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[project_vectorstrength] text improvements

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Jan Grewe 2019-01-13 12:22:27 +01:00
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projects/project_vector_strength/vector_strength.tex
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@ -11,9 +11,16 @@
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Quantifying the coupling of action potentials to the EOD.} \section*{Quantifying the coupling of action potentials to the EOD.}
P-unit electroreceptors are driven by the fish's self-generated field, Phase coupling of neuronal activity is observed in several
the EOD. In this project you have to quantify the strength of this system. This means that the action potentials fired by a neuron occur
coulpling using the \textbf{vector strength}: 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} \begin{equation}
VS = \sqrt{\left(\frac{1}{n}\sum_{i=1}^{n}\cos 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 \alpha_i\right)^2 + \left(\frac{1}{n}\sum_{i = 1}^{n} \sin \alpha_i
@ -26,20 +33,22 @@ locking, respectively.
\begin{questions} \begin{questions}
\question In the accompanying datasets you find recordings of the \question In the accompanying datasets you find recordings of the
``baseline'' activity of P-unit electroreceptors of different weakly ``baseline'' activity of P-unit electroreceptors (in the absence of
electric fish of the species \textit{Apteronotus leptorhynchus}. an external stimulus) of different weakly electric fish of the
The files further contain respective recordings of the \textit{eod}, species \textit{Apteronotus leptorhynchus}. The files further
i.e. the fish's field The data is sampled with 20\,kHz and the spike contain respective recordings of the \textit{eod}, i.e. the fish's
times are given in seconds. electric field. The data is sampled with 20\,kHz and the spike times
are given in seconds.
\begin{parts} \begin{parts}
\part Plot the average EOD waveform of each fish together with an respective PSTH. \part Illustrate the phase locking by plotting the PSTH within the EOD cycle.
\part Implement a function that estimates the vector strength \part Implement a function that estimates the vector strength
between the \textit{eod} and the spikes. between the \textit{EOD} and the spikes.
\part Create a polar plot that shows the timing of the spikes \part Create a polar plot that shows the timing of the spikes
relatve to the EOD. relatve to the EOD.
\part Analyze the baseline responses of each fish and extrace measures as were introduced in chapter 8 of the script. Plot the results \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. appropriately.
\part Does the vector strength correlate with the EOD frequency? \part Does the vector strength correlate with the EOD frequency or the reponse variability (CV)?
\end{parts} \end{parts}
\end{questions} \end{questions}