From 6b98300bdf0e277878a542bbfa3fd1f8f84200f1 Mon Sep 17 00:00:00 2001 From: Dennis Huben Date: Wed, 25 Sep 2024 14:48:50 +0200 Subject: [PATCH] Add figures for experimental results. 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..._and_fits_firing_rate_diff_firing_rate.pdf | Bin 0 -> 16614 bytes .../scatter_and_fits_firing_rate_quot.pdf | Bin 0 -> 15881 bytes ...ter_and_fits_firing_rate_quot_contrast.pdf | Bin 0 -> 17438 bytes ..._and_fits_firing_rate_quot_firing_rate.pdf | Bin 0 -> 16797 bytes .../scatter_and_fits_sigma_diff.pdf | Bin 0 -> 16278 bytes .../scatter_and_fits_sigma_diff_contrast.pdf | Bin 0 -> 16248 bytes ...catter_and_fits_sigma_diff_firing_rate.pdf | Bin 0 -> 17428 bytes .../scatter_and_fits_sigma_quot.pdf | Bin 0 -> 16205 bytes .../scatter_and_fits_sigma_quot_contrast.pdf | Bin 0 -> 16433 bytes ...catter_and_fits_sigma_quot_firing_rate.pdf | Bin 0 -> 17618 bytes img/sigma/narrow_50_100/separate_plots.pdf | Bin 0 -> 11363 bytes main.tex | 55 ++++++++++++------ 191 files changed, 36 insertions(+), 19 deletions(-) create mode 100644 img/explain_analysis/after_timeshift_11.pdf create mode 100644 img/sigma/0_300/2_by_2_overview.pdf create mode 100644 img/sigma/0_300/averaged_4parts.pdf create mode 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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. \notedh{This will be much clearer with a plot.} + 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. @@ -639,7 +639,6 @@ To confirm that the $\sigma$ parameter estimated from the fit is indeed a good m \begin{figure} \centering %\includegraphics[width=0.45\linewidth]{img/ordnung/base_D_sigma}\\ - \includegraphics[width=0.23\linewidth]{img/ISI_explanation.pdf} \includegraphics[width=0.23\linewidth]{img/cv_psth_sigma_compare/dataframe_scatter_labels_D_sigma_membrane_50.pdf} \includegraphics[width=0.23\linewidth]{img/cv_psth_sigma_compare/dataframe_scatter_labels_D_cv_membrane_50.pdf} \includegraphics[width=0.23\linewidth]{img/cv_psth_sigma_compare/dataframe_scatter_labels_D_psth_1ms_membrane_50.pdf} @@ -671,6 +670,15 @@ simulated neurons we used in our simulations because they do not receive any input other than the signal they are encoding. Individual cells fire independently of each other and there is no feedback. +\begin{figure} + \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. + } + \label{timeshift} +\end{figure} + \subsection*{Electrophysiology} @@ -679,11 +687,8 @@ We can see from figure \ref{sigmafits_example} that the fits look very close to \begin{figure} \includegraphics[width=0.4\linewidth]{img/ordnung/cropped_fitcurve_0_2010-08-31-ad-invivo-1_0.pdf} \includegraphics[width=0.4\linewidth]{img/ordnung/cropped_fitcurve_0_2010-08-11-aq-invivo-1_0.pdf} - \includegraphics[width=0.23\linewidth]{img/simulation_sigma_examples/fitcurve_50hz_0.0002noi500s_0_capped.pdf} - \includegraphics[width=0.23\linewidth]{img/simulation_sigma_examples/fitcurve_50hz_0.001noi500s_0_capped.pdf} - \includegraphics[width=0.23\linewidth]{img/simulation_sigma_examples/fitcurve_50hz_0.1noi500s_0_capped.pdf} % cropped_fitcurve_0_2010-08-31-ad-invivo-1_0.pdf: 0x0 px, 300dpi, 0.00x0.00 cm, bb= - \caption{Histogram of spike count distribution (firing rate) and errorfunction fits. 50 bins represent different values of the amplitude of the Gaussian distributed input signal \notedh{[maybe histogram in background again] - or better: One plot where I show the raw data - histrogram in background, number of spikes as dots.}. The value of each of those bins is the number of spikes during the times the signal was in that bin. Each of the values was normalized by the signal distribution. To account for delay, we first calculated the cross-correlation of signal and spike train and took its peak as the delay. The lines show fits according to equation \eqref{errorfct}. + \caption{Histogram of spike count distribution (firing rate) and errorfunction fits. 50 bins represent different values of the amplitude of the Gaussian distributed input signal \notedh{[maybe histogram in background again] - or better: One plot where I show the raw data - histrogram in background, number of spikes as dots.}. The value of each of those bins is the number of spikes during the times the signal was in that bin. Each of the values was normalized by the signal distribution. To account for delay, we first calculated the cross-correlation of signal and spike train and took its peak as the delay. This is necessary because there are delays between the signal being emitted and being registered by the cell. For an explanation, see figure \ref{timeshift}. The lines show fits according to equation \eqref{errorfct}. Below are some examples of different cells, with differently wide distributions. one with a relatively narrow distribution and one with a distribution that is more broad, as indicated by the parameter \(\sigma\). Different amounts of bins (30 and 100) showed no difference in resulting parameters. \notedh{Show a plot.} \notedh{Show more than two plots?