updated remaining comments

ampullary.py

@@ -50,4 +50,5 @@ if __name__ == '__main__':
             ampullary_punit(cells_plot2=cells_plot2, RAM=False)
     else:
         cells_plot2 = p_units_to_show(type_here='amp')#permuted = True,
+        print(cells_plot2)
         ampullary_punit(eod_metrice = False, base_extra = True,color_same = False, fr_name = '$f_{base}$',  tags_individual = True, isi_delta = 5, titles=[''],cells_plot2=cells_plot2, RAM=False, scale_val = False, add_texts = [0.25,1.3])#Low-CV ampullary cell,

cells_suscept.py

@@ -7,4 +7,5 @@ if __name__ == '__main__':
 
     #stack_file = pd.read_csv('..\calc_RAM\calc_nix_RAM-eod_2022-01-28-ag-invivo-1_all__amp_20.0_filename_InputArr_400hz_30_P-unitApteronotusleptorhynchus.csv')
     cells_plot2 = p_units_to_show(type_here = 'contrasts')#permuted = True,
+    print(cells_plot2)
     ampullary_punit(eod_metrice = False, color_same = False, base_extra = True, fr_name = label_fr_name_rm(), cells_plot2=[cells_plot2[0]], isi_delta = 5, titles=[''], tags_individual = True, xlim_p = [0, 1.15])#Low-CV P-unit,

cells_suscept_high_CV.py

@@ -6,4 +6,5 @@ from threefish.plot_suscept import ampullary_punit
 if __name__ == '__main__':
 
     cells_plot2 = p_units_to_show(type_here='contrasts')#permuted = True,
+    print(cells_plot2)
     ampullary_punit(base_extra = True, eod_metrice = False, color_same = False, fr_name = label_fr_name_rm(), tags_individual = True, isi_delta = 5, cells_plot2=[cells_plot2[1]], titles=['', 'Ampullary cell,'], )#High-CV P-unit,

susceptibility1.tex

@@ -522,7 +522,7 @@ While the sensory periphery can often be well described by linear models, this i
 
 \begin{figure*}[!ht]
   \includegraphics[width=\columnwidth]{motivation}
-  \caption{\label{fig:motivation} Nonlinearity in an electrophysiologically recorded P-unit of \lepto{} in a three-fish setting. Receiver with EOD frequency $\feod{} =664$\,Hz encounters fish with EOD frequencies $f_{1}=631$\,Hz and $f_{2}=797$\,Hz. Both encountered fish lead to a beat contrast of 10\,\%. Top: Sheme of a nonlinear system. Second row: Interference of the receiver EOD with the EODs of other fish. Third row: Spike trains of the P-unit. Forth row: Firing rate, retrieved as the convolution of the spike trains with a Gaussian kernel ($\sigma = 1$\,ms). Bottom row: Power spectrum of the firing rate. \figitem{A} Baseline condition: Only the receiver is present. The baseline firing rate \fbase{} dominates the power spectrum of the firing rate. \figitem{B} The receiver and the fish with EOD frequency $f_{1}=631$\,Hz are present. \figitem{C} The receiver and the fish with EOD frequency $f_{2}=797$\,Hz are present. \figitem{D} All three fish with the EOD frequencies \feod{}, $f_{1}$ and $f_{2}$ are present. Nonlinear peaks occur at the sum and difference of the two beat frequencies in the power spectrum of the firing rate.
+  \caption{\label{fig:motivation} Nonlinearity in an electrophysiologically recorded P-unit of \lepto{} in a three-fish setting (cell identifier ``2021-08-03-ac"). Receiver with EOD frequency $\feod{} =664$\,Hz encounters fish with EOD frequencies $f_{1}=631$\,Hz and $f_{2}=797$\,Hz. Both encountered fish lead to a beat contrast of 10\,\%. Top: Sheme of a nonlinear system. Second row: Interference of the receiver EOD with the EODs of other fish. Third row: Spike trains of the P-unit. Forth row: Firing rate, retrieved as the convolution of the spike trains with a Gaussian kernel ($\sigma = 1$\,ms). Bottom row: Power spectrum of the firing rate. \figitem{A} Baseline condition: Only the receiver is present. The baseline firing rate \fbase{} dominates the power spectrum of the firing rate. \figitem{B} The receiver and the fish with EOD frequency $f_{1}=631$\,Hz are present. \figitem{C} The receiver and the fish with EOD frequency $f_{2}=797$\,Hz are present. \figitem{D} All three fish with the EOD frequencies \feod{}, $f_{1}$ and $f_{2}$ are present. Nonlinear peaks occur at the sum and difference of the two beat frequencies in the power spectrum of the firing rate.
   }
 \end{figure*}
 
@@ -543,7 +543,7 @@ Nonlinear encoding as quantified by the second-order susceptibility is expected
 
