47 lines
1.9 KiB
TeX
47 lines
1.9 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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%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
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\section*{Quantifying the coupling of action potentials to the EOD.}
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P-unit electroreceptors are driven by the fish's self-generated field,
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the EOD. In this project you have to quantify the strength of this
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coulpling 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 $0$ and $1$ for no phase locking to perfect phase
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locking, respectively.
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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 of different weakly
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electric fish of the species \textit{Apteronotus leptorhynchus}.
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The files further contain respective recordings of the \textit{eod},
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i.e. the fish's field The data is sampled with 20\,kHz and the spike
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times are given in seconds.
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\begin{parts}
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\part Plot the average EOD waveform of each fish together with an respective PSTH.
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\part Implement a function that estimates the vector strength
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between the \textit{eod} and the spikes.
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\part Create a polar plot that shows the timing of the spikes
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relatve to the EOD.
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\part Analyze the baseline responses of each fish and extrace measures as were introduced in chapter 8 of the script. Plot the results
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appropriately.
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\part Does the vector strength correlate with the EOD frequency?
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\end{parts}
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\end{questions}
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\end{document}
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