Added figures to appendix. Added figure notes
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main.tex
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main.tex
@ -34,7 +34,8 @@
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\newcommand{\notejb}[1]{\note[JB]{#1}}
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\newcommand{\notedh}[1]{\note[DH]{#1}}
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\newcommand{\newdh}[1]{\textcolor{green}{#1}}
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\newcommand{\todo}[1]{\textcolor{green}{#1}}
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\newcommand{\todo}[1]{\textcolor{green}{TODO: {#1}}}
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\newcommand{\sig}{$\sigma$ }
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\begin{document}
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@ -514,8 +515,10 @@ We created populations out of each cell. For each p-unit, we took the different
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\label{fig:ex_data}
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\caption{Examples of coherence in the p-Units of \lepto. Each plot shows
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the coherence of the response of a single cell to a stimulus for different numbers of trials.
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Like in the simulations, increased population sizes lead to a higher coherence.
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Left: One signal with a maximum frequency of 300Hz. Right: Three different signals (0-50Hz, 150-200Hz and 350-400Hz). With increasing population size the increase in coherence was especially noticeable for the higher frequency ranges. See also figure \ref{fish_result_summary_yue} b). \notedh{Show a different cell with all five narrowband signals?}
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Left: One signal with a maximum frequency of 300Hz.
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Like in the simulations, increased population sizes lead to a higher coherence. Again this is true especially for the higher frequencies, where coherence is small for small population sizes.
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With increased population size the coherence becomes flatter in the low frequencies. Compare figure \ref{CodingFrac}. \todo{Firing rate would be interesting to know to explain some of the dips}
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Right: Three different signals (0-50Hz, 150-200Hz and 350-400Hz). With increasing population size the increase in coherence was especially noticeable for the higher frequency ranges. See also figure \ref{fish_result_summary_yue} b). Interestingly, for this cell coherence is higher for higher frequency signals, given a large enough population. \notedh{Show a different cell with all five narrowband signals?}
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}
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\end{figure}
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@ -553,6 +556,8 @@ This histogram is then normalized by the distribution of the signal. The result
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\subsection*{Simulation}
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To confirm that the $\sigma$ parameter estimated from the fit is indeed a good measure for the noisiness, we validated it against D, the noise parameter from the simulations. We find that there is a strictly monotonous relationship between the two for different sets of simulation parameters. Other parameters often used to determine noisiness (citations) such as the variance of the spike PSTH, the coefficient of variation (CV) of the interspike interval are not as useful (see figure \ref{noiseparameters}) The variance of the psth is not always monotonous in D and is very flat for low values of D.
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The membrane constant $\tau$ determines how quickly the voltage of a LIF-neuron changes, with lower constants meaning faster changes. Only $\sigma$ does not change its values with different $\tau$.
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%describe what happens to the others
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%check Fano-factor maybe?
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@ -567,9 +572,9 @@ To confirm that the $\sigma$ parameter estimated from the fit is indeed a good m
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\includegraphics[width=0.23\linewidth]{img/cv_psth_sigma_compare/dataframe_scatter_labels_D_cv_refractory_50.pdf}
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\includegraphics[width=0.23\linewidth]{img/cv_psth_sigma_compare/dataframe_scatter_labels_D_psth_1ms_refractory_50.pdf}
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\includegraphics[width=0.23\linewidth]{img/cv_psth_sigma_compare/dataframe_scatter_labels_D_psth_5ms_refractory_50.pdf}
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\caption{a)The parameter \(\sigma\) as a function of the noise parameter D in LIF-simulations. There is a strictly monotonous relationship between the two, which allows us to use \(\sigma\) as a susbtitute for D in the analysis of electrophysiological experiments.
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b-e) Left to right: $\sigma$, CV and standard deviation of the psth with two diffrent kernel widths as a function of D for different membrane constants (4ms, 10ms and 16ms). The membrane constant $\tau$ determines how quickly the voltage of a LIF-neuron changes, with lower constants meaning faster changes. Only $\sigma$ does not change its values with different $\tau$. The CV (c)) is not even monotonous in the case of a timeconstant of 4ms, ruling out any potential usefulness.
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f-i) Left to right: $\sigma$, CV and standard deviation of the psth with two diffrent kernel widths as a function of D for different refractory periods (0ms, 1ms and 5ms). Only $\sigma$ does not change with different refractory periods.
