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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}
\firstpagefooter{}{}{{\bf Supervisor:} Jan Grewe}
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\section*{Quantifying the responsiveness of a neuron using the F-I curve.}
The responsiveness of a neuron is often quantified using an F-I
curve. The F-I curve plots the \textbf{F}iring rate of the neuron as a function
of the stimulus \textbf{I}ntensity.

\begin{questions}
  \question In the accompanying datasets you find the
  \textit{spike\_times} of an P-unit electrorecptor of the weakly
  electric fish \textit{Apteronotus leptorhynchus} to a stimulus of a
  certain intensity, i.e. the \textit{contrast}. The contrast is also
  part of the file name itself.
  \begin{parts}
    \part Estimate for each stimulus intensity the average response 
    (PSTH) and plot it. You will see that there are three parts.  (i)
    The first 200 ms is the baseline (no stimulus) activity. (ii) During
    the next 1000 ms the stimulus was switched on. (iii) After stimulus
    offset the neuronal activity was recorded for further 825 ms.
    \part Extract the neuron's activity in the last 200 ms before
    stimulus offset and plot it against the stimulus intensity or the
    contrast, respectively.
    \part Fit a Boltzmann function to the FI-curve. The Boltzmann function
    is defined as:
    \begin{equation}
       y=\frac{\alpha-\beta}{1+e^{(x-x_0)/\Delta x}}+\beta,
    \end{equation}
    where $\alpha$ is the starting firing rate, $\beta$ the saturation
    firing rate, $x$ the current stimulus intensity, $x_0$ starting
    stimulus intensity, and $\Delta x$ a measure of the slope.
  \end{parts}
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