description of nonlin_regime

susceptibility1.tex

@@ -449,7 +449,7 @@ Theoretical work on leaky integrate-and-fire and conductance-based models sugges
 
 \begin{figure*}[t]
   \includegraphics[width=\columnwidth]{nonlin_regime.pdf}
-  \caption{\label{fig:nonlin_regime} The model used has the identifier 2013-01-08-aa.\fone{} is 30\,Hz and \ftwo{} is 130\, Hz, that is eqaul to \fbase{}. Both contrasts increase equally in strength.}
+  \caption{\label{fig:nonlin_regime} Nonlinear response of a model P-unit in response to increasing beat amplitudes in a three-fish or two-beat setting. The model used has the cell identifier 2013-01-08-aa (table~\ref{modelparams}). \figitem{A--D}. Top -- stimulus consisting of two beats. The beat frequencies are 30\,Hz (\bone{}) and 130\,Hz (\btwo{}). \btwo{} is equal to the baseline firing rate \fbase{}. The beat contrasts are equal in the respective example, and increase from \panel{A} to \panel{D}. Middle -- spike response of the model P-unit to the stimulus above. Bottom -- power spectrum of the firing rate of this P-unit. Nonlinear effects at \bsum{} (orange marker) and at \bdiff{} (red marker) increase for intermediate contrasts (\panel{B}), decrease for stronger contrasts (\panel{C}) and again increase for very strong contrasts (\panel{D}). \figitem{E} Amplitude of the linear (\bone{} and \btwo{}) and nonlinear (\bdiff{} and \bsum{}) responses of the model P-units plotted for increasing beat contrasts (contrasts equal for both beats). }
 \end{figure*}
 
 Without any external stimulation, a P-unit fires action potentials at a spontaneous baseline rate \fbase{} to the fish's own EOD of frequency \feod{}. Accordingly, a peak at \fbase{} is present in the power spectrum of this baseline activity (\subfigrefb{fig:motivation}{A}). Superposition of the receiver's EOD with an EOD of another fish with frequency $f_1$ results in a beat, a periodic amplitude modulation of the receiver's EOD. The frequency of the beat is given by the difference frequency $\Delta f_1 = f_1 - \feod$ between the two fish. P-units encode this beat in their firing rate \citep{Bastian1981a, Barayeu2023} and consequently, a peak at this beat frequency appears the the power spectrum of the response (\subfigrefb{fig:motivation}{B}). A second peak at the first harmonic indicates a nonlinear response that here is easily identified by the clipping of the P-unit's firing rate at zero. Pairing the fish with another fish with a higher beat frequency $\Delta f_2 = f_2 - \feod$ results in a weaker response with a single peak in the response power spectrum (\subfigrefb{fig:motivation}{C}). Note that $\Delta f_2$ has been chosen to match the P-unit's baseline firing rate.
@@ -894,7 +894,7 @@ CVs in P-units can range up to 1.5 \citep{Grewe2017, Hladnik2023}. We show the s
 
 \begin{figure*}[t]
   \includegraphics[width=\columnwidth]{trialnr.pdf}
-  \caption{\label{fig:trialnr} Dependence of the estimate of the second-order susceptibility on the number of trials $\n$. While the estimate of the noise floor (10th and 90th percentile) of the $|\chi_2(f_1, f_2)|$ matrix does not saturate yet, the estimates of the high values in the matrix that make up the characteristic ridges saturate for $N>10^6$. The model used has the identifier 2013-01-08-aa.
+  \caption{\label{fig:trialnr} Dependence of the estimate of the second-order susceptibility on the number of trials $\n$. While the estimate of the noise floor (10th and 90th percentile) of the $|\chi_2(f_1, f_2)|$ matrix does not saturate yet, the estimates of the high values in the matrix that make up the characteristic ridges saturate for $N>10^6$. The model used has the identifier 2013-01-08-aa (table~\ref{modelparams}).
   }
 \end{figure*}
 

susceptibility1.tex.bak

@@ -449,7 +449,7 @@ Theoretical work on leaky integrate-and-fire and conductance-based models sugges
 
