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Add to results summary the part about the intervals in the broadband signal

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Dennis Huben 2025-01-22 18:40:04 +01:00
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@ -813,21 +813,15 @@ Figure \ref{overview_fits_narrow} compiles the results for the narrowband signal
\notedh{link to the appropriate chapter from theory results}
In addition to the ``pure'' narrowband signals, I also analysed the coding fraction change for a smaller part of the spectrum in the experiments using the broadband signal. Figure \ref{increases_narow_in_broad} shows part of the results and again we see the strong correlation between $\sigma$ and the gain and a lesser correlation between the firing rate and the gain. In this case we see the same correlation also for the coding fraction difference.
Similar results can be observed for the other frequency bands. \notedh{Images to the appendix? The sigma/gain of all in one plot?}
In addition to the ``pure'' narrowband signals, I also analysed the coding fraction change for a smaller part of the spectrum in the experiments using the 0-300Hz broadband signal. To relate the results to the results from the narrowband experiments, we split the frequency range in six disctinct 50Hz ranges (0-50Hz, 50-100Hz, ... 250-300Hz). The results we see are very similar to what we saw for the broadband signal (figure \ref{overview_fits_broad}, some details in figure \ref{increases_narow_in_broad}).
Considering the ratio between the coding fraction for a population size of 64 neurons ($c_{64}$) and the coding fraction for a single cell ($c_1$) we find that the correlation between the ratio and the noisiness \sig is best in the analysis using the entire signal range. But we also find correlations for all of the 50Hz ranges. In general, the correlations are slightly weaker than the result for the entire range (0.60 for the whole range, 0.42-0.58 for the smaller ranges).
With regards to the difference between the coding fractions for the different population sizes, for the whole range we didn't see any correlation. Analysing the smaller frequency intervals, we now find a correlation for the two lowest intervals (0-50Hz, $r^2=0.37$ and 50-100Hz, $r^2=0.44$), but not for any of the other ranges.
Previously, when we investigated the correlation between the two measures of population size effects and the firing rate, for the broadband signal we didn't see any correlation. This was very different for the narrowband signals, where in many cases we could show some correlation. When we repeat the analysis for the frequency ranges inside the broadband signal, we find the same we did for the entire broadband signal: No correlations that are distinguishable from noise.
%figures created with result_fits.py
\begin{figure}
\centering
\includegraphics[width=0.45\linewidth]{img/sigma/0_50/scatter_and_fits_sigma_quot_firing_rate}%
\includegraphics[width=0.45\linewidth]{img/sigma/0_50/scatter_and_fits_firing_rate_quot_contrast}%
\includegraphics[width=0.45\linewidth]{img/sigma/0_50/scatter_and_fits_sigma_diff_firing_rate}%
\includegraphics[width=0.45\linewidth]{img/sigma/0_50/scatter_and_fits_firing_rate_diff_contrast}%
\caption{Broadband signal with a cutoff frequency of 300Hz, but the coding fraction was calculated in the range 0Hz-50Hz. Top: The relative increase in coding fraction for population sizes 64 and 1. Note that the y-axis scales logarithmically Left: As a function of $\sigma$. Red curve shows a regression between $\sigma$ and $\log(c_{64}/c_{1})$. Right: As a function of cell firing rate. No correlation is observed.
Bottom: Same as above, but using the difference in coding fraction instead of the logarithm of the ratio. The result shows a smaller correlation between the increase in coding fraction and $\sigma$. The firing rate still doesn't show a correlation to the increase. }
\label{increases_narow_in_broad}
\end{figure}
In almost every analysis here, our results for the broadband signal are the same or at least very similar, independent of whether we apply the analysis to the whole range or just part of it.
In particular, there was a good correlation between the noisiness of the cells measured in \sig and the improvement.
However, for the broadband signal the neural firing rate allows no prediction of the improvement trough increased population size. This is in contrast to the narrowband signals. There, firing rate and noisiness (\sig) were very similar in their correlations to the increase in coding fraction from increased population size. We also saw a stronger influence of the firing rate on the coding fraction of a single neuron \todo{Add to table 29 and 30, instead of CV and turned, so that column 1 has sigma, column 2 firing rate and it goes n=1, c/c, c-c as in fig 28}.
\notedh{what to conclude here?}
\begin{figure}
\centering
@ -844,6 +838,20 @@ Left columns shows results for the difference in coding fraction, right column s
\label{overview_fits_broad}
\end{figure}
%figures created with result_fits.py
\begin{figure}
\centering
\includegraphics[width=0.45\linewidth]{img/sigma/0_50/scatter_and_fits_sigma_quot_firing_rate}%
\includegraphics[width=0.45\linewidth]{img/sigma/0_50/scatter_and_fits_firing_rate_quot_contrast}%
\includegraphics[width=0.45\linewidth]{img/sigma/0_50/scatter_and_fits_sigma_diff_firing_rate}%
\includegraphics[width=0.45\linewidth]{img/sigma/0_50/scatter_and_fits_firing_rate_diff_contrast}%
\caption{Broadband signal with a cutoff frequency of 300Hz, but the coding fraction was calculated in the range 0Hz-50Hz. Top: The relative increase in coding fraction for population sizes 64 and 1. Note that the y-axis scales logarithmically Left: As a function of $\sigma$. Red curve shows a regression between $\sigma$ and $\log(c_{64}/c_{1})$. Right: As a function of cell firing rate. No correlation is observed.
Bottom: Same as above, but using the difference in coding fraction instead of the logarithm of the ratio. The result shows a smaller correlation between the increase in coding fraction and $\sigma$. The firing rate still doesn't show a correlation to the increase. }
\label{increases_narow_in_broad}
\end{figure}
\section*{Appendix}
%compare_params_300.py auf oilbird