 \begin{figure*}[t]
 \includegraphics[width=\columnwidth]{cells_suscept} 
-\caption{\label{fig:cells_suscept} Estimation of linear and nonlinear stimulus encoding in a low-CV P-unit. \figitem{A} Interspike interval (ISI) distribution of the cell's baseline activity, i.e. the cell is driven only by the unperturbed own electric field. The low CV of the ISIs indicates quite regular firing. \figitem{B} Power spectral density of the baseline response with peaks at the cell's baseline firing rate \fbase{} and the fish's EOD frequency \feod{}. \figitem{C} Random amplitude modulation stimulus (top, \notejb{cutoff frequency?}) and evoked responses (spike raster, bottom) of the same P-unit. The stimulus contrast (right) reflects the strength of the AM. \figitem{D} Gain of the transfer function (first-order susceptibility), \Eqnref{linearencoding_methods}, of the responses to 10\,\% (light purple) and 20\,\% contrast (dark purple) RAM stimulation. \figitem{E, F} Absolute value of the second-order susceptibility, \Eqnref{eq:susceptibility}, for both the low and high stimulus contrast. Pink triangles mark vertical, horizontal, and diagonal lines where \fone, \ftwo{} or \fsum{} are equal to \fbase{}. \figitem{G} Second-order susceptibilities projected onto the diagonal (means of all anti-diagonals of the matrices  shown in \panel{E, F}). Dots mark \fbase{}, horizontal dashed lines mark medians of the projected susceptibilities.  \notejb{``Calculated based on the first frozen noise repeat.'' Really? Only one trial has been used for computing the susceptibilities?} \noteab{Yes. In the population statistics of the last 20 years I was trying to maximize the number cells and maximize the duration. In the end the susceptibility is calculated based on 10 seconds. The susceptibility has always to be calculated with newly initiated noise, with 10 seconds and 0.5 nfft durations this results in 20 trials. For the overview figure the mean of all NLI values for each frozen noise was calculated. It is not possible to take the mean over several frozen noise matrices since the baseline properties sometimes change and this disrupts the second order susceptibility.}}
+\caption{\label{fig:cells_suscept} Estimation of linear and nonlinear stimulus encoding in a low-CV P-unit (cell identifier ``2010-06-21-ai"). \figitem{A} Interspike interval (ISI) distribution of the cell's baseline activity, i.e. the cell is driven only by the unperturbed own electric field. The low CV of the ISIs indicates quite regular firing. \figitem{B} Power spectral density of the baseline response with peaks at the cell's baseline firing rate \fbase{} and the fish's EOD frequency \feod{}. \figitem{C} Random amplitude modulation stimulus (top, with cutoff frequency of 300\,Hz) and evoked responses (spike raster, bottom) of the same P-unit. The stimulus contrast (right) reflects the strength of the AM. \figitem{D} Gain of the transfer function (first-order susceptibility), \Eqnref{linearencoding_methods}, of the responses to 10\,\% (light purple) and 20\,\% contrast (dark purple) RAM stimulation. \figitem{E, F} Absolute value of the second-order susceptibility, \Eqnref{eq:susceptibility}, for both the low and high stimulus contrast. Pink triangles mark vertical, horizontal, and diagonal lines where \fone, \ftwo{} or \fsum{} are equal to \fbase{}. \figitem{G} Second-order susceptibilities projected onto the diagonal (means of all anti-diagonals of the matrices  shown in \panel{E, F}). Dots mark \fbase{}, horizontal dashed lines mark medians of the projected susceptibilities.  \notejb{``Calculated based on the first frozen noise repeat.'' Really? Only one trial has been used for computing the susceptibilities?} \noteab{Yes. In the population statistics of the last 20 years I was trying to maximize the number cells and maximize the duration. In the end the susceptibility is calculated based on 10 seconds. The susceptibility has to be calculated with newly initiated noise, with 10 seconds and 0.5 nfft durations this results in 20 trials. For the overview figure the mean of all NLI values for each frozen noise was calculated. It is not possible to take the mean over several frozen noise matrices since the baseline properties sometimes change and this disrupts the shape of the second order susceptibility.}}
 \end{figure*}
 
 Noise stimuli, here random amplitude modulations (RAM) of the EOD (\subfigref{fig:cells_suscept}{C}, top trace, red line), are commonly used to characterize stimulus driven responses of sensory neurons by means of transfer functions (first-order susceptibility), spike-triggered averages, or stimulus-response coherences. Here, we additionally estimate the second-order susceptibility to quantify nonlinear encoding. P-unit spikes align more or less clearly to fluctuations in the RAM stimulus. A higher stimulus intensity, here a higher contrast of the RAM relative to the EOD amplitude (see methods), entrains the P-unit response more clearly (light and dark purple for low and high contrast stimuli, \subfigrefb{fig:cells_suscept}{C}). Linear encoding, quantified by the transfer function \Eqnref{linearencoding_methods}, is similar for the two RAM contrasts in this low-CV P-unit (\subfigrefb{fig:cells_suscept}{D}), as expected for a linear system. The first-order susceptibility is low for low frequencies, peaks in the range below 100\,Hz and then falls off again \notejb{Cite Moe paper?}.
@@ -561,13 +561,13 @@ In contrast, a high-CV P-unit (CV$_{\text{base}}=0.4$) does not exhibit pronounc
 
 \begin{figure*}[t]
 \includegraphics[width=\columnwidth]{ampullary}
-  \caption{\label{fig:ampullary} Estimation of linear and nonlinear stimulus encoding in an ampullary afferent. \figitem{A} Interspike interval (ISI) distribution of the cell's baseline activity. The very low CV of the ISIs indicates almost perfect periodic spiking. \figitem{B} Power spectral density of baseline activity with peaks at the cell's baseline firing rate and its harmonics. \figitem{C} Bad-limited white noise stimulus (top, \notejb{cutoff frequency?}) added to the fish's self-generated electric field and spike raster of the evoked responses (bottom) for two stimulus contrasts as indicated (right). \figitem{D} Gain of the transfer function, \Eqnref{linearencoding_methods}, of the responses to stimulation with 2\,\% (light green) and 20\,\% contrast (dark green). \figitem{E, F} Absolute value of the second-order susceptibility, \Eqnref{eq:susceptibility}, for both stimulus contrasts as indicated. Pink triangles indicate baseline firing rate. \figitem{G} Projections of the second-order susceptibilities in \panel{E, F} onto the diagonal. \notejb{`` Calculated based on the first frozen noise repeat.''}
+  \caption{\label{fig:ampullary} Estimation of linear and nonlinear stimulus encoding in an ampullary afferent (cell identifier ``2012-04-26-ae"). \figitem{A} Interspike interval (ISI) distribution of the cell's baseline activity. The very low CV of the ISIs indicates almost perfect periodic spiking. \figitem{B} Power spectral density of baseline activity with peaks at the cell's baseline firing rate and its harmonics. \figitem{C} Bad-limited white noise stimulus (top, with cutoff frequency of 150\,Hz) added to the fish's self-generated electric field and spike raster of the evoked responses (bottom) for two stimulus contrasts as indicated (right). \figitem{D} Gain of the transfer function, \Eqnref{linearencoding_methods}, of the responses to stimulation with 2\,\% (light green) and 20\,\% contrast (dark green). \figitem{E, F} Absolute value of the second-order susceptibility, \Eqnref{eq:susceptibility}, for both stimulus contrasts as indicated. Pink triangles indicate baseline firing rate. \figitem{G} Projections of the second-order susceptibilities in \panel{E, F} onto the diagonal. \notejb{`` Calculated based on the first frozen noise repeat.''}
   }
 \end{figure*}
 
