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Jan Grewe
2019-01-11 11:57:14 +01:00
parent 10a3fa580a
commit ae51f8c3e1
4 changed files with 72 additions and 37 deletions
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projects/project_stimulus_reconstruction/stimulus_reconstruction.tex
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@@ -10,29 +10,29 @@
\input{../instructions.tex}
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Reverse reconstruction of the stimulus evoking neuronal responses.}
\section*{Reverse reconstruction of the stimulus that evoked a neuronal response.}
To analyse encoding properties of a neuron one often calculates the
Spike-Triggered-Average (STA).
\[ STA(\tau) = \frac{1}{\langle n \rangle} \left\langle
\displaystyle\sum_{i=1}^{n}{s(t_i - \tau)} \right\rangle \]
The STA is the average stimulus that led to a spike in the neuron and
is calculated by cutting out snippets form the stimulus centered on
the respective spike time. The Spike-Triggered-Average can be used to
reconstruct the stimulus a neuron has been stimulated with.
Spike-Triggered-Average (STA). The STA is the average stimulus that
led to a spike in the neuron and is calculated by cutting out snippets
form the stimulus centered on the respective spike time:
\[ STA(\tau) = \frac{1}{n} \displaystyle\sum_{i=1}^{n}{s(t_i - \tau)} \],
where $n$ is the number of trials and $t_i$ is the time of the
$i_{th}$ spike. The Spike-Triggered-Average can be used to reconstruct
the stimulus from the neuronal response. The reconstructed stimulus
can then be compared to the original stimulus.
\begin{questions}
\question In the accompanying files you find the spike responses of
P-units and pyramidal neurons of the weakly electric fish
a p-type electroreceptor afferent (P-unit) and a pyramidal neurons
recorded in the hindbrain of the weakly electric fish
\textit{Apteronotus leptorhynchus}. The respective stimuli are
stored in separate files. The data is sampled with 20\,kHz temporal
resolution and spike times are given in seconds. Start with the
P-unit and, in the end, apply the same functions to the pyramidal
data.
P-unit and, in the end, apply the same analyzes/functions to the
pyramidal data.
\begin{parts}
\part Estimate the STA and plot it.
\part Implement a function that does the reconstruction of the
stimulus using the STA.
\part Implement a function that does the reverse reconstruction and uses the STA to recopnstruct the stimulus.
\part Implement a function that estimates the reconstruction
error using the mean-square-error and express it relative to the
variance of the original stimulus.
@@ -44,8 +44,8 @@ reconstruct the stimulus a neuron has been stimulated with.
\part Analyze the robustness of the reconstruction: Estimate
the STA with less and less data and estimate the reconstruction
error.
\part Plot the reconstruction error as a function of the data
amount used to estimate the STA.
\part Plot the reconstruction error as a function of the amount of data
used to estimate the STA.
\part Repeat the above steps for the pyramidal neuron, what do you
observe?
\end{parts}