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Jan Grewe 2019-01-19 10:00:16 +01:00
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projects/project_stimulus_reconstruction/stimulus_reconstruction.tex
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%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Reverse reconstruction of the stimulus that evoked a neuronal response.} \section*{Reverse reconstruction of the stimulus that evoked a neuronal response.}
To analyse encoding properties of a neuron one often calculates the To analyse the encoding properties of a neuron one often calculates the
Spike-Triggered-Average (STA). The STA is the average stimulus that Spike-Triggered-Average (STA). The STA is the average stimulus that
led to a spike in the neuron: led to a spike in the neuron:
\[ STA(\tau) = \frac{1}{n} \displaystyle\sum_{i=1}^{n}{s(t_i - \tau)} \] \[ STA(\tau) = \frac{1}{n} \displaystyle\sum_{i=1}^{n}{s(t_i - \tau)} \]
where $n$ is the number of spikes and $t_i$ is the time of the where $n$ is the number of spikes and $t_i$ is the time of the
$i_{th}$ spike. $\tau$ is a temporal shift relative to the spike $i_{th}$ spike. $\tau$ is a temporal shift relative to the spike
time. For the beginning let $\tau$ assume values in the range time. For the beginning let $\tau$ assume values in the range
$\pm50$\,ms. It can be estimated by cutting out snippets form the $\pm50$\,ms. The STA can be estimated by cutting out snippets from the
stimulus centered on the respective spike time and averaging them. The stimulus that are centered on the respective spike time and by
Spike-Triggered-Average can be used to reconstruct the stimulus from subsequently averaging them. The STA can be used to reconstruct the
the neuronal response. The reconstructed stimulus can then be compared stimulus from the neuronal response. The reconstructed stimulus can
to the original stimulus. then be compared to the original stimulus and provides a good
impression about the features that are encoded in the neuronal
response.
\begin{questions} \begin{questions}
\question In the accompanying data files you find the spike responses of \question In the accompanying data files you find the spike
a p-type electroreceptor afferent (P-unit) and a pyramidal neuron responses of a p-type electroreceptor afferent (P-unit) and a
recorded in the hindbrain of the weakly electric fish pyramidal neuron recorded in the hindbrain of the weakly electric
\textit{Apteronotus leptorhynchus}. The respective stimuli are fish \textit{Apteronotus leptorhynchus}. The respective stimuli are
stored in separate files. The data is sampled with 20\,kHz temporal stored in separate files. The neron is stimulated with an amplitude
resolution and spike times are given in seconds. Start with the modulation of the fish's own electric field. The stored stimulus
P-unit and, in the end, apply the same analyzes/functions to the trace is the modulator that is applied to the field and is
responses from the pyramidal neuron. dimensionless, i.e. it has not unit. 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
analyzes/functions to the responses from the pyramidal neuron.
\begin{parts} \begin{parts}
\part Estimate the STA and plot it. What does it tell? \part Estimate the STA and plot it. What does it tell?
\part Implement a function that does the reverse reconstruction and uses the STA to reconstruct the stimulus. \part Implement a function that does the reverse reconstruction and uses the STA to reconstruct the stimulus.