 
 \subsection*{Ampullary afferents exhibit strong nonlinear interactions}
-Irrespective of the CV, neither of the two example P-units shows the complete expected structure of nonlinear interactions. Electric fish posses an additional electrosensory system, the passive or ampullary electrosensory system, that responds to low-frequency exogeneous electric stimuli. The population of ampullary afferents is much less heterogeneous, and known for the much lower CVs of their baseline ISIs (CV$_{\text{base}}=0.08$--$0.22$)\notejb{in the figure the CV is 0.07, below this range!}\cite{Grewe2017}. Ampullary cells do not phase-lock to the EOD and the ISIs are unimodally distributed (\subfigrefb{fig:ampullary}{A}). As a consequence of the high regularity of their baseline spiking activity, the corresponding power spectrum shows distinct peaks at the baseline firing rate \fbase{} and harmonics of it. Since the cells do not fire phase locked to the EOD, there is no peak at \feod{} (\subfigrefb{fig:ampullary}{B}). When driven by a low-contrast noise stimulus (note: this is not an AM but a stimulus that is added to the self-generated EOD, \subfigref{fig:ampullary}{C}), ampullary cells exhibit very pronounced bands in the second-order susceptibility, where \fsum{} is equal to \fbase{} or its harmonic (yellow diagonals in \subfigrefb{fig:ampullary}{E}), implying strong nonlinear response components at these frequency combinations (\subfigrefb{fig:ampullary}{G}, top). With higher stimulus contrasts these bands disappear (\subfigrefb{fig:ampullary}{F}), the projection onto the diagonal looses its distinct peak at \fsum{} and its overal level is reduced (\subfigrefb{fig:ampullary}{G}, bottom). 
+Irrespective of the CV, neither of the two example P-units shows the complete expected structure of nonlinear interactions. Electric fish posses an additional electrosensory system, the passive or ampullary electrosensory system, that responds to low-frequency exogeneous electric stimuli. The population of ampullary afferents is much less heterogeneous, and known for the much lower CVs of their baseline ISIs (CV$_{\text{base}}=0.06$--$0.22$)\cite{Grewe2017}. Ampullary cells do not phase-lock to the EOD and the ISIs are unimodally distributed (\subfigrefb{fig:ampullary}{A}). As a consequence of the high regularity of their baseline spiking activity, the corresponding power spectrum shows distinct peaks at the baseline firing rate \fbase{} and harmonics of it. Since the cells do not fire phase locked to the EOD, there is no peak at \feod{} (\subfigrefb{fig:ampullary}{B}). When driven by a low-contrast noise stimulus (note: this is not an AM but a stimulus that is added to the self-generated EOD, \subfigref{fig:ampullary}{C}), ampullary cells exhibit very pronounced bands in the second-order susceptibility, where \fsum{} is equal to \fbase{} or its harmonic (yellow diagonals in \subfigrefb{fig:ampullary}{E}), implying strong nonlinear response components at these frequency combinations (\subfigrefb{fig:ampullary}{G}, top). With higher stimulus contrasts these bands disappear (\subfigrefb{fig:ampullary}{F}), the projection onto the diagonal looses its distinct peak at \fsum{} and its overal level is reduced (\subfigrefb{fig:ampullary}{G}, bottom). 
 
 
 
@@ -577,7 +577,7 @@ In the example recordings shown above (\figsrefb{fig:cells_suscept} and \fref{fi
 
