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\firstpageheader{Scientific Computing}{Project Assignment}{11/05/2014
  -- 11/06/2014}
%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
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\section*{Reverse reconstruction of the stimulus evoking neuronal responses.}
During the course we have used the Spike-Triggered-Average to
reconstruct the stimulus a neuron has been stimulated with.
\begin{questions}
  \question In the accompanying files you find the spike responses of
  P-units and pyramidal neurons of the weakly electric fish
  \textit{Apteronotus leptorhynchus}. The respective stimuli are
  stored in separate files.  Start with the P-unit and, in the end,
  apply the same functions to the pyramidal data.
  \begin{parts}
    \part Estimate the STA and plot it.
    \part Implement a function that estimates the reconstruction 
    error using the mean-square-error and express it relative to the
    variance of the original stimulus.
    \begin{equation}
      err = \frac{1}{N} \cdot \displaystyle\sum^{N}_{i=1}(x_i - \bar{x}),
    \end{equation}
    with $N$ the number of data points, $x_i$ the current value and
    $\bar{x}$, the average of all $x$.
    \part Analyze the robustness of the reconstruction. Estimate 
    the STA with less and less data and estimate the reconstruction
    error.
    \part Plot the reconstruction error as a function of the data 
    amount used to estimate the STA.
    \part Do the same for the pyramidal neuron, what do you observe?
  \end{parts}
\end{questions}

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