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\caption{a)The parameter \(\sigma\) as a function of the noise parameter D in LIF-simulations. There is a almost strictly monotonous relationship between the two, which allows us to use \(\sigma\) as a susbtitute for D in the analysis of electrophysiological experiments. Furthermore, changing the membrane constant of the simulated neurons has no influence on \sig, indicating that it really is a function of the noise and not additionally influenced by the firing rate.
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b-d) Left to right: $\sigma$, CV and standard deviation of the psth with two diffrent kernel widths as a function of D for different membrane constants (4ms, 10ms and 16ms). The CV (c)) is not even monotonous in the case of a timeconstant of 4ms, ruling out any potential usefulness.
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e-h) Left to right: $\sigma$, CV and standard deviation of the psth with two diffrent kernel widths as a function of D for different refractory periods (0ms, 1ms and 5ms). Only $\sigma$ does not change with different refractory periods.
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}
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\label{noiseparameters}
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\end{figure}
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@ -593,8 +598,8 @@ of each other and there is no feedback.
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\begin{figure}
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\includegraphics[width=0.7\linewidth]{img/explain_analysis/after_timeshift_11.pdf}
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\caption{Top: Spike train of a p-unit.
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Middle: Situation as recorded: Signal is blue, the response from the cells created from the spike train is orange.
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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.
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Middle: The original signal is blue represented by the blue line. The orange line is the response from the cells re-created from the spike train. The recreation was done by a convolution of a simple gaussian and the spike train.
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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, whether technical or biological.
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}
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\label{timeshift}
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\end{figure}
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@ -618,7 +623,7 @@ Figure \ref{fr_sigma} shows that between the firing rate and the cell and its no
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\begin{figure}
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\includegraphics[width=0.45\linewidth]{img/sigma/0_300/scatter_and_fits_sigma_firing_rate_contrast.pdf}
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\includegraphics[width=0.45\linewidth]{img/sigma/0_300/scatter_and_fits_cv_firing_rate_contrast.pdf}
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\caption{Relationship between firing rate and $\sigma$ and firing rate and CV respectively. Noisier cells might overall be cells that fire slower, but the relationship is very weak, if present at all.}
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\caption{Relationship between firing rate and $\sigma$ and firing rate and CV respectively. Noisier cells might overall be cells that fire slower, but the relationship is very weak, if present at all. The color of the markers indicates the contrast, a measure for the strength of the signal. For the values used in the experiments, there doesn't appear to be much of a correlation between firing rate and the contrast (figure \ref{contrast_firing_rate} in the appendix.}
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\label{fr_sigma}
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\end{figure}
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@ -626,7 +631,7 @@ Figure \ref{fr_sigma} shows that between the firing rate and the cell and its no
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\begin{figure}
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\includegraphics[width=0.8\linewidth]{img/sigma/0_300/averaged_4parts.pdf}
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\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 the curves seen previously in the simulations (figure \ref{cf_limit}): The cells which are less noisy (orange and blue) start of with a larger coding fraction at a population size of 1 than the noisier cells (green and red). The least noisy cells (blue) don't show an increase in coding fraction for relatively small population sizes, and the noisier cells show a higher coding fraction then the less noisy cells for larger populations.}
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\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 the curves seen previously in the simulations (figure \ref{cf_limit}): The cells which are less noisy (orange and blue) start of with a larger coding fraction at a population size of 1 than the noisier cells (green and red). The least noisy cells (blue) don't show a very slow increase in coding fraction for increasing population size, and the noisier cells show a higher coding fraction then the less noisy cells for larger populations.}
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\label{ephys_sigma}
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\end{figure}
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@ -643,7 +648,7 @@ The curves from which the averages were created can be seen in figure \ref{2_by_
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\begin{figure}
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\includegraphics[width=0.8\linewidth]{img/sigma/0_300/2_by_2_overview.pdf}
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\caption{Individual plots of the cells used in figure \ref{ephys_sigma}. Shown is the coding fraction as a function of population size in the range of 1 to 64 cells. Top left represents the cells in the first quartile (low $\sigma$, so little noise). The curves start relatively high, but flatten out soon. Note that there is one outlier curve at the bottom. Top right represents the second quartile: curves start a bit lower, but increase more. Some curves can be seen that begin to flatten. Bottom left shows the curves in the third quartile: They start lower than the curves in the previous quartiles. Very few of them show signs of flattening, and several seem to be increasing super-linearly. Also note the darker color of the lines, indicating there are no cells here with high firing rates. Bottom right shows the noisiest cells with the largest $\sigma$. They start closest to 0 and all of them are still increasing by the time the population reaches 64 neurons.}
