Update susceptibility1.tex.bak

susceptibility1.tex.bak

@@ -893,8 +893,9 @@ According to previous works \cite{Lindner2022} the total noise of a LIF model ($
 
 
 
-In the here used model a small portion of the original noise was assigned to the noise component ($c_{\rm{noise}} = 0.1$, \subfigrefb{flowchart}\,\panel[iii]{C}) and a big portion used as the signal component ($c_{\rm{signal}} = 0.9$, \subfigrefb{flowchart}\,\panel[iii]{A}). For the noise split to be valid \cite{Lindner2022} it is critical that both components add up to the initial 100\,$\%$ of the total noise and the baseline properties as the firing rate and the CV of the model cell are maintained. This is easily achieved in a model without a carrier if the condition $c_{\rm{signal}}+c_{\rm{noise}}=1$ is satisfied. The situation here is more complicated. After the original noise was split into a signal component with $c_{\rm{signal}}$ and the frequencies above 300\,Hz were discarded and the signal strength was transformed during the dendritic low pass filtering. To compensate for these transformations the signal the signal component was multiplying with the factor $\rho$, then resulting in $s_\xi(t)$. $\rho$ was found by minimizing the error between the baseline CV (only carrier) and the CV during stimulation with noise split.
+In the here used model a small portion of the original noise was assigned to the noise component ($c_{\rm{noise}} = 0.1$, \subfigrefb{flowchart}\,\panel[iii]{C}) and a big portion used as the signal component ($c_{\rm{signal}} = 0.9$, \subfigrefb{flowchart}\,\panel[iii]{A}). For the noise split to be valid \cite{Lindner2022} it is critical that both components add up to the initial 100\,$\%$ of the total noise and the baseline properties as the firing rate and the CV of the model are maintained. This is easily achieved in a model without a carrier if the condition $c_{\rm{signal}}+c_{\rm{noise}}=1$ is satisfied. The situation here is more complicated. After the original noise was split into a signal component with $c_{\rm{signal}}$, the frequencies above 300\,Hz were discarded and the signal strength was reduced after the dendritic low pass filtering. To compensate for these transformations the initial signal component was multiplying with the factor $\rho$, keeping the baseline CV (only carrier) and the CV during the noise split comparable, and resulting in $s_\xi(t)$. $\rho$ was found by bisecting the plane of possible factors and minimizing the error between the CV during baseline and stimulation.
 
+%that was found by minimizing the error between the
 %Furutsu-Novikov Theorem \cite{Novikov1965, Furutsu1963}\Eqnref{eq:ram_split},  (red in \subfigrefb{flowchart}\,\panel[iii]{A})  bisecting the space of possible $\rho$ scaling factors
 %$\rho$ a scaling factor that compensates (see below) for the signal transformations the amplitude modulation stimulus undergoes in the model, i.e. the threshold and the dendritic lowpass. 
 %In our case the model has a carrier (the fish's self-generated EOD) and we thus want to drive the model with an amplitude modulation stimulus
@@ -943,7 +944,7 @@ In the here used model a small portion of the original noise was assigned to the
 
 
 \paragraph*{S1 Second-order susceptibility of high-CV P-unit}
-CVs in P-units can range up to 1.5 \cite{Grewe2017, Hladnik2023}. We show the same analysis as in (\figrefb{fig:cells_suscept}) for an example higher-CV P-unit. Similar to the low-CV cell, high-CV P-units fire at multiples of the EOD period (\subfigrefb{fig:cells_suscept_high_CV}{A}). In contrast to low-CV P-unit, however, the higher CV characterizes the noisier baseline firing pattern and the peak at \fbase{} is less pronounced in the power spectrum of the baseline activity (\subfigrefb{fig:cells_suscept_high_CV}{B}). High-CV P-units do not exhibit a clear nonlinear structure related to \fbase{} neither in the second-order susceptibility matrices (\subfigrefb{fig:cells_suscept_high_CV}{E--F}), nor in the projected diagonals (\subfigrefb{fig:cells_suscept_high_CV}{G}). The overall level of nonlinearity, however shows the same dependence on the stimulus contrast. It is much reduced for high-contrast stimuli that drive the neuron much stronger (\subfigrefb{fig:cells_suscept_high_CV}{F}). 
+CVs in P-units can range up to 1.5 \cite{Grewe2017, Hladnik2023}. We show the same analysis as in \figrefb{fig:cells_suscept} for an example higher-CV P-unit. Similar to the low-CV cell, high-CV P-units fire at multiples of the EOD period (\subfigrefb{fig:cells_suscept_high_CV}{A}). In contrast to low-CV P-units, however, the higher CV characterizes the noisier baseline firing pattern and the peak at \fbase{} is less pronounced in the power spectrum of the baseline activity (\subfigrefb{fig:cells_suscept_high_CV}{B}). High-CV P-units do not exhibit a clear nonlinear structure related to \fbase{} neither in the second-order susceptibility matrices (\subfigrefb{fig:cells_suscept_high_CV}{E--F}), nor in the projected diagonals (\subfigrefb{fig:cells_suscept_high_CV}{G}). The overall level of nonlinearity, however shows the same dependence on the stimulus contrast. It is much reduced for high-contrast stimuli that drive the neuron much stronger (\subfigrefb{fig:cells_suscept_high_CV}{F}). 
 
 \label{S1:highcvpunit}
 \begin{figure*}[!ht]