66 lines
2.6 KiB
TeX
66 lines
2.6 KiB
TeX
\documentclass[a4paper,12pt,pdftex]{exam}
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\newcommand{\ptitle}{Adaptation time-constant}
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\input{../header.tex}
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\firstpagefooter{Supervisor: Lukas Sonnenberg}{phone:}%
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{email: lukas.sonnenberg@uni-tuebingen.de}
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\begin{document}
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\input{../instructions.tex}
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Stimulating a neuron with a constant stimulus for an extended period
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of time often results in a decay of an initially strong response. This
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process is called adaptation. Your task here is to estimate the
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time-constant of the firing-rate adaptation in P-unit electroreceptors
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of the weakly electric fish \textit{Apteronotus leptorhynchus}.
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\begin{questions}
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\question In the accompanying datasets you find the
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\textit{spike\_times} of an P-unit electroreceptor to a stimulus of
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a certain intensity, i.e. the \textit{contrast} which is also stored
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in the file. The contrast of the stimulus is a measure relative to
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the amplitude of fish's field and is given in percent. The data is sampled
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with 20\,kHz sampling frequency and spike times are given in
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milliseconds (not seconds!) relative to stimulus onset.
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\begin{parts}
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\part Plot spike rasters of the data.
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\part Estimate for each stimulus intensity the PSTH. You will see
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that there are three parts: (i) The first 200\,ms is the baseline
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(no stimulus) activity. (ii) During the next 1000\,ms the stimulus
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was switched on. (iii) After stimulus offset the neuronal activity
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was recorded for further 825\,ms. Find an appropriate bin-width
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for the PSTH.
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\part Estimate the adaptation time-constant for both the stimulus
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on- and offset. To do this, fit an exponential function
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$f_{A,\tau,y_0}(t)$ to appropriate regions of the data:
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\begin{equation}
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f_{A,\tau,y_0}(t) = A \cdot e^{-\frac{t}{\tau}} + y_0,
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\end{equation}
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where $t$ is time, $A$ the (positive or negative) amplitude of the
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exponential decay, $\tau$ the adaptation time-constant, and $y_0$
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an offset.
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Before you do the fitting, familiarize yourself with the three
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parameter of the exponential function. What is the value of
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$f_{A,\tau,y_0}(t)$ at $t=0$? What is the value for large times? How does
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$f_{A,\tau,y_0}(t)$ change if you change either of the parameter?
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Which of the parameter could you directly estimate from the data
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(without fitting)?
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How could you get good estimates for the other parameter?
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Do the fit and show the resulting exponential function together
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with the data.
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\part Do the estimated time-constants depend on stimulus intensity?
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Use an appropriate statistical test to support your observation.
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\end{parts}
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\end{questions}
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\end{document}
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