From 1f7ad45f8439b852a61fa49adc668f0744c4837e Mon Sep 17 00:00:00 2001 From: Dennis Huben Date: Mon, 13 Jan 2025 13:59:39 +0100 Subject: [PATCH] Add new figures (overview of fit results that show sigma works better than cv or fr) and some text --- img/sigma/0_300/2_by_2_overview.pdf | Bin 15830 -> 15830 bytes img/sigma/0_300/averaged_4parts.pdf | Bin 12725 -> 12713 bytes ...its_contrast_coding_fractions_contrast.pdf | Bin 16690 -> 16690 bytes ..._contrast_coding_fractions_firing_rate.pdf | Bin 18005 -> 18005 bytes ...d_fits_contrast_coding_fractions_sigma.pdf | Bin 17436 -> 17436 bytes ...and_fits_contrast_firing_rate_contrast.pdf | Bin 17758 -> 17758 bytes ..._fits_contrast_firing_rate_firing_rate.pdf | Bin 17029 -> 17029 bytes ...er_and_fits_contrast_firing_rate_sigma.pdf | Bin 18055 -> 18055 bytes ..._and_fits_cv_coding_fractions_contrast.pdf | Bin 17167 -> 17163 bytes ...d_fits_cv_coding_fractions_firing_rate.pdf | Bin 17617 -> 17614 bytes 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However, this might not be ideal in case of cells which need a population size larger than the 64 neurons observed here; the coding fraction increase from 1 to 64 neurons might then look small, even though the cells actually fit our model very well. Examples for neurons like this are in figure \ref{2_by_2_overview}: in the bottom right panel there are the bottom two lines with only a small increase in coding fraction, but both lines appear to become steeper with rising population size, so it is not unthinkable that they would rise much further for very large populations. It's a limitation of the current experiments that we can only record a finite amount of trials from each neuron.\notedh{Discussion??} The result shown in figure \ref{increases_broad} is that $\sigma$ is a good predictor of the gain (quotient between coding fraction at 64 cells and coding fraction at 1 cell). Additionally, the firing rate negatively correlates with the gain, but more weakly. -For the difference between coding fraction of a single neuron and a population we do not see any correlation neither with $\sigma$ nor with the firing rate. +For the difference between coding fraction of a single neuron and a population we do not see any correlation neither with $\sigma$ nor with the firing rate. As seen in figure \ref{2_by_2_overview} some of the cells only begin to take off in coding fraction near that population size. So the absolute difference is quite small at this point. If we had population sizes larger than 64, the regression would make more sense; the less noisy cells will have similar values of $c_{64}$ and e.g. $c_{512}$, but for the noisier cells there can be a huge difference. + %figures created with result_fits.py @@ -701,6 +702,20 @@ Bottom: Using the difference in coding fraction instead of the quotient makes th \label{increases_broad} \end{figure} +\begin{figure} +\centering +\includegraphics[width=0.45\linewidth]{img/sigma/fit_results_overviews/fit_results_sigma_broad_diff.pdf} +\includegraphics[width=0.45\linewidth]{img/sigma/fit_results_overviews/fit_results_sigma_broad_quot.pdf} + +\includegraphics[width=0.45\linewidth]{img/sigma/fit_results_overviews/fit_results_firing_rate_broad_diff.pdf} +\includegraphics[width=0.45\linewidth]{img/sigma/fit_results_overviews/fit_results_firing_rate_broad_quot.pdf} + +\includegraphics[width=0.45\linewidth]{img/sigma/fit_results_overviews/fit_results_cv_broad_diff.pdf} +\includegraphics[width=0.45\linewidth]{img/sigma/fit_results_overviews/fit_results_cv_broad_quot.pdf} \notedh{leave CV out? Consistent with narrow band?} +\caption{\todo{write}} +\label{overview_fits_broad} +\end{figure} + \subsubsection{Narrowband} 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. @@ -713,7 +728,7 @@ Qualitatively we see very similar results when instead of the broadband signal w \label{overview_experiment_results_narrow} \end{figure} -Figures \ref{increases_narrow} and \ref{increases_narrow_high} both show that the results with regards to the increase of coding fraction for different population sizes seen for the broadband signal also appear when we use narrowband signals. For the high frequency signal (250Hz to 300Hz, figure \ref{increases_narrow_high} the correlation between the coding fraction increase and the firing rate is higher than the correlation between the coding fraction increase and $\sigma$. +Figures \ref{increases_narrow} and \ref{increases_narrow_high} both