diff --git a/projects/project_stimulus_reconstruction/stimulus_reconstruction.tex b/projects/project_stimulus_reconstruction/stimulus_reconstruction.tex index eae2513..54fe252 100644 --- a/projects/project_stimulus_reconstruction/stimulus_reconstruction.tex +++ b/projects/project_stimulus_reconstruction/stimulus_reconstruction.tex @@ -15,24 +15,24 @@ To analyse encoding properties of a neuron one often calculates the 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: -\[ STA(\tau) = \frac{1}{n} \displaystyle\sum_{i=1}^{n}{s(t_i - \tau)} \], +\[ STA(\tau) = \frac{1}{n} \displaystyle\sum_{i=1}^{n}{s(t_i - \tau)} \] 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 - a p-type electroreceptor afferent (P-unit) and a pyramidal neurons + \question In the accompanying data files you find the spike responses of + a p-type electroreceptor afferent (P-unit) and a pyramidal neuron 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 analyzes/functions to the - pyramidal data. + responses from the pyramidal neuron. \begin{parts} - \part Estimate the STA and plot it. - \part Implement a function that does the reverse reconstruction and uses the STA to recopnstruct the stimulus. + \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 estimates the reconstruction error using the mean-square-error and express it relative to the variance of the original stimulus. @@ -45,7 +45,8 @@ can then be compared to the original stimulus. the STA with less and less data and estimate the reconstruction error. \part Plot the reconstruction error as a function of the amount of data - used to estimate the STA. + used to estimate the STA and apply a statistical test to test if + estimating the STA from more data improves the reconstruction. \part Repeat the above steps for the pyramidal neuron, what do you observe? \end{parts}