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Dennis Huben 2024-09-25 15:33:02 +02:00
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@ -616,7 +616,7 @@ We also tried different other methods of quantifying noise commonly used (citati
We calculate the cross correlation between the signal and the discrete output spikes.
The signal values were binned in 50 bins. The result is a discrete Gaussian distribution around 0mV, the mean of the signal, as is expected from the way the signal was created.
We have to account for the delay between the moment we play the signal and when it gets processed in the cell, which can for example depend on the position of the cell on the skin. We can easily reconstruct the delay from the measurements.
The position of the peak of the crosscorrelation is the time shift for which the signal influences the result of the output the most. For an explanation, see figure \ref{timeshift}
The position of the peak of the crosscorrelation is the time shift for which the signal influences the result of the output the most. For an explanation, see figure \ref{timeshift}.
Then for every spike we assign the value of the signal at the time of the spike minus the time shift.
The result is a histogram, where each signal value bin has a number of spikes.
This histogram is then normalized by the distribution of the signal. The result is another histogram, whose values are firing frequencies for each signal value. Because those frequencies are just firing probabilities multiplied by time, we can fit a Gaussian error function to those probabilities.
@ -674,7 +674,7 @@ of each other and there is no feedback.
\includegraphics[width=0.7\linewidth]{img/explain_analysis/after_timeshift_11.pdf}
\caption{Top: Spike train of a p-unit.
Middle: Situation as recorded: Signal is blue, the response from the cells created from the spike train is orange.
Bottom: The signal was shifted back in time, so that the response fits the signal better. This corrects for any delays in the recording process.
Bottom: The signal was shifted forward in time, so that the response fits the signal better. This corrects for any delays in the recording process.
}
\label{timeshift}
\end{figure}
@ -714,10 +714,6 @@ The noisiest cells which make up the fourth quartile interval (largest $\sigma$,
These results qualitatively do not depend on the choice of separating the cells into quartiles. Please see the appendix (figures \ref{3_groups_cf_vs_pop} and \ref{5_groups_cf_vs_pop}) for similar results with splitting the cells into tertiles and quintiles.
The curves from which the averages were created can be seen in figure \ref{2_by_2_overview}. The curves in the top left which make up the blue curve in figure \ref{ephys_sigma} are in the majority very flat. On the other hand, most of the curves in the bottom right that make up the red curve in figure \ref{ephys_sigma} start very low and bend to the left, showing the coding fraction increase is larger for the larger population sizes observed here.
Noisier cells (larger $\sigma$, red) have a lower coding fraction for small populations. However, coding fraction mostly stops increasing with population sizes once a population size of about 16 is reached. The increase is much larger for noisy cells (orange). The averages of the coding fraction for the noisy cells does not increase above the coding fraction of the less noisy cells for the population sizes investigated here (N=128). In contrast to the more regular cells, coding fraction is still improving for the noisy cells, so it is plausible that at a certain population size the noisy cells can outperform the less noisy cells.
Indeed, if results are not averaged and single cells are considered, we find that for large population sizes the noisy cells show a better linear encoding of the signal than the more regular cells (figure \ref{ephys_sigma} b), red).
\begin{figure}
\includegraphics[width=0.8\linewidth]{img/sigma/0_300/2_by_2_overview.pdf}
\caption{Individual plots of the cells used in figure \ref{ephys_sigma}. Top left represents the cells in the first quartile (low $\sigma$, so little noise). Top right represents the second quartile, bottom left the third quartile. Bottom right shows the noisiest cells with the largest $\sigma$}
@ -747,14 +743,25 @@ Indeed, if results are not averaged and single cells are considered, we find tha
%\includegraphics[width=0.45\linewidth]{img/ordnung/sigma_popsize_curves_0to300}
\centering
%\includegraphics[width=0.45\linewidth]{img/sigma/cf_N_ex_lines}
\includegraphics[width=0.45\linewidth]{img/sigma/sigma_cf_quot.pdf}%
\includegraphics[width=0.45\linewidth]{img/sigma/check_fr_quot.pdf}%
\includegraphics[width=0.45\linewidth]{img/sigma/0_300/scatter_and_fits_sigma_quot_firing_rate}%
\includegraphics[width=0.45\linewidth]{img/sigma/0_300/scatter_and_fits_firing_rate_quot_contrast}%
\caption{Left: Coding fraction as a function of population size for all recorded neurons. Cells are grouped by \(\sigma\) from the fit of the function in equation \ref{errorfct}. Lines are averages over three cells each, with the shading showing the standard deviation. For stronger noise, coding fraction is far smaller for a single neuron. With increasing population size, coding fraction increases much faster for the noisy cells than for the less noisy cells.
Right: Examples for the two cells with lowest, intermediate and highest $\sigma$. For a population size of N=1, the cell with the largest $\sigma$ (brown) has the lowest coding fraction out of all the cells here. The coding fraction of that cell increases hugely with population size. At a population of N=128, coding fraction is second highest among the pictured cells.}
\label{ephys_sigma}
\end{figure}
%The value of $\sigma$ is not signal independent. The same cell can have different values for $\sigma$ for different input signals.
Qualitatively we see very similar results when instead of the broadband signal we use the narrowband signal with a frequency cutoff of 50Hz (figure \ref{overview_experiment_results_narrow}. Again the cells in the first quantile interval show on average only a very slightly increasing coding fraction with increasing population size. Coding fraction for a population size of one on average decreases for the higher quartile intervals. The seperate coding fraction curves also show the typical flatness for the first quartile interval. The fourth quartile interval in particular contains several curves that are only just beginning to increase in coding fraction at a population size of 64 neurons.
\begin{figure}
\includegraphics[width=0.8\linewidth]{img/sigma/narrow_0_50/averaged_4parts.pdf}
\includegraphics[width=0.8\linewidth]{img/sigma/narrow_0_50/2_by_2_overview.pdf}
\caption{Equivalent plots to \ref{ephys_sigma} and \ref{2_by_2_overview}, just for the narrowband signal with a cutoff frequency of 50Hz. The general trend is the same.}
\label{overview_experiment_results_narrow}
\end{figure}
\subsection*{Results}