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\firstpageheader{Scientific Computing}{Project Assignment}{11/02/2015
  -- 11/05/2015}
%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
\firstpagefooter{}{}{{\bf Supervisor:} Jan Grewe}
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\section*{Quantifying the coupling of action potentials to the EOD.}
P-unit electroreceptors are driven by the fish's self-generated field,
the EOD. In this project you have to quantify the strength of this
coulpling using the \textbf{vector strength}:
\begin{equation}
 VS = \sqrt{\left(\frac{1}{n}\sum_{i=1}^{n}\cos
 \alpha_i\right)^2 + \left(\frac{1}{n}\sum_{i = 1}^{n} \sin \alpha_i
 \right)^2},
\end{equation}
with $n$ the number of spikes and $\alpha_i$ the timing of the each
spike expressed as the phase relative to the EOD. The vector strength
varies between $0$ and $1$ for no phase locking to perfect phase
locking, respectively.

\begin{questions}
  \question In the accompanying datasets you find recordings of the
  ``baseline'' activity of P-unit electroreceptors of different weakly
  electric fish of the species \textit{Apteronotus leptorhynchus}.
  The files further contain respective recordings of the \textit{eod},
  i.e. the fish's field The data is sampled with 20\,kHz and the spike
  times are given in seconds.
  \begin{parts}
    \part Plot an average of the single EOD cylces of each fish 
    together with an respective PSTH.
    \part Implement a function that estimates the vector strength
    between the \textit{eod} and the spikes.
    \part Create a polar plot that shows the timing of the spikes 
    relatve to the EOD.
    \part Analyze the baseline responses of each fish and extract 
    measures from them as you have done in week 3. Plot the results
    appropriately.
    \part Does the vector strength correlate with the EOD frequency? 
  \end{parts}
\end{questions}

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