}} \label{sigmafits_example} \end{figure} @@ -693,18 +698,39 @@ We can see from figure \ref{sigmafits_example} that the fits look very close to %TODO insert plot with sigma x-axis and delta_cf on y-axis here; also, plot with sigma as function of firing rate, also absoulte cf for different population size as function of sigma. \begin{figure} -\includegraphics[width=0.45\linewidth]{img/ordnung/sigma_popsize_curves_0to300} - \caption{Left: Coding fraction as a function of population size for all recorded neurons. Color are by \(\sigma\) from the fit of the function in equation \ref{errorfct}, so that there are roughly an equal number of neurons in each category. Red: \(\sigma = \) 0 to 0.5, pink: 0.5 to 1.0, purple: 1.0 to 1.5, blue: 1.5 and above. Thick colored lines are average of the neurons in each group. For a population size of 1, coding fraction descreases on average with increasing \(\sigma\). As population sizes increase, coding fraction for weak noise neurons quickly stops increasing. Strong noise neurons show better coding performance for larger popuation sizes (about 8 to 32 neurons). Right [missing]: Increase in coding as a function of sigma. y-axis shows the difference in coding fraction between N=1 and N=32,} +\includegraphics[width=0.8\linewidth]{img/sigma/0_300/averaged_4parts.pdf} + \caption{Coding fraction as a function of population size for the recorded trials; some neurons provided multiple trials. The trials have been grouped in ascending order with regards to $\sigma$. Plotted are the means and (shaded) the standard deviation of the quartile. Curves look similar to figure \ref{cf_limit}} \label{ephys_sigma} \end{figure} +% TODO insert plot with sigma x-axis and delta_cf on y-axis here; also, plot with sigma as function of firing rate, also absoulte cf for different population size as function of sigma. + +When we group neurons by their noise and plot coding fraction as a function of population size for averages of the groups, we see results similar to what we see for simulations (figure \ref{ephys_sigma}, compare to figure \ref{cf_limit}): +Cells which are not very noisy (small $\sigma$, blue) on average start with a larger coding fraction than noisier cells (for this, compare also fig \ref{c1_by_sigma}). While they show an increasing coding fraction for larger populations, the increase is small, less than a factor of 2. +The cells in the next quartile interval show on average only a slightly lower coding fraction for a population size of 1 than the cells in the first quartile interval. Their rise is much faster however, and somewhere between 4 and 8 cells they begin showing a higher coding fraction than the cells in the first quartile. +Cells in the third quartile interval have on average a coding fraction half as large as the cells in the first quartile for a single neuron. With increasing population size, the growth in coding fraction also becomes steeper and between 32 and 64 cells their average coding fraction passes the average coding fraction of the cells in the first quartile interval. +The noisiest cells which make up the fourth quartile interval (largest $\sigma$, red) start with the lowest coding fraction on average for small populations. For a single cell, the coding fraction is on average only about a quarter of the cells in the first quartile interval. The increase of coding fraction with increasing population size is quite slow at first, an effect we have also seen with very noisy cells in our simulations (see figure \ref{cf_limit} b)). For increasing population sizes the coding fraction increase becomes larger. +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 $\sigma$} + \label{2_by_2_overview} +\end{figure} + + + \begin{figure} \centering - \includegraphics[width=0.4\linewidth]{img/sigma/example_spikes_sigma.pdf} + \includegraphics[width=0.4\linewidth]{img/sigma/example_spikes_sigma_with_input.pdf} \includegraphics[width=0.28\linewidth]{img/ordnung/cropped_fitcurve_0_2010-08-11-aq-invivo-1_0.pdf} \includegraphics[width=0.28\linewidth]{img/sigma/cropped_fitcurve_0_2010-08-31-aj-invivo-1_0.pdf} - \notedh{Daraus ergibt sich nicht direkt eine Intuition, wieso das noisy ist. H\"angt einfach sehr am Eingangssignal; wenn es im eventplot (un-)regelm\"a\ss{}ig w\"are, k\"onnten wir auch einfach cv nehmen...}\\ % \includegraphics[width=0.28\linewidth]{img/ordnung/cropped_fitcurve_0_2010-08-31-ad-invivo-1_0.pdf} \includegraphics[width=0.4\linewidth]{img/fish/dataframe_scatter_sigma_cv.pdf} \includegraphics[width=0.4\linewidth]{img/fish/dataframe_scatter_sigma_firing_rate.pdf} @@ -716,15 +742,6 @@ We can see from figure \ref{sigmafits_example} that the fits look very close to \label{sigmafits} \end{figure} - -% TODO insert plot with sigma x-axis and delta_cf on y-axis here; also, plot with sigma as function of firing rate, also absoulte cf for different population size as function of sigma. - - - -When we group neurons by their noise and plot coding fraction as a function of population size for averages of the groups, we see results similar to what we see for simulations (figure \ref{ephys_sigma} a)): -Noisier cells (larger $\sigma$, purple) 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). - %figures created with box_script.py \begin{figure} %\includegraphics[width=0.45\linewidth]{img/ordnung/sigma_popsize_curves_0to300}