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susceptibility1.tex
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@ -507,7 +507,7 @@ These nonlinearity bands are more pronounced in ampullary cells than they were i
\subsection{Full nonlinear structure visible only in P-unit models}
In the following nonlinear interactions were systematically compared between an electrophysiologically recorded low-CV P-unit and the according P-unit LIF models with a RAM contrast of 1\,$\%$ (red, \subfigrefb{model_and_data}\,\panel[i]{A}). For a homogeneous population with size $\n{}=11$ one could observe a diagonal band in the absolute value of the second-order susceptibility at \fsumb{} of the recorded P-unit (yellow diagonal in pink edges, \subfigrefb{model_and_data}\,\panel[ii]{A}) and in the according model (\subfigrefb{model_and_data}\,\panel[iii]{A}). A nonlinear band appeared at \fsumehalf{}, but only in the recorded P-unit (orange line, \subfigrefb{model_and_data}\,\panel[ii]{A}). The signal-to-noise ratio and estimation of the nonlinearity structures can be improved if the number of RAM stimulus realizations is increased. Models have the advantage that they allow for data amounts that cannot be acquired experimentally. Still, even if a RAM stimulus is generated 1 million times, no changes are observable in the nonlinearity structures in the model second-order susceptibility (\subfigrefb{model_and_data}\,\panel[iv]{A}).
In the following nonlinear interactions were systematically compared between an electrophysiologically recorded low-CV P-unit and the according P-unit LIF models with a RAM contrast of 1\,$\%$ (red, \subfigrefb{model_and_data}\,\panel[i]{A}). For a homogeneous population with size $\n{}=11$ one could observe a diagonal band in the absolute value of the second-order susceptibility at \fsumb{} of the recorded P-unit (yellow diagonal in pink edges, \subfigrefb{model_and_data}\,\panel[ii]{A}) and in the according model (\subfigrefb{model_and_data}\,\panel[iii]{A}). A nonlinear band appeared at \fsumehalf{}, but only in the recorded P-unit (orange line, \subfigrefb{model_and_data}\,\panel[ii]{A}). The signal-to-noise ratio and estimation of the nonlinearity structures can be improved if the number of RAM stimulus realizations is increased. Models have the advantage that they allow for data amounts that cannot be acquired experimentally. Still, even if a RAM stimulus is generated 1 million times, no changes are observable in the nonlinearity structures in the model second-order susceptibility (\subfigrefb{model_and_data}\,\panel[iv]{A}). An improved signal-to-noise ratio with 1 million stimuli is associated with smaller second-order susceptibility values (\subfigrefb{model_and_data}\,\panel[iv]{A}).
%Note that this line doesn't appear in the susceptibility matrix of the model (\subfigrefb{model_and_data}{C})Each cell has an intrinsic noise level (\subfigrefb{model_and_data}{A}, bottom).
%The signal component (purple) compensates for this total noise reduction, is not a weak signal anymore and
@ -541,7 +541,7 @@ In the previous paragraphs, the nonlinearity at \fsum{} in the P-unit response w
Instead, the full second-order susceptibility matrix in \figrefb{model_full}, which depicts nonlinearities in the P-unit response at \fsum{} in the upper right and lower left quadrants and nonlinearities at \fdiff{} in the lower right and upper left quadrants (\eqnref{susceptibility}, \citealp{Voronenko2017}), has to be considered. Once calculating this full second-order susceptibility matrix based on the experimentally recorded data (\subfigrefb{model_full}{A}) and the corresponding model (\subfigrefb{model_full}{B}), one can observe that the diagonal structures are present in the upper right quadrant and for the lower right quadrants. The vertical and horizontal lines at \foneb{} and \ftwob{} are very pronounced in the upper right quadrant for the nonlinearity at \fsum{} and are prolonged to the lower right quadrant with lower nonlinearity values at \fdiff{} in the P-unit response.
Instead, the full second-order susceptibility matrix in \figrefb{model_full}, which depicts nonlinearities in the P-unit response at \fsum{} in the upper right and lower left quadrants and nonlinearities at \fdiff{} in the lower right and upper left quadrants (\eqnref{susceptibility}, \citealp{Voronenko2017}), has to be considered. Once calculating this full second-order susceptibility matrix based on the experimentally recorded data (\subfigrefb{model_full}{A}) and the corresponding model (\subfigrefb{model_full}{B}), one can observe that the diagonal structures are present in the upper right quadrant and for the lower right quadrants. The vertical and horizontal lines at \foneb{} and \ftwob{} are very pronounced in the upper right quadrant for the nonlinearity at \fsum{} and are prolonged to the lower right quadrant with lower nonlinearity values at \fdiff{} in the P-unit response. Note that the different scale of the second-order susceptibility is associated with the higher signal-to-ratio in case of 1 million repeats in \subfigrefb{model_full}{B}.
%, that quantifies the nonlinearity at \fdiff{} in the response , that quantifies the nonlinearity at \fsum{} in the response,

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susceptibility1.tex.bak
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@ -878,13 +878,13 @@ A big portion of the total noise was assigned to the signal component ($c_{signa
\begin{table*}[hp!]
\caption{\label{modelparams} Model parameters of LIF models, fitted to 42 electrophysiologically recorded P-units (\citealp{Ott2020}). See section \ref{lifmethods} for model and parameter description.}
\caption{\label{modelparams} Model parameters of LIF models, fitted to 2 electrophysiologically recorded P-units (\citealp{Ott2020}). See section \ref{lifmethods} for model and parameter description.}
\begin{center}
\begin{tabular}{lrrrrrrrr}
\hline
\bfseries $cell$ & \bfseries $\beta$ & \bfseries $\tau_{m}$/ms & \bfseries $\mu$ & \bfseries $D$/$\mathbf{ms}$ & \bfseries $\tau_{A}$/ms & \bfseries $\Delta_A$ & \bfseries $\tau_{d}$/ms & \bfseries $t_{ref}$/ms \\\hline
2012-07-03-ak& $10.6$& $1.38$& $-1.32$& $0.001$& $96.05$& $0.01$& $1.18$& $0.12$ \\
2013-01-08-aa& $4.5$& $1.20$& $0.59$& $0.001$& $37.52$& $0.01$& $1.18$& $0.38$ \\
2018-05-08-ae& $139.6$& $1.49$& $-21.09$& $0.214$& $123.69$& $0.16$& $3.93$& $1.31$ \\
\hline
\end{tabular}
\end{center}