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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 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 electroreceptor of the weakly
  electric fish \textit{Apteronotus leptorhynchus} to a stimulus of a
  certain intensity, i.e. the \textit{contrast}. The spike times are
  given in milliseconds relative to the stimulus onset.
  \begin{parts}
    \part For each stimulus intensity estimate 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 first 50\,ms after
    stimulus onset and plot it against the stimulus intensity,
    respectively the contrast, in an appropriate way.
    \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.
    \part Plot the fit into the data.
  \end{parts}
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