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\caption{Individual plots of the cells used in figure \ref{ephys_sigma}. Shown is the coding fraction as a function of population size in the range of 1 to 64 cells. Top left represents the cells in the first quartile (low $\sigma$, corresponding to little noise). The curves start relatively high, but flatten out soon. Note that there is one outlier curve at the bottom. Top right represents the second quartile: curves start a bit lower, but increase more. Some curves can be seen that begin to flatten. Bottom left shows the curves in the third quartile: They start lower than the curves in the previous quartiles. Very few of them show signs of flattening, and several seem to be increasing super-linearly. Also note the darker color of the lines, indicating there are no cells here with high firing rates. Bottom right shows the noisiest cells with the largest $\sigma$. They start closest to 0 and all of them are still increasing by the time the population reaches 64 neurons.}
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\label{2_by_2_overview}
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\end{figure}
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@ -693,12 +698,12 @@ For the difference between coding fraction of a single neuron and a population w
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\centering
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%\includegraphics[width=0.45\linewidth]{img/sigma/cf_N_ex_lines}
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\includegraphics[width=0.45\linewidth]{img/sigma/0_300/scatter_and_fits_sigma_quot_firing_rate}%
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\includegraphics[width=0.45\linewidth]{img/sigma/0_300/scatter_and_fits_firing_rate_quot_contrast}%
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\includegraphics[width=0.45\linewidth]{img/sigma/0_300/scatter_and_fits_firing_rate_quot_sigma}%
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\includegraphics[width=0.45\linewidth]{img/sigma/0_300/scatter_and_fits_sigma_diff_firing_rate}%
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\includegraphics[width=0.45\linewidth]{img/sigma/0_300/scatter_and_fits_firing_rate_diff_contrast}%
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\caption{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 $\log(c_{64}/c_{1})$. There is a strong relationship between the noisiness and the increase. Noisier cells (larger $\sigma$) have generally lower coding fractions for a single neuron, so they have a bigger potential for gain. Right: As a function of cell firing rate. The relationship is much weaker, but still there.
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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.}
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\includegraphics[width=0.45\linewidth]{img/sigma/0_300/scatter_and_fits_firing_rate_diff_sigma}%
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\caption{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 $\log(c_{64}/c_{1})$. There is a strong relationship between the noisiness and the increase. Noisier cells (larger $\sigma$) have generally lower coding fractions for a single neuron, so they have a bigger potential for gain. Right: As a function of cell firing rate. There is very little correlation between the firing rate and the increase in coding fraction.
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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, because coding fraction might have saturated for less noisy cells, but might still increase with population size for noisier cells.}
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\label{increases_broad}
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\end{figure}
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@ -711,7 +716,9 @@ Qualitatively we see very similar results when instead of the broadband signal w
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\begin{figure}
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\includegraphics[width=0.8\linewidth]{img/sigma/narrow_0_50/averaged_4parts.pdf}
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\includegraphics[width=0.8\linewidth]{img/sigma/narrow_0_50/2_by_2_overview.pdf}
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\caption{Equivalent plots to \ref{ephys_sigma} and \ref{2_by_2_overview}, just for the narrowband signal with a cutoff frequency of 50Hz. Even though the general trend is the same, there are some differences compared to the broadband signal. Even the noisier cells appear not to profit as much off of an increase in population size as before. \todo{Relate in Flie\ss{}text to CMS (low frequency -> small populations!!!}}.
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\caption{Equivalent plots to figures \ref{ephys_sigma} and \ref{2_by_2_overview}, but for a narrowband signal with a cutoff frequency of 50Hz.
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Top: Curves for the least noisy cells (blue and orange) are very flat, meaning coding fraction does not increase much with increasing population size. Cells which are noisier (green) start with a lower coding fraction for a single cell, but with increasing population size catch up with the less noisy cells. Near the maximum population size considered here, the curve flattens. The noisiest cells (red) start off with the smallest coding fraction for a single cell. Coding fraction keeps increasing throughout the entire range of population sizes considered here. Note the large spread (shaded area) around the mean, indicating that the cells in this group behave very differently from each other. This is confirmed if we look at the curves of the individual cells (bottom). The bottom right again shows the curves for the noisiest cells and we find cells that have relatively flat curves throughout, cells where coding fraction increases and then flattens off, and curves where coding fraction is only beginning to increase around the largest population sizes considered here.