show that the results with regards to the increase of coding fraction for different population sizes seen for the broadband signal also appear when we use narrowband signals. For the high frequency signal (250Hz to 300Hz, figure \ref{increases_narrow_high} the correlation between the coding fraction increase and the firing rate is higher than the correlation between the coding fraction increase and $\sigma$. As seen before, taking the difference between the coding fraction of a population size of 64 ($c_{64}$) and at a population of 1 ($c_1$) might not work out. With the narrowband signal even more than with the broadband signal some of the cells only begin to take off in coding fraction near that population size of 64 \ref{overview_experiment_results_narrow}. So the absolute difference is quite small at this point. If we had population sizes larger than 64, the regression would make more sense; the less noisy cells will have similar values of $c_{64}$ and e.g. $c_{512}$, but for the noisier cells there can be a huge difference. %figures created with result_fits.py @@ -733,6 +748,25 @@ Figures \ref{increases_narrow} and \ref{increases_narrow_high} both show that th \end{figure} +The results (figure \ref{overview_fits}) show \todo{write} + +\begin{figure} +\centering +\includegraphics[width=0.45\linewidth]{img/sigma/fit_results_overviews/fit_results_sigma_narrow_diff.pdf} +\includegraphics[width=0.45\linewidth]{img/sigma/fit_results_overviews/fit_results_sigma_narrow_quot.pdf} + +\includegraphics[width=0.45\linewidth]{img/sigma/fit_results_overviews/fit_results_firing_rate_narrow_diff.pdf} +\includegraphics[width=0.45\linewidth]{img/sigma/fit_results_overviews/fit_results_firing_rate_narrow_quot.pdf} + +\includegraphics[width=0.45\linewidth]{img/sigma/fit_results_overviews/fit_results_cv_narrow_diff.pdf} +\includegraphics[width=0.45\linewidth]{img/sigma/fit_results_overviews/fit_results_cv_narrow_quot.pdf} \notedh{leave them out? No idea why the fits aren't working for the smaller intervals} +\caption{\todo{write} +For the frequency range of 150-200Hz only four data points are present (compare figure \ref{experiments_narrow_150_200}); for 50-100Hz only six trials were available (compare figure \ref{experiments_narrow_50_100}).} +\label{overview_fits_narrow} +\end{figure} + + + %figures created with result_fits.py \begin{figure} \centering @@ -742,7 +776,7 @@ Figures \ref{increases_narrow} and \ref{increases_narrow_high} both show that th \centering \includegraphics[width=0.45\linewidth]{img/sigma/narrow_250_300/scatter_and_fits_sigma_diff_firing_rate}% \includegraphics[width=0.45\linewidth]{img/sigma/narrow_250_300/scatter_and_fits_firing_rate_diff_contrast}% - \caption{Narrowband signal with 250Hz-300Hz. 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. + \caption{Narrowband signal with 250Hz-300Hz. 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. Both cell firing rate and $sigma$ determine the increase, even though firing rate and $sigma$ themselves are almost independent of each other (figure \ref{fr_sigma}) Bottom: Using the difference in coding fraction instead of the quotient makes the relationship between the increase in coding fraction and the two parameters $\sigma$ and firing rate disappear. This might be different for larger population sizes.} \label{increases_narrow_high} \end{figure} @@ -810,11 +844,11 @@ Bottom: Using the difference in coding fraction instead of the quotient makes th \end{figure} \begin{figure} -\includegraphics[width=0.49\linewidth]{img/experiments/narrow_50_100/2_by_2_overview.pdf} -\includegraphics[width=0.49\linewidth]{img/experiments/narrow_50_100/averaged_4parts.pdf} -\includegraphics[width=0.49\linewidth]{img/experiments/narrow_50_100/scatter_and_fits_sigma_quot_firing_rate.pdf} -\includegraphics[width=0.49\linewidth]{img/experiments/narrow_50_100/scatter_and_fits_sigma_diff_firing_rate.pdf} - \label{experiments_narrow_50_100} +\includegraphics[width=0.49\linewidth]{img/sigma/narrow_50_100/2_by_2_overview.pdf} +\includegraphics[width=0.49\linewidth]{img/sigma/narrow_50_100/averaged_4parts.pdf} +\includegraphics[width=0.49\linewidth]{img/sigma/narrow_50_100/scatter_and_fits_sigma_quot_firing_rate.pdf} +\includegraphics[width=0.49\linewidth]{img/sigma/narrow_50_100/scatter_and_fits_sigma_diff_firing_rate.pdf} + \label{sigma_narrow_50_100} \caption{Experimental data for a signal with a lower cutoff frequency of 50Hz and an upper cutoff of 