 \begin{figure*}[t]
   \includegraphics[width=\columnwidth]{model_and_data}
-  \caption{\label{model_and_data} Estimating second-order susceptibilities in the limit of weak stimuli. \figitem{A} \suscept{} estimated from $N=11$ trials of an electrophysiological recording of the\notejb{same as in Fig 2?} \noteab{No it is a different cell. In this cell we do not have several contrasts recorded, but a model.} low-CV P-unit (cell 2012-07-03-ak, see table~\ref{modelparams} for model parameters) \noteab{auch für die Datenzellen die identifier raussuchen?} driven with a weak RAM stimulus. The stimulus strength was with 2.5\,\% contrast in the electrophysiologically recorded P-unit. The contrast for the P-unit model was with 0.009\,\%, thus reproducing the CV of the electrophysiolgoical recorded P-unit during the 2.5\,\% contrast stimulation.  Pink edges mark baseline firing rate where enhanced nonlinear responses are expected. \figitem[i]{B} \textit{Standard condition} of model simulations with intrinsic noise (bottom) and a RAM stimulus (top). \figitem[ii]{B} \suscept{} estimated from simulations of the cell's LIF model counterpart (cell 2012-07-03-ak, table~\ref{modelparams}) based on the same number of trials as in the electrophysiological recording. \figitem[iii]{B} Same as \panel[ii]{B} but using $10^6$ stimulus repetitions. \figitem[i-iii]{C} Same as in \panel[i-iii]{B} but in the \textit{noise split} condition: there is no external RAM signal driving the model. Instead, a large part (90\,\%) of the total intrinsic noise is treated as signal and is presented as an equivalent amplitude modulation (\signalnoise, center), while the intrinsic noise is reduced to 10\,\% of its original strength (see methods for details). In addition to one million trials, this reveals the full expected structure of the second-order susceptibility. \notejb{to methods: ``Note that the signal component \signalnoise{} is added as an amplitude modulation and is thus limited with respect to its spectral content by the Nyquist frequency of the carrier, half the EOD frequency. It thus has a reduced high frequency content as compared to the intrinsic noise. Adding this discarded high frequency components to the intrinsic noise does not affect the results here (not shown).''}
+  \caption{\label{model_and_data} Estimating second-order susceptibilities in the limit of weak stimuli. \figitem{A} \suscept{} estimated from $N=11$ trials of an electrophysiological recording of the\notejb{same as in Fig 2?} \noteab{No it is a different cell. In this cell we do not have several contrasts recorded, but a model.} low-CV P-unit (cell 2012-07-03-ak, see table~\ref{modelparams} for model parameters) driven with a weak RAM stimulus. The stimulus strength was with 2.5\,\% contrast in the electrophysiologically recorded P-unit. The contrast for the P-unit model was with 0.009\,\%, thus reproducing the CV of the electrophysiolgoical recorded P-unit during the 2.5\,\% contrast stimulation.  Pink edges mark baseline firing rate where enhanced nonlinear responses are expected. \figitem[i]{B} \textit{Standard condition} of model simulations with intrinsic noise (bottom) and a RAM stimulus (top). \figitem[ii]{B} \suscept{} estimated from simulations of the cell's LIF model counterpart (cell 2012-07-03-ak, table~\ref{modelparams}) based on the same number of trials as in the electrophysiological recording. \figitem[iii]{B} Same as \panel[ii]{B} but using $10^6$ stimulus repetitions. \figitem[i-iii]{C} Same as in \panel[i-iii]{B} but in the \textit{noise split} condition: there is no external RAM signal driving the model. Instead, a large part (90\,\%) of the total intrinsic noise is treated as signal and is presented as an equivalent amplitude modulation (\signalnoise, center), while the intrinsic noise is reduced to 10\,\% of its original strength (see methods for details). In addition to one million trials, this reveals the full expected structure of the second-order susceptibility. \notejb{to methods: ``Note that the signal component \signalnoise{} is added as an amplitude modulation and is thus limited with respect to its spectral content by the Nyquist frequency of the carrier, half the EOD frequency. It thus has a reduced high frequency content as compared to the intrinsic noise. Adding this discarded high frequency components to the intrinsic noise does not affect the results here (not shown).''}
 }
 \end{figure*}
 
@@ -597,11 +597,11 @@ We estimated the second-order susceptibility of P-unit responses using RAM stimu
 
 \begin{figure*}[t]
   \includegraphics[width=\columnwidth]{model_full}
-  \caption{\label{fig:model_full} Using second-order susceptibility to predict responses to sine-wave stimuli. \figitem[]{A} Absolute value of the second-order susceptibility,  \Eqnref{eq:susceptibility}, for both positive and negative frequencies. \susceptf{} was estimated from $N=10^6$ trials of model simulations in the noise-split condition (cell 2012-07-03-ak, see table~\ref{modelparams} for model parameters). White lines indicate zero frequencies. Nonlinear responses at \fsum{} are quantified in the upper right and lower left quadrants.  Nonlinear responses at \fdiff{} are quantified in the upper left and lower right quadrants. Baseline firing rate of this cell was at $\fbase=120$\,Hz. The position of the orange/red letters correspond to the beat frequencies used for the stimulation with pure sine-waves in the subsequent panels and indicate the sum/difference of those beat frequencies. \figitem{B--E} Power spectral density of model simulations in response to stimulation with two pure sine waves, \fone{} and \ftwo, in addition to the receiving fish's own EOD (three fish scenario). \figitem{B} The sum of the two beat frequencies match \fbase{}. \figitem{C} The difference of \fone{} and \ftwo{} match \fbase{}. \figitem{D} Only the first beat frequency matches \fbase{}. \figitem{C} None of the two beat frequencies matches \fbase{}.}
+  \caption{\label{fig:model_full} Using second-order susceptibility to predict responses to sine-wave stimuli. \figitem[]{A} Absolute value of the second-order susceptibility,  \Eqnref{eq:susceptibility}, for both positive and negative frequencies. \susceptf{} was estimated from $N=10^6$ trials of model simulations in the noise-split condition (cell 2012-07-03-ak, see table~\ref{modelparams} for model parameters). White lines indicate zero frequencies. Nonlinear responses at \fsum{} are quantified in the upper right and lower left quadrants.  Nonlinear responses at \fdiff{} are quantified in the upper left and lower right quadrants. Baseline firing rate of this cell was at $\fbase=120$\,Hz. The position of the orange/red letters correspond to the beat frequencies used for the stimulation with pure sine-waves in the subsequent panels and indicate the sum/difference of those beat frequencies.  \figitem[]{B} Absolute value of the first-order susceptibility. \figitem{C--F} Black line -- power spectral density of model simulations in response to stimulation with two pure sine waves, \fone{} and \ftwo, in addition to the receiving fish's own EOD (three fish scenario). The contrasts of beat beats is 0.0065.  Colored circles highlight the height of selected peaks in the power spectrum. Black circles highlight the peak height that can be predicted from \panel{A, B}. Grey line -- power spectral density of model in the baseline condition. \figitem{B} The sum of the two beat frequencies match \fbase{}. \figitem{C} The difference of \fone{} and \ftwo{} match \fbase{}. \figitem{D} Only the first beat frequency matches \fbase{}. \figitem{C} None of the two beat frequencies matches \fbase{}.}
 \end{figure*}
 
