diff --git a/main.tex b/main.tex index 4e917dc..496e02d 100644 --- a/main.tex +++ b/main.tex @@ -804,22 +804,67 @@ Bottom: Using the difference in coding fraction instead of the quotient makes th \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? }} \end{figure} -\subsection{Discussion} +\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} + \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. + } +\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} + \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. + } +\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} + \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. + } +\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} + \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. + } +\end{figure} + -We also confirmed that the results from the theory part of the paper play a role in a -real world example. Inside the brain of the weakly electric fish -\textit{Apteronotus leptorhynchus} pyramidal cells in different areas -are responsible for encoding different frequencies. In each of those areas, -cells integrate over different numbers of the same receptor cells. -Artificial populations consisting of different trials of the same receptor cell -show what we have seen in our simulations: Larger populations help -especially with the encoding of high frequency signals. These results -are in line with what is known about the pyramidal cells of \lepto: -The cells which encode high frequency signals best are the cells which -integrate over the largest number of neurons. \section{Literature} + \clearpage \bibliography{citations.bib}