57 lines
2.7 KiB
TeX
57 lines
2.7 KiB
TeX
\documentclass[a4paper,12pt,pdftex]{exam}
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\newcommand{\ptitle}{Reverse reconstruction}
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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*{Reverse reconstruction of the stimulus that evoked a neuronal response.}
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To analyse the encoding properties of a neuron one often calculates the
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Spike-Triggered-Average (STA). The STA is the average stimulus that
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led to a spike in the neuron:
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\[ STA(\tau) = \frac{1}{n} \displaystyle\sum_{i=1}^{n}{s(t_i - \tau)} \]
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where $n$ is the number of spikes and $t_i$ is the time of the
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$i_{th}$ spike. $\tau$ is a temporal shift relative to the spike
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time. For the beginning let $\tau$ assume values in the range
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$\pm50$\,ms. The STA can be estimated by cutting out snippets from the
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stimulus that are centered on the respective spike time and by
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subsequently averaging these stimulus snippets. The STA can be used to
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reconstruct the stimulus from the neuronal response (reverse
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reconstruction). The reconstructed stimulus can then be compared to
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the original stimulus and provides a good impression about the
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features that are encoded in the neuronal response.
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\begin{questions}
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\question In the accompanying data files you find the spike
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responses of a p-type electroreceptor afferent (P-unit) and a
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pyramidal neuron recorded in the hindbrain of the weakly electric
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fish \textit{Apteronotus leptorhynchus}. The respective stimuli are
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stored in separate files. The neron is stimulated with an amplitude
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modulation of the fish's own electric field. The stored stimulus
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trace is the modulator that is applied to the field and is
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dimensionless, i.e. it has no unit. The data is sampled with
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20\,kHz temporal resolution and spike times are given in
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seconds. Start with the P-unit and, in the end, apply the same
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analyzes/functions to the pyramidal cell.
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\begin{parts}
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\part Estimate the STA and plot it. What does it tell?
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\part Implement a function that does the reverse reconstruction and uses the STA to reconstruct the stimulus.
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\part Implement a function that estimates the reconstruction quality.
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\part Test the robustness of the reconstruction: Estimate
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the STA with less and less data and estimate the reconstruction
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error.
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\part Plot the reconstruction error as a function of the amount of data
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used to estimate the STA and apply a statistical test to test if
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estimating the STA from more data improves the reconstruction.
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\part Repeat the above steps for the pyramidal neuron, what do you
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observe?
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\end{parts}
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\end{questions}
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\end{document}
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