 However, the second-order susceptibility \Eqnref{eq:susceptibility} is a spectral measure that is based on Fourier transforms and thus is also defined for negative stimulus frequencies. The full \susceptf{} matrix is symmetric with respect to the origin. In the upper-right and lower-left quadrants of \susceptf{}, stimulus-evoked responses at \fsum{} are shown, whereas in the lower-right and upper-left quadrants nonlinear responses at the difference \fdiff{} are shown (\figref{fig:model_full}). The vertical and horizontal lines at \foneb{} and \ftwob{} are very pronounced in the upper-right quadrant of \subfigrefb{fig:model_full}{A} for nonlinear responses at \fsum{} and extend into the upper-left quadrant (representing \fdiff) where they fade out towards more negative $f_1$ frequencies. The peak in the response power-spectrum at \fdiff{} evoked by pure sine-wave stimulation (\subfigrefb{fig:motivation}{D}) is predicted by the horizontal line in the upper-left quadrant (\subfigrefb{fig:model_full}{A}, \cite{Schlungbaum2023}). 
-Is it possible based on the second-order susceptibility estimated by means of RAM stimuli (\subfigrefb{fig:model_full}{A}) to predict nonlinear responses in a three-fish setting? We can test this by stimulating the same model with two beats with weak amplitudes \notejb{specify the contrast at least in the figure legend!} (\subfigrefb{fig:model_full}{B--E}). If we choose a frequency combination where the sum of the two beat frequencies is equal to the model's baseline firing rate \fbase{}, a peak at the sum of the two beat frequencies appears in the power spectrum of the response (\subfigrefb{fig:model_full}{B}), as expected from \suscept. If instead we choose two beat frequencies that differ by \fbase{}, a peak is present at the difference frequency (\subfigrefb{fig:model_full}{C}). If only one beat frequency is equal to \fbase{}, both a peak at the sum and at the difference frequency is present in the P-unit response (\subfigrefb{fig:model_full}{D}). And if none of these conditions are met, neither a peak at the sum nor at the difference of the two beat frequencies appears (\subfigrefb{fig:model_full}{E}).
+Is it possible based on the second-order susceptibility estimated by means of RAM stimuli (\subfigrefb{fig:model_full}{A}) to predict nonlinear responses in a three-fish setting? We can test this by stimulating the same model with two beats with weak amplitudes (\subfigrefb{fig:model_full}{C--F}). If we choose a frequency combination where the sum of the two beat frequencies is equal to the model's baseline firing rate \fbase{}, a peak at the sum of the two beat frequencies appears in the power spectrum of the response (\subfigrefb{fig:model_full}{C}), as expected from \suscept. If instead we choose two beat frequencies that differ by \fbase{}, a peak is present at the difference frequency (\subfigrefb{fig:model_full}{D}). If only one beat frequency is equal to \fbase{}, both a peak at the sum and at the difference frequency is present in the P-unit response (\subfigrefb{fig:model_full}{E}). And if none of these conditions are met, neither a peak at the sum nor at the difference of the two beat frequencies appears (\subfigrefb{fig:model_full}{F}).
 
 \notejb{Note in the discussion that \suscept{} predicts stimulus evoked responses whereas in the power spectrum we see peaks even if they are unrelated to the stimulus. Like the baseline firing rate.}
 
@@ -960,7 +960,7 @@ CVs in P-units can range up to 1.5 \cite{Grewe2017, Hladnik2023}. We show the sa
 \label{S1:highcvpunit}
 \begin{figure*}[!ht]
 \includegraphics[width=\columnwidth]{cells_suscept_high_CV}  
-  \caption{\label{fig:cells_suscept_high_CV} Response of experimentally measured P-units to RAM stimuli. Light purple -- low RAM contrast. Dark purple -- high RAM contrast. Noisy high-CV P-Unit. \figitem{A} Interspike intervals (ISI) distribution during baseline. \figitem{B} Baseline power spectrum of the firing rate. \figitem{C} Top: EOD carrier (gray) with RAM (red). Middle: Spike trains in response to a low RAM contrast. Bottom: Spike trains in response to a high RAM contrast. \figitem{D} First-order susceptibility (see \Eqnref{linearencoding_methods}). \figitem{E} Absolute value of the second-order susceptibility, \Eqnref{eq:susceptibility}, for the low RAM contrast. 
+  \caption{\label{fig:cells_suscept_high_CV} Response of experimentally measured P-units (cell identifier ``2018-08-24-af") to RAM stimuli. Light purple -- low RAM contrast. Dark purple -- high RAM contrast. Noisy high-CV P-Unit. \figitem{A} Interspike intervals (ISI) distribution during baseline. \figitem{B} Baseline power spectrum of the firing rate. \figitem{C} Top: EOD carrier (gray) with RAM (red). Middle: Spike trains in response to a low RAM contrast. Bottom: Spike trains in response to a high RAM contrast. \figitem{D} First-order susceptibility (see \Eqnref{linearencoding_methods}). \figitem{E} Absolute value of the second-order susceptibility, \Eqnref{eq:susceptibility}, for the low RAM contrast. 
  Pink lines -- edges of the structure when \fone, \ftwo{} or \fsum{} are equal to \fbase{}. \figitem{F} Absolute value of the second-order susceptibility for the higher RAM contrast. \figitem{G} Projected diagonals, calculated as the mean of the anti-diagonals of the matrices in \panel{E--F}. Gray dots: \fbase{}. Dashed lines: Medians of the projected diagonals.
   }
 \end{figure*}
@@ -968,7 +968,7 @@ CVs in P-units can range up to 1.5 \cite{Grewe2017, Hladnik2023}. We show the sa
 
 \begin{figure*}[hp]%hp!
 \includegraphics[width=\columnwidth]{trialnr}  
-  \caption{\label{fig:trialnr} Saturation of the second-order susceptibility depending on the stimulus repetition number $\n{}$. Gray line -- 99.9th percentile of the second-order susceptibility matrix.
+  \caption{\label{fig:trialnr} Saturation of the second-order susceptibility depending on the stimulus repetition number $\n{}$. \figitem{A} Gray line -- 99.9th percentile of the second-order susceptibility matrix. \figitem{B} Gray line -- 10th percentile of the second-order susceptibility matrix.
   }
 \end{figure*}
 