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Even though the general trend is the same, there are some differences compared to the broadband signal. Even the noisier cells appear not to profit as much off of an increase in population size as before. \todo{Relate in Flie\ss{}text to CMS (low frequency -> small populations!!!}}.
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\label{overview_experiment_results_narrow}
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\end{figure}
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@ -726,7 +733,8 @@ Qualitatively we see very similar results when instead of the broadband signal w
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\begin{figure}
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\includegraphics[width=0.45\linewidth]{img/sigma/narrow_0_50/scatter_and_fits_sigma_firing_rate_contrast}
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\includegraphics[width=0.45\linewidth]{img/sigma/narrow_250_300/scatter_and_fits_sigma_firing_rate_contrast}
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\caption{}
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\caption{The correlation between noise and firing rate is stronger for narrowband signals than it was for the broadband signal (compare to figure \ref{fr_sigma}).
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Left: Cell firing rate in the presence of a 0-50Hz input signal and \sig for the cells which have at least 64 trials recorded with that signal. The red line indicates a fitted linear regression. Color of the markers indicates the contrast with which the signal was applied. Results indicate that cells that fire slowly on narrowband inputs tend to be noisier cells. Right: Same, but for an input signal with a frequency of 250-300Hz.}
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\label{sigma_vs_firing_rate_for_narrow}
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\end{figure}
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@ -763,7 +771,7 @@ Figures \ref{increases_narrow} and \ref{increases_narrow_high} both show that th
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\centering
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\includegraphics[width=0.45\linewidth]{img/sigma/narrow_250_300/scatter_and_fits_sigma_diff_firing_rate}%
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\includegraphics[width=0.45\linewidth]{img/sigma/narrow_250_300/scatter_and_fits_firing_rate_diff_contrast}%
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\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})
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\caption{Same graphs as in figure \ref{increases_narrow}, but with a 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})
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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.}
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\label{increases_narrow_high}
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\end{figure}
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@ -779,9 +787,8 @@ The results (figure \ref{overview_fits}) show \todo{write}
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\includegraphics[width=0.45\linewidth]{img/sigma/fit_results_overviews/fit_results_firing_rate_narrow_quot.pdf}
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\includegraphics[width=0.45\linewidth]{img/sigma/fit_results_overviews/fit_results_cv_narrow_diff.pdf}
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\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}
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\caption{\todo{write}
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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}). For 350-400 only 5 points.}
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\includegraphics[width=0.45\linewidth]{img/sigma/fit_results_overviews/fit_results_cv_narrow_quot.pdf} \notedh{leave cv out? No idea why the fits aren't working for the smaller intervals}
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\caption{Overview of r-squared and p-value for the linear regressions for the increase in coding fraction from a population size of 1 to a population size of 64. Results are shown for the different narrowband input signals used in the experiments. Left columns shows results for the difference in coding fraction, right column shows results for the logarithm of the ratio. For the frequency range of 150-200Hz only four data points are present (compare figure \ref{sigma_narrow_150_200}); for the range 350-400Hz only five trials were available (figure \ref{sigma_narrow_350_400} and for 50-100Hz only six trials were available (compare figure \ref{sigma_narrow_50_100}).}
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\label{overview_fits_narrow}
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\end{figure}
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@ -797,8 +804,8 @@ Similar results can be observed for the other frequency bands. \notedh{Images to
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\includegraphics[width=0.45\linewidth]{img/sigma/0_50/scatter_and_fits_sigma_diff_firing_rate}%
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\includegraphics[width=0.45\linewidth]{img/sigma/0_50/scatter_and_fits_firing_rate_diff_contrast}%
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\caption{Broadband signal, analyzed 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.
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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.}
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\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.
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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. }
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\label{increases_narow_in_broad}
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\end{figure}
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@ -812,7 +819,8 @@ Bottom: Using the difference in coding fraction instead of the quotient makes th
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\includegraphics[width=0.45\linewidth]{img/sigma/fit_results_overviews/fit_results_cv_broad_diff.pdf}
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\includegraphics[width=0.45\linewidth]{img/sigma/fit_results_overviews/fit_results_cv_broad_quot.pdf} \notedh{leave CV out? Consistent with narrow band?}
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\caption{\todo{write}}
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\caption{Overview of r-squared and p-value for the linear regressions for the increase in coding fraction from a population size of 1 to a population size of 64. Results are shown for the different frequency ranges in the 0-300Hz broadband input signal used in the experiments.
