulated by the fish's
own unperturbed electric field.

In this project we want to analyze how the baseline firing rates and
the serial correlations of the interspike intervals vary between
different P-units.

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{questions}
  \question Baseline firing properties
  \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 interspike-interval histograms and the
    coefficient-of-variation of the interspike intervals, $C_{ISI}$,
    for each of the cells.
  \end{parts}

  \question Serial correlations
  \begin{parts}
    \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 Illustrate relevant serial correlations with a return
    map. How is the return map related to what you see in the
    corresponding raster plot? How is it related to the corresponding
    serial correlation?

    \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}