 \begin{figure*}[t]
   \includegraphics[width=\columnwidth]{nonlin_regime.pdf}
-  \caption{\label{fig:nonlin_regime} The model used has the identifier 2013-01-08-aa.\fone{} is 30\,Hz and \ftwo{} is 130\, Hz, that is eqaul to \fbase{}. Both contrasts increase equally in strength.}
+  \caption{\label{fig:nonlin_regime} Nonlinear response of a model P-unit in response to increasing beat amplitudes in a three-fish or two-beat setting. The model used has the cell identifier 2013-01-08-aa (table~\ref{modelparams}). \figitem{A--D}. Top -- stimulus consisting of two beats. The frequency of the two present beats are 30\,Hz (\fone{}) and 130\,Hz (\ftwo{}). The \ftwo{} is equal to the baseline firing rate \fbase{}. The contrasts of the beats are equal in all examples and increase in the panels \panel{A--D}. Middle -- spike response of the model P-unit to the stimulus above. Bottom -- power spectrum of the firing rate of this P-unit. Nonlinear effects at \fsum{} (orange marker) and at \fdiff{} (red marker) increase for intermediate contrasts (\panel{B}), decrease for stronger contrasts (\panel{C}) and again increase for very strong contrasts (\panel{D}). \figitem{E} Amplitude the linear (\bone{} and \btwo{}) and nonlinear (\bdiff{} and \bsum{}) responses of the model P-units plotted for increasing beat contrasts (contrasts equal for both beats). }
 \end{figure*}
 
 Without any external stimulation, a P-unit fires action potentials at a spontaneous baseline rate \fbase{} to the fish's own EOD of frequency \feod{}. Accordingly, a peak at \fbase{} is present in the power spectrum of this baseline activity (\subfigrefb{fig:motivation}{A}). Superposition of the receiver's EOD with an EOD of another fish with frequency $f_1$ results in a beat, a periodic amplitude modulation of the receiver's EOD. The frequency of the beat is given by the difference frequency $\Delta f_1 = f_1 - \feod$ between the two fish. P-units encode this beat in their firing rate \citep{Bastian1981a, Barayeu2023} and consequently, a peak at this beat frequency appears the the power spectrum of the response (\subfigrefb{fig:motivation}{B}). A second peak at the first harmonic indicates a nonlinear response that here is easily identified by the clipping of the P-unit's firing rate at zero. Pairing the fish with another fish with a higher beat frequency $\Delta f_2 = f_2 - \feod$ results in a weaker response with a single peak in the response power spectrum (\subfigrefb{fig:motivation}{C}). Note that $\Delta f_2$ has been chosen to match the P-unit's baseline firing rate.
@@ -894,7 +894,7 @@ CVs in P-units can range up to 1.5 \citep{Grewe2017, Hladnik2023}. We show the s
 
 \begin{figure*}[t]
   \includegraphics[width=\columnwidth]{trialnr.pdf}
-  \caption{\label{fig:trialnr} Dependence of the estimate of the second-order susceptibility on the number of trials $\n$. While the estimate of the noise floor (10th and 90th percentile) of the $|\chi_2(f_1, f_2)|$ matrix does not saturate yet, the estimates of the high values in the matrix that make up the characteristic ridges saturate for $N>10^6$. The model used has the identifier 2013-01-08-aa.
+  \caption{\label{fig:trialnr} Dependence of the estimate of the second-order susceptibility on the number of trials $\n$. While the estimate of the noise floor (10th and 90th percentile) of the $|\chi_2(f_1, f_2)|$ matrix does not saturate yet, the estimates of the high values in the matrix that make up the characteristic ridges saturate for $N>10^6$. The model used has the identifier 2013-01-08-aa (table~\ref{modelparams}).
   }
 \end{figure*}
 
@@ -911,7 +911,7 @@ CVs in P-units can range up to 1.5 \citep{Grewe2017, Hladnik2023}. We show the s
 %\item \notejb{ \citep{Marmarelis1973} Temporal 2nd order kernels, how well do kernels predict responses}
 %\item \notejb{ \citep{Victor1988} Cat retinal ganglion cells, the sum of sinusoids, very technical, one measurement similar to \citep{Victor1977}.}
 %\item \notejb{\citep{Nikias1993} Third order spectra or bispectra. Very technical overview to higher order spectra}
-%\item \notejb{ \citep{Mitsis2007} Spider mechanoreceptor. Linear filters, multivariate nonlinearity, and threshold. Second-order kernel is needed for this. Gaussian noise stimuli.}
+%\item \notejb{ \citep{Mitsis2007} Spider mechanoreceptor. Linear filters, multivariate nonlinearity, and threshold. The second-order kernel is needed for this. Gaussian noise stimuli.}
 %\item \notejb{ \citep{French2001} Time kernels up to 3rd order for predicting spider mechanoreceptor responses (spikes!)}
 %\item \notejb{ \citep{French1999} Review on time domain nonlinear systems identification}
 %\item \notejb{ \citep{Temchin2005, RecioSpinosa2005} 2nd order Wiener kernel for predicting chinchilla auditory nerve fiber firing rate responses. Strong 2nd order blob at characteristic frequency}