susceptibility1.tex.bak

@@ -543,7 +543,7 @@ Nonlinear encoding as quantified by the second-order susceptibility is expected
 
 \begin{figure*}[t]
 \includegraphics[width=\columnwidth]{cells_suscept} 
-\caption{\label{fig:cells_suscept} Estimation of linear and nonlinear stimulus encoding in a low-CV P-unit. \figitem{A} Interspike interval (ISI) distribution of the cell's baseline activity, i.e. the cell is driven only by the unperturbed own electric field. The low CV of the ISIs indicates quite regular firing. \figitem{B} Power spectral density of the baseline response with peaks at the cell's baseline firing rate \fbase{} and the fish's EOD frequency \feod{}. \figitem{C} Random amplitude modulation stimulus (top, \notejb{cutoff frequency?}) and evoked responses (spike raster, bottom) of the same P-unit. The stimulus contrast (right) reflects the strength of the AM. \figitem{D} Gain of the transfer function (first-order susceptibility), \Eqnref{linearencoding_methods}, of the responses to 10\,\% (light purple) and 20\,\% contrast (dark purple) RAM stimulation. \figitem{E, F} Absolute value of the second-order susceptibility, \Eqnref{eq:susceptibility}, for both the low and high stimulus contrast. Pink triangles mark vertical, horizontal, and diagonal lines where \fone, \ftwo{} or \fsum{} are equal to \fbase{}. \figitem{G} Second-order susceptibilities projected onto the diagonal (means of all anti-diagonals of the matrices  shown in \panel{E, F}). Dots mark \fbase{}, horizontal dashed lines mark medians of the projected susceptibilities.  \notejb{``Calculated based on the first frozen noise repeat.'' Really? Only one trial has been used for computing the susceptibilities?} \noteab{Yes. In the population statistics of the last 20 years I was trying to maximize the number cells and maximize the duration. In the end the susceptibility is calculated based on 10 seconds. The susceptibility has always to be calculated with newly initiated noise, with 10 seconds and 0.5 nfft durations this results in 20 trials. For the overview figure the mean of all NLI values for each frozen noise was calculated. It is not possible to take the mean over several frozen noise matrices since the baseline properties sometimes change and this disrupts the second order susceptibility.}}
+\caption{\label{fig:cells_suscept} Estimation of linear and nonlinear stimulus encoding in a low-CV P-unit (cell identifier ``2010-06-21-ai"). \figitem{A} Interspike interval (ISI) distribution of the cell's baseline activity, i.e. the cell is driven only by the unperturbed own electric field. The low CV of the ISIs indicates quite regular firing. \figitem{B} Power spectral density of the baseline response with peaks at the cell's baseline firing rate \fbase{} and the fish's EOD frequency \feod{}. \figitem{C} Random amplitude modulation stimulus (top, with cutoff frequency of 300\,Hz) and evoked responses (spike raster, bottom) of the same P-unit. The stimulus contrast (right) reflects the strength of the AM. \figitem{D} Gain of the transfer function (first-order susceptibility), \Eqnref{linearencoding_methods}, of the responses to 10\,\% (light purple) and 20\,\% contrast (dark purple) RAM stimulation. \figitem{E, F} Absolute value of the second-order susceptibility, \Eqnref{eq:susceptibility}, for both the low and high stimulus contrast. Pink triangles mark vertical, horizontal, and diagonal lines where \fone, \ftwo{} or \fsum{} are equal to \fbase{}. \figitem{G} Second-order susceptibilities projected onto the diagonal (means of all anti-diagonals of the matrices  shown in \panel{E, F}). Dots mark \fbase{}, horizontal dashed lines mark medians of the projected susceptibilities.  \notejb{``Calculated based on the first frozen noise repeat.'' Really? Only one trial has been used for computing the susceptibilities?} \noteab{Yes. In the population statistics of the last 20 years I was trying to maximize the number cells and maximize the duration. In the end the susceptibility is calculated based on 10 seconds. The susceptibility has to be calculated with newly initiated noise, with 10 seconds and 0.5 nfft durations this results in 20 trials. For the overview figure the mean of all NLI values for each frozen noise was calculated. It is not possible to take the mean over several frozen noise matrices since the baseline properties sometimes change and this disrupts the shape of the second order susceptibility.}}
 \end{figure*}
 
 Noise stimuli, here random amplitude modulations (RAM) of the EOD (\subfigref{fig:cells_suscept}{C}, top trace, red line), are commonly used to characterize stimulus driven responses of sensory neurons by means of transfer functions (first-order susceptibility), spike-triggered averages, or stimulus-response coherences. Here, we additionally estimate the second-order susceptibility to quantify nonlinear encoding. P-unit spikes align more or less clearly to fluctuations in the RAM stimulus. A higher stimulus intensity, here a higher contrast of the RAM relative to the EOD amplitude (see methods), entrains the P-unit response more clearly (light and dark purple for low and high contrast stimuli, \subfigrefb{fig:cells_suscept}{C}). Linear encoding, quantified by the transfer function \Eqnref{linearencoding_methods}, is similar for the two RAM contrasts in this low-CV P-unit (\subfigrefb{fig:cells_suscept}{D}), as expected for a linear system. The first-order susceptibility is low for low frequencies, peaks in the range below 100\,Hz and then falls off again \notejb{Cite Moe paper?}.
@@ -561,13 +561,13 @@ In contrast, a high-CV P-unit (CV$_{\text{base}}=0.4$) does not exhibit pronounc
 