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Left columns shows results for the difference in coding fraction, right column shows results for the logarithm of the ratio. For the frequency range of 150-200Hz only four data points are present (compare figure \ref{sigma_narrow_150_200}); for the range 350-400Hz only five trials were available (figure \ref{sigma_narrow_350_400} and for 50-100Hz only six trials were available (compare figure \ref{sigma_narrow_50_100}).}
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\label{overview_fits_broad}
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\end{figure}
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@ -856,22 +864,108 @@ Bottom: Using the difference in coding fraction instead of the quotient makes th
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\begin{figure}
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\includegraphics[width=0.49\linewidth]{img/fish/ratio_narrow.pdf}
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\includegraphics[width=0.49\linewidth]{img/fish/broad_ratio.pdf}
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\label{freq_delta_cf}
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\caption{This is about frequency and how it determines $delta_cf$. In other paper I have used $quot_cf$. \notedh{The x-axis labels don't make sense to me. Left is broad and right is narrow? }}
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\label{freq_delta_cf}
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\end{figure}
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\begin{figure}
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\centering
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\includegraphics[width=0.49\linewidth]{img/sigma/0_300/scatter_and_fits_contrast_firing_rate_contrast}
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\caption{No correlation between firing rate and contrast.}
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\label{contrast_firing_rate}
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\end{figure}
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%figures created with result_fits.py
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\begin{figure}
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\centering
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\includegraphics[width=0.49\linewidth]{img/sigma/50_100/2_by_2_overview.pdf}
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\includegraphics[width=0.49\linewidth]{img/sigma/50_100/averaged_4parts.pdf}
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\includegraphics[width=0.45\linewidth]{img/sigma/50_100/scatter_and_fits_sigma_quot_firing_rate}%
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\includegraphics[width=0.45\linewidth]{img/sigma/50_100/scatter_and_fits_firing_rate_quot_contrast}%
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\includegraphics[width=0.45\linewidth]{img/sigma/50_100/scatter_and_fits_sigma_diff_firing_rate}%
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\includegraphics[width=0.45\linewidth]{img/sigma/50_100/scatter_and_fits_firing_rate_diff_contrast}%
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\caption{Broadband signal with a cutoff frequency of 300Hz, but the coding fraction was calculated in the range 50-100Hz.
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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.
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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. }
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\label{increases_narow_in_broad_50_100}
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\end{figure}
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\begin{figure}
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\centering
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||||
\includegraphics[width=0.49\linewidth]{img/sigma/100_150/2_by_2_overview.pdf}
|
||||
\includegraphics[width=0.49\linewidth]{img/sigma/100_150/averaged_4parts.pdf}
|
||||
\includegraphics[width=0.45\linewidth]{img/sigma/100_150/scatter_and_fits_sigma_quot_firing_rate}%
|
||||
\includegraphics[width=0.45\linewidth]{img/sigma/100_150/scatter_and_fits_firing_rate_quot_contrast}%
|
||||
|
||||
\includegraphics[width=0.45\linewidth]{img/sigma/100_150/scatter_and_fits_sigma_diff_firing_rate}%
|
||||
\includegraphics[width=0.45\linewidth]{img/sigma/100_150/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 100-150Hz.
|
||||
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 similar 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_100_150}
|
||||
\end{figure}
|
||||
|
||||
|
||||
\begin{figure}
|
||||
\centering
|
||||
\includegraphics[width=0.49\linewidth]{img/sigma/150_200/2_by_2_overview.pdf}
|
||||
\includegraphics[width=0.49\linewidth]{img/sigma/150_200/averaged_4parts.pdf}
|
||||
\includegraphics[width=0.45\linewidth]{img/sigma/150_200/scatter_and_fits_sigma_quot_firing_rate}%
|
||||
\includegraphics[width=0.45\linewidth]{img/sigma/150_200/scatter_and_fits_firing_rate_quot_contrast}%
|
||||
|
||||
\includegraphics[width=0.45\linewidth]{img/sigma/150_200/scatter_and_fits_sigma_diff_firing_rate}%
|
||||
\includegraphics[width=0.45\linewidth]{img/sigma/150_200/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 150-200Hz.
