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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*{Estimating the adaptation time-constant.}
Stimulating a neuron with a constant stimulus for an extended period of time
often leads to a strong initial response that relaxes over time. This
process is called adaptation and is ubiquitous. Your task here is to
estimate the time-constant of the firing-rate adaptation in P-unit
electroreceptors of the weakly electric fish \textit{Apteronotus
  leptorhynchus}.

\begin{questions}
  \question In the accompanying datasets you find the
  \textit{spike\_times} of an P-unit electrorecptor to a stimulus of a
  certain intensity, i.e. the \textit{contrast} which is also stored
  in the file.
  \begin{parts}
    \part Estimate for each stimulus intensity the  
    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 Estimate the adaptation time-constant of the adaptation for 
    both the stimulus on- and offset. To do this fit an exponential
    function to the data. For the decay use:
    \begin{equation}
       f_{A,\tau,y_0}(t) = y_0 + A \cdot e^{-\frac{t}{\tau}},
    \end{equation}
    where $y_0$ the offset, $A$ the amplitude, $t$ the time, $\tau$
    the time-constant.
    For the increasing phases use an exponential of the form:
    \begin{equation}
       f_{A,\tau, y_0}(t) = y_0 + A \cdot \left(1 - e^{-\frac{t}{\tau}}\right ),
    \end{equation}
    \part Plot the decays into the data.
    \part Plot the estimated time-constants as a function of stimulus intensity.
  \end{parts}
\end{questions}

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