 \begin{figure*}[t]
 \includegraphics[width=\columnwidth]{ampullary}
-  \caption{\label{fig:ampullary} Estimation of linear and nonlinear stimulus encoding in an ampullary afferent. \figitem{A} Interspike interval (ISI) distribution of the cell's baseline activity. The very low CV of the ISIs indicates almost perfect periodic spiking. \figitem{B} Power spectral density of baseline activity with peaks at the cell's baseline firing rate and its harmonics. \figitem{C} Bad-limited white noise stimulus (top, \notejb{cutoff frequency?}) added to the fish's self-generated electric field and spike raster of the evoked responses (bottom) for two stimulus contrasts as indicated (right). \figitem{D} Gain of the transfer function, \Eqnref{linearencoding_methods}, of the responses to stimulation with 2\,\% (light green) and 20\,\% contrast (dark green). \figitem{E, F} Absolute value of the second-order susceptibility, \Eqnref{eq:susceptibility}, for both stimulus contrasts as indicated. Pink triangles indicate baseline firing rate. \figitem{G} Projections of the second-order susceptibilities in \panel{E, F} onto the diagonal. \notejb{`` Calculated based on the first frozen noise repeat.''}
+  \caption{\label{fig:ampullary} Estimation of linear and nonlinear stimulus encoding in an ampullary afferent. \figitem{A} Interspike interval (ISI) distribution of the cell's baseline activity. The very low CV of the ISIs indicates almost perfect periodic spiking. \figitem{B} Power spectral density of baseline activity with peaks at the cell's baseline firing rate and its harmonics. \figitem{C} Bad-limited white noise stimulus (top, with cutoff frequency of 150\,Hz) added to the fish's self-generated electric field and spike raster of the evoked responses (bottom) for two stimulus contrasts as indicated (right). \figitem{D} Gain of the transfer function, \Eqnref{linearencoding_methods}, of the responses to stimulation with 2\,\% (light green) and 20\,\% contrast (dark green). \figitem{E, F} Absolute value of the second-order susceptibility, \Eqnref{eq:susceptibility}, for both stimulus contrasts as indicated. Pink triangles indicate baseline firing rate. \figitem{G} Projections of the second-order susceptibilities in \panel{E, F} onto the diagonal. \notejb{`` Calculated based on the first frozen noise repeat.''}
   }
 \end{figure*}
 
 
 \subsection*{Ampullary afferents exhibit strong nonlinear interactions}
-Irrespective of the CV, neither of the two example P-units shows the complete expected structure of nonlinear interactions. Electric fish posses an additional electrosensory system, the passive or ampullary electrosensory system, that responds to low-frequency exogeneous electric stimuli. The population of ampullary afferents is much less heterogeneous, and known for the much lower CVs of their baseline ISIs (CV$_{\text{base}}=0.08$--$0.22$)\notejb{in the figure the CV is 0.07, below this range!}\cite{Grewe2017}. Ampullary cells do not phase-lock to the EOD and the ISIs are unimodally distributed (\subfigrefb{fig:ampullary}{A}). As a consequence of the high regularity of their baseline spiking activity, the corresponding power spectrum shows distinct peaks at the baseline firing rate \fbase{} and harmonics of it. Since the cells do not fire phase locked to the EOD, there is no peak at \feod{} (\subfigrefb{fig:ampullary}{B}). When driven by a low-contrast noise stimulus (note: this is not an AM but a stimulus that is added to the self-generated EOD, \subfigref{fig:ampullary}{C}), ampullary cells exhibit very pronounced bands in the second-order susceptibility, where \fsum{} is equal to \fbase{} or its harmonic (yellow diagonals in \subfigrefb{fig:ampullary}{E}), implying strong nonlinear response components at these frequency combinations (\subfigrefb{fig:ampullary}{G}, top). With higher stimulus contrasts these bands disappear (\subfigrefb{fig:ampullary}{F}), the projection onto the diagonal looses its distinct peak at \fsum{} and its overal level is reduced (\subfigrefb{fig:ampullary}{G}, bottom). 
+Irrespective of the CV, neither of the two example P-units shows the complete expected structure of nonlinear interactions. Electric fish posses an additional electrosensory system, the passive or ampullary electrosensory system, that responds to low-frequency exogeneous electric stimuli. The population of ampullary afferents is much less heterogeneous, and known for the much lower CVs of their baseline ISIs (CV$_{\text{base}}=0.06$--$0.22$)\cite{Grewe2017}. Ampullary cells do not phase-lock to the EOD and the ISIs are unimodally distributed (\subfigrefb{fig:ampullary}{A}). As a consequence of the high regularity of their baseline spiking activity, the corresponding power spectrum shows distinct peaks at the baseline firing rate \fbase{} and harmonics of it. Since the cells do not fire phase locked to the EOD, there is no peak at \feod{} (\subfigrefb{fig:ampullary}{B}). When driven by a low-contrast noise stimulus (note: this is not an AM but a stimulus that is added to the self-generated EOD, \subfigref{fig:ampullary}{C}), ampullary cells exhibit very pronounced bands in the second-order susceptibility, where \fsum{} is equal to \fbase{} or its harmonic (yellow diagonals in \subfigrefb{fig:ampullary}{E}), implying strong nonlinear response components at these frequency combinations (\subfigrefb{fig:ampullary}{G}, top). With higher stimulus contrasts these bands disappear (\subfigrefb{fig:ampullary}{F}), the projection onto the diagonal looses its distinct peak at \fsum{} and its overal level is reduced (\subfigrefb{fig:ampullary}{G}, bottom). 
 