|
||||
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 no 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_150_200}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}
|
||||
\centering
|
||||
\includegraphics[width=0.49\linewidth]{img/sigma/200_250/2_by_2_overview.pdf}
|
||||
\includegraphics[width=0.49\linewidth]{img/sigma/200_250/averaged_4parts.pdf}
|
||||
\includegraphics[width=0.45\linewidth]{img/sigma/200_250/scatter_and_fits_sigma_quot_firing_rate}%
|
||||
\includegraphics[width=0.45\linewidth]{img/sigma/200_250/scatter_and_fits_firing_rate_quot_contrast}%
|
||||
|
||||
\includegraphics[width=0.45\linewidth]{img/sigma/200_250/scatter_and_fits_sigma_diff_firing_rate}%
|
||||
\includegraphics[width=0.45\linewidth]{img/sigma/200_250/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 200-250Hz.
|
||||
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 no 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_200_250}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}
|
||||
\centering
|
||||
\includegraphics[width=0.49\linewidth]{img/sigma/250_300/2_by_2_overview.pdf}
|
||||
\includegraphics[width=0.49\linewidth]{img/sigma/250_300/averaged_4parts.pdf}
|
||||
\includegraphics[width=0.45\linewidth]{img/sigma/250_300/scatter_and_fits_sigma_quot_firing_rate}%
|
||||
\includegraphics[width=0.45\linewidth]{img/sigma/250_300/scatter_and_fits_firing_rate_quot_contrast}%
|
||||
|
||||
\includegraphics[width=0.45\linewidth]{img/sigma/250_300/scatter_and_fits_sigma_diff_firing_rate}%
|
||||
\includegraphics[width=0.45\linewidth]{img/sigma/250_300/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 250-300Hz.
|
||||
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. 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 no 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_250_300}
|
||||
\end{figure}
|
||||
|
||||
|
||||
|
||||
\begin{figure}
|
||||
\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.
|
||||
C: Increase in coding fraction for N=1 to N=64 as a function of $\sigma$. The y-axis shows the quotient of coding fraction at N=64 divided by coding fraction at N=1.
|
||||
D: Same as C, only with the difference instead of the quotient.
|
||||
}
|
||||
\label{sigma_narrow_50_100}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}
|
||||
@ -879,13 +973,15 @@ Bottom: Using the difference in coding fraction instead of the quotient makes th
|
||||
\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}
|
||||
\includegraphics[width=0.49\linewidth]{img/sigma/narrow_150_200/scatter_and_fits_firing_rate_quot_sigma.pdf}
|
||||
\includegraphics[width=0.49\linewidth]{img/sigma/narrow_150_200/scatter_and_fits_firing_rate_diff_sigma.pdf}
|
||||
\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.
|
||||
C: Increase in coding fraction for N=1 to N=64 as a function of $\sigma$. The y-axis shows the quotient of coding fraction at N=64 divided by coding fraction at N=1.
|
||||
D: Same as C, only with the difference instead of the quotient.
|
||||
}
|
||||
\label{sigma_narrow_150_200}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}
|
||||
@ -895,13 +991,13 @@ Bottom: Using the difference in coding fraction instead of the quotient makes th
|
||||
\includegraphics[width=0.49\linewidth]{img/sigma/narrow_250_300/scatter_and_fits_sigma_diff_firing_rate.pdf}
|
||||
\includegraphics[width=0.49\linewidth]{img/sigma/narrow_250_300/scatter_and_fits_firing_rate_quot_sigma.pdf}
|
||||
\includegraphics[width=0.49\linewidth]{img/sigma/narrow_250_300/scatter_and_fits_firing_rate_diff_sigma.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.
|
||||
C: Increase in coding fraction for N=1 to N=64 as a function of $\sigma$. The y-axis shows the quotient of coding fraction at N=64 divided by coding fraction at N=1.
|
||||
D: Same as C, only with the difference instead of the quotient.
|
||||
}
|
||||
\label{sigma_narrow_250_300}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}
|
||||
@ -909,13 +1005,15 @@ Bottom: Using the difference in coding fraction instead of the quotient makes th
|
||||
\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}
|
||||
\includegraphics[width=0.49\linewidth]{img/sigma/narrow_350_400/scatter_and_fits_firing_rate_quot_sigma.pdf}
|
||||
\includegraphics[width=0.49\linewidth]{img/sigma/narrow_350_400/scatter_and_fits_firing_rate_diff_sigma.pdf}
|
||||
\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.
|
||||
C: Increase in coding fraction for N=1 to N=64 as a function of $\sigma$. The y-axis shows the quotient of coding fraction at N=64 divided by coding fraction at N=1.
|
||||
D: Same as C, only with the difference instead of the quotient.
|
||||
}
|
||||
\label{sigma_narrow_350_400}
|
||||
\end{figure}
|
||||
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user