100Hz. A: Coding fraction as a function of population size. Cells are grouped in quartiles according to $\sigma$. B: Coding fraction as a function of population size. Each curve shows an average over the cells in one panel of A. Shaded area shows the standard deviation. @@ -824,11 +858,11 @@ Bottom: Using the difference in coding fraction instead of the quotient makes th \end{figure} \begin{figure} -\includegraphics[width=0.49\linewidth]{img/experiments/narrow_150_200/2_by_2_overview.pdf} -\includegraphics[width=0.49\linewidth]{img/experiments/narrow_150_200/averaged_4parts.pdf} -\includegraphics[width=0.49\linewidth]{img/experiments/narrow_150_200/scatter_and_fits_sigma_quot_firing_rate.pdf} -\includegraphics[width=0.49\linewidth]{img/experiments/narrow_150_200/scatter_and_fits_sigma_diff_firing_rate.pdf} - \label{experiments_narrow_150_200} +\includegraphics[width=0.49\linewidth]{img/sigma/narrow_150_200/2_by_2_overview.pdf} +\includegraphics[width=0.49\linewidth]{img/sigma/narrow_150_200/averaged_4parts.pdf} +\includegraphics[width=0.49\linewidth]{img/sigma/narrow_150_200/scatter_and_fits_sigma_quot_firing_rate.pdf} +\includegraphics[width=0.49\linewidth]{img/sigma/narrow_150_200/scatter_and_fits_sigma_diff_firing_rate.pdf} + \label{sigma_narrow_150_200} \caption{Experimental data for a signal with a lower cutoff frequency of 150Hz and an upper cutoff of 200Hz. A: Coding fraction as a function of population size. Cells are grouped in quartiles according to $\sigma$. B: Coding fraction as a function of population size. Each curve shows an average over the cells in one panel of A. Shaded area shows the standard deviation. @@ -838,11 +872,11 @@ Bottom: Using the difference in coding fraction instead of the quotient makes th \end{figure} \begin{figure} -\includegraphics[width=0.49\linewidth]{img/experiments/narrow_250_300/2_by_2_overview.pdf} -\includegraphics[width=0.49\linewidth]{img/experiments/narrow_250_300/averaged_4parts.pdf} -\includegraphics[width=0.49\linewidth]{img/experiments/narrow_250_300/scatter_and_fits_sigma_quot_firing_rate.pdf} -\includegraphics[width=0.49\linewidth]{img/experiments/narrow_250_300/scatter_and_fits_sigma_diff_firing_rate.pdf} - \label{experiments_narrow_250_300} +\includegraphics[width=0.49\linewidth]{img/sigma/narrow_250_300/2_by_2_overview.pdf} +\includegraphics[width=0.49\linewidth]{img/sigma/narrow_250_300/averaged_4parts.pdf} +\includegraphics[width=0.49\linewidth]{img/sigma/narrow_250_300/scatter_and_fits_sigma_quot_firing_rate.pdf} +\includegraphics[width=0.49\linewidth]{img/sigma/narrow_250_300/scatter_and_fits_sigma_diff_firing_rate.pdf} + \label{sigma_narrow_250_300} \caption{Experimental data for a signal with a lower cutoff frequency of 250Hz and an upper cutoff of 300Hz. A: Coding fraction as a function of population size. Cells are grouped in quartiles according to $\sigma$. B: Coding fraction as a function of population size. Each curve shows an average over the cells in one panel of A. Shaded area shows the standard deviation. @@ -852,11 +886,11 @@ Bottom: Using the difference in coding fraction instead of the quotient makes th \end{figure} \begin{figure} -\includegraphics[width=0.49\linewidth]{img/experiments/narrow_350_400/2_by_2_overview.pdf} -\includegraphics[width=0.49\linewidth]{img/experiments/narrow_350_400/averaged_4parts.pdf} -\includegraphics[width=0.49\linewidth]{img/experiments/narrow_350_400/scatter_and_fits_sigma_quot_firing_rate.pdf} -\includegraphics[width=0.49\linewidth]{img/experiments/narrow_350_400/scatter_and_fits_sigma_diff_firing_rate.pdf} - \label{experiments_narrow_350_400} +\includegraphics[width=0.49\linewidth]{img/sigma/narrow_350_400/2_by_2_overview.pdf} +\includegraphics[width=0.49\linewidth]{img/sigma/narrow_350_400/averaged_4parts.pdf} +\includegraphics[width=0.49\linewidth]{img/sigma/narrow_350_400/scatter_and_fits_sigma_quot_firing_rate.pdf} +\includegraphics[width=0.49\linewidth]{img/sigma/narrow_350_400/scatter_and_fits_sigma_diff_firing_rate.pdf} + \label{sigma_narrow_350_400} \caption{Experimental data for a signal with a lower cutoff frequency of 350Hz and an upper cutoff of 400Hz. A: Coding fraction as a function of population size. Cells are grouped in quartiles according to $\sigma$. B: Coding fraction as a function of population size. Each curve shows an average over the cells in one panel of A. Shaded area shows the standard deviation.

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