67 lines
2.5 KiB
TeX
67 lines
2.5 KiB
TeX
\documentclass[a4paper,12pt,pdftex]{exam}
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\newcommand{\ptitle}{Vector strength}
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\input{../header.tex}
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\firstpagefooter{Supervisor: Jan Grewe}{phone: 29 74588}%
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{email: jan.grewe@uni-tuebingen.de}
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\begin{document}
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\input{../instructions.tex}
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Phase coupling of neuronal activity is observed in many systems. This
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means that the action potentials fired by a neuron occur with a
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specific phase relation to a driving periodic signal. For example,
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sensory neurons in auditory systems and electrosensory systems fire in
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close phase relation to the stimulus frequency. P-type
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electroreceptor afferents (P-units) of the weakly electric fish
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\emph{Apteronotus leptorhynchus} are driven by the fish's
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self-generated field, the electric organ discharge (EOD), and fire
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action potentials phase locked to it.
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In this project you quantify the strength of the coupling of P-unit
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spikes to the EOD using the \textbf{vector strength}:
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\begin{equation}
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VS = \sqrt{\left(\frac{1}{n}\sum_{i=1}^{n}\cos
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\alpha_i\right)^2 + \left(\frac{1}{n}\sum_{i = 1}^{n} \sin \alpha_i
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\right)^2},
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\end{equation}
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with $n$ the number of spikes and $\alpha_i$ the timing of the each
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spike expressed as the phase relative to the EOD. The vector strength
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varies between $0$ for no phase locking and $1$ for perfect phase
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locking.
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\begin{questions}
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\question In the accompanying datasets you find recordings of the
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``baseline'' activity of P-unit electroreceptors (in the absence of
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an external stimulus) of different weakly electric fish of the
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species \textit{Apteronotus leptorhynchus}. The files further
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contain respective recordings of the EOD, i.e. the fish's
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electric field. The data is sampled with 20\,kHz and the spike times
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are given in seconds.
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\begin{parts}
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\part Plot the EOD with the evoked spikes on top.
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\part Illustrate the phase locking by plotting the PSTH within the
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EOD cycle.
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\part Implement a function that estimates the vector strength
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between the EOD and the spikes.
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\part Create a polar plot that shows the timing of the spikes
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relative to the EOD.
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\part Apply an appropriate statistical test to check whether
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locking is statistically significant.
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\part Analyze the baseline responses of each fish and extract
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measures as were introduced in chapter 10 of the script. Plot the
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results appropriately.
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\part Does the vector strength correlate with the EOD frequency or
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the reponse variability (CV)?
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\end{parts}
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\end{questions}
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\end{document}
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