Fixed and added more figure text

main.tex

@@ -34,6 +34,7 @@
 \newcommand{\notejb}[1]{\note[JB]{#1}}
 \newcommand{\notedh}[1]{\note[DH]{#1}}
 \newcommand{\newdh}[1]{\textcolor{green}{#1}}
+\newcommand{\todo}[1]{\textcolor{green}{#1}}
 
 \begin{document}
 
@@ -242,7 +243,8 @@ For faster signals, the coding fraction calculated through the tuning curve stay
  \includegraphics[width=0.48\linewidth]{img/tuningcurves/tuningcurve_vs_simulation_10Hz.pdf}
  \includegraphics[width=0.48\linewidth]{img/tuningcurves/tuningcurve_vs_simulation_200Hz.pdf}
  \label{accuracy}
- \caption{Tuningcurve works for 10Hz but not for 200Hz.}
+ \caption{Coding fraction obtained from the simulations and coding fraction calculated from the tuningcurve. For the low frequency (10Hz) signal (left) the results are quite close to each other. Calculating the coding fraction from the tuningcurve appears to consistently yield slightly larger numbers than we get from the simulations. For the faster signal (200 Hz, right) the results for the two different methods are quite far apart from each other; note the different scales on the axes. \notedh{The labels are off; also use different symbols! Make the axes scale the same, but have an inset on the left?}
+ Using the tuningcurve to predict the coding fraction works for 10Hz but not for 200Hz.}
 \end{figure}
  
 For high-frequency signals, the method does not work. The effective and implicit refractory period prohibits the instantaneous firing rate from being useful, because the neurons spike only in very short intervals around a signal peak. They are very unlikely to immediately spike again and signal peaks that are too close to the preceding one will not be resolved properly.\notedh{Add a figure.}
@@ -615,8 +617,8 @@ Figure \ref{fr_sigma} shows that between the firing rate and the cell and its no
 
 \begin{figure}
  \includegraphics[width=0.45\linewidth]{img/sigma/0_300/scatter_and_fits_sigma_firing_rate_contrast.pdf}
- \includegraphics[width=0.45\linewidth]{img/sigma/0_300/scatter_and_fits_contrast_firing_rate_sigma.pdf}
- \caption{Relationship between firing rate and $\sigma$ and cv respectively. Noisier cells tend to be cells that fire slower, but the relationship is very weak.}
+ \includegraphics[width=0.45\linewidth]{img/sigma/0_300/scatter_and_fits_cv_firing_rate_contrast.pdf}
+ \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.}
  \label{fr_sigma}
 \end{figure}
 
@@ -624,7 +626,7 @@ Figure \ref{fr_sigma} shows that between the firing rate and the cell and its no
 
 \begin{figure}
 \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}}
+ \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.}
  \label{ephys_sigma}
 \end{figure}
 
@@ -641,7 +643,7 @@ The curves from which the averages were created can be seen in figure \ref{2_by_
 
 \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 $\sigma$}
+ \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.}
  \label{2_by_2_overview}
 \end{figure}
 
@@ -671,7 +673,7 @@ Figure \ref{coding_fraction_n_1} shows the link between noisiness and coding fra
 \begin{figure}
  \includegraphics[width=0.45\linewidth]{img/sigma/0_300/scatter_and_fits_sigma_coding_fractions_firing_rate.pdf}
  \includegraphics[width=0.45\linewidth]{img/sigma/0_300/scatter_and_fits_firing_rate_coding_fractions_sigma.pdf}
- \caption{Low firing rate and strong noise both lead a a small coding fraction for single neurons.}
+ \caption{Coding fraction for a single cell as a function of $\sigma$ (left) and firing rate (right). Cells for which $\sigma$ is large, i.e. noisier cells, have a lower single cell coding fraction than cells with a smaller $\sigma$. The relationship for firing rate is much weaker; cells with a higher firing rate tend to have a larger single cell coding fraction, but the spread is much larger. \notedh{Do it also without the outlier?}}
  \label{coding_fraction_n_1}
 \end{figure}
 
@@ -707,7 +709,7 @@ Qualitatively we see very similar results when instead of the broadband signal w
 \begin{figure}
  \includegraphics[width=0.8\linewidth]{img/sigma/narrow_0_50/averaged_4parts.pdf}
  \includegraphics[width=0.8\linewidth]{img/sigma/narrow_0_50/2_by_2_overview.pdf}
- \caption{Equivalent plots to \ref{ephys_sigma} and \ref{2_by_2_overview}, just for the narrowband signal with a cutoff frequency of 50Hz. The general trend is the same.}
+ \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!!!}}.
  \label{overview_experiment_results_narrow}
 \end{figure}
 
@@ -722,8 +724,11 @@ Figures \ref{increases_narrow} and \ref{increases_narrow_high} both show that th
 
 \includegraphics[width=0.45\linewidth]{img/sigma/narrow_0_50/scatter_and_fits_sigma_diff_firing_rate}%
 \includegraphics[width=0.45\linewidth]{img/sigma/narrow_0_50/scatter_and_fits_firing_rate_diff_contrast}%
- \caption{Narrowband signal with 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. 
-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.}
+ \caption{Narrowband signal with 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. The linear fit over the whole range is probably not very good here. It appears that increasing population size has less of an impact in case of this relatively slow signal. For firing rates over 150Hz the increase is very small, almost exclusively below 2. Coding fraction $c_1$ is close to 0.3 or over for most of the cells with those firing rates \notedh{Plot?%scatter_and_fits_firing_rate_coding_fractions_sigma
+ }. In contrast, $c_1$ for the broadband signal was always lower than 0.25. If the base coding fraction already is large, there is less potential for an increase in the quotient.
+ 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}
 \end{figure}