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