 
 
@@ -577,7 +577,7 @@ In the example recordings shown above (\figsrefb{fig:cells_suscept} and \fref{fi
 
 \begin{figure*}[t]
   \includegraphics[width=\columnwidth]{model_and_data}
-  \caption{\label{model_and_data} Estimating second-order susceptibilities in the limit of weak stimuli. \figitem{A} \suscept{} estimated from $N=11$ trials of an electrophysiological recording of the\notejb{same as in Fig 2?} \noteab{No it is a different cell. In this cell we do not have several contrasts recorded, but a model.} low-CV P-unit (cell 2012-07-03-ak, see table~\ref{modelparams} for model parameters) \notesr{auch für die Datenzellen die identifier raussuchen?} driven with a weak RAM stimulus. The stimulus strength was with 2.5\,\% contrast in the electrophysiologically recorded P-unit. The contrast for the P-unit model was with 0.009\,\%, thus reproducing the CV of the electrophysiolgoical recorded P-unit during the 2.5\,\% contrast stimulation.  Pink edges mark baseline firing rate where enhanced nonlinear responses are expected. \figitem[i]{B} \textit{Standard condition} of model simulations with intrinsic noise (bottom) and a RAM stimulus (top). \figitem[ii]{B} \suscept{} estimated from simulations of the cell's LIF model counterpart (cell 2012-07-03-ak, table~\ref{modelparams}) based on the same number of trials as in the electrophysiological recording. \figitem[iii]{B} Same as \panel[ii]{B} but using $10^6$ stimulus repetitions. \figitem[i-iii]{C} Same as in \panel[i-iii]{B} but in the \textit{noise split} condition: there is no external RAM signal driving the model. Instead, a large part (90\,\%) of the total intrinsic noise is treated as signal and is presented as an equivalent amplitude modulation (\signalnoise, center), while the intrinsic noise is reduced to 10\,\% of its original strength (see methods for details). In addition to one million trials, this reveals the full expected structure of the second-order susceptibility. \notejb{to methods: ``Note that the signal component \signalnoise{} is added as an amplitude modulation and is thus limited with respect to its spectral content by the Nyquist frequency of the carrier, half the EOD frequency. It thus has a reduced high frequency content as compared to the intrinsic noise. Adding this discarded high frequency components to the intrinsic noise does not affect the results here (not shown).''}
+  \caption{\label{model_and_data} Estimating second-order susceptibilities in the limit of weak stimuli. \figitem{A} \suscept{} estimated from $N=11$ trials of an electrophysiological recording of the\notejb{same as in Fig 2?} \noteab{No it is a different cell. In this cell we do not have several contrasts recorded, but a model.} low-CV P-unit (cell 2012-07-03-ak, see table~\ref{modelparams} for model parameters) \noteab{auch für die Datenzellen die identifier raussuchen?} driven with a weak RAM stimulus. The stimulus strength was with 2.5\,\% contrast in the electrophysiologically recorded P-unit. The contrast for the P-unit model was with 0.009\,\%, thus reproducing the CV of the electrophysiolgoical recorded P-unit during the 2.5\,\% contrast stimulation.  Pink edges mark baseline firing rate where enhanced nonlinear responses are expected. \figitem[i]{B} \textit{Standard condition} of model simulations with intrinsic noise (bottom) and a RAM stimulus (top). \figitem[ii]{B} \suscept{} estimated from simulations of the cell's LIF model counterpart (cell 2012-07-03-ak, table~\ref{modelparams}) based on the same number of trials as in the electrophysiological recording. \figitem[iii]{B} Same as \panel[ii]{B} but using $10^6$ stimulus repetitions. \figitem[i-iii]{C} Same as in \panel[i-iii]{B} but in the \textit{noise split} condition: there is no external RAM signal driving the model. Instead, a large part (90\,\%) of the total intrinsic noise is treated as signal and is presented as an equivalent amplitude modulation (\signalnoise, center), while the intrinsic noise is reduced to 10\,\% of its original strength (see methods for details). In addition to one million trials, this reveals the full expected structure of the second-order susceptibility. \notejb{to methods: ``Note that the signal component \signalnoise{} is added as an amplitude modulation and is thus limited with respect to its spectral content by the Nyquist frequency of the carrier, half the EOD frequency. It thus has a reduced high frequency content as compared to the intrinsic noise. Adding this discarded high frequency components to the intrinsic noise does not affect the results here (not shown).''}
 }
 \end{figure*}
 
@@ -597,11 +597,11 @@ We estimated the second-order susceptibility of P-unit responses using RAM stimu
 
 \begin{figure*}[t]
   \includegraphics[width=\columnwidth]{model_full}
-  \caption{\label{fig:model_full} Using second-order susceptibility to predict responses to sine-wave stimuli. \figitem[]{A} Absolute value of the second-order susceptibility,  \Eqnref{eq:susceptibility}, for both positive and negative frequencies. \susceptf{} was estimated from $N=10^6$ trials of model simulations in the noise-split condition (cell 2012-07-03-ak, see table~\ref{modelparams} for model parameters). White lines indicate zero frequencies. Nonlinear responses at \fsum{} are quantified in the upper right and lower left quadrants.  Nonlinear responses at \fdiff{} are quantified in the upper left and lower right quadrants. Baseline firing rate of this cell was at $\fbase=120$\,Hz. The position of the orange/red letters correspond to the beat frequencies used for the stimulation with pure sine-waves in the subsequent panels and indicate the sum/difference of those beat frequencies. \figitem{B--E} Power spectral density of model simulations in response to stimulation with two pure sine waves, \fone{} and \ftwo, in addition to the receiving fish's own EOD (three fish scenario). \figitem{B} The sum of the two beat frequencies match \fbase{}. \figitem{C} The difference of \fone{} and \ftwo{} match \fbase{}. \figitem{D} Only the first beat frequency matches \fbase{}. \figitem{C} None of the two beat frequencies matches \fbase{}.}
+  \caption{\label{fig:model_full} Using second-order susceptibility to predict responses to sine-wave stimuli. \figitem[]{A} Absolute value of the second-order susceptibility,  \Eqnref{eq:susceptibility}, for both positive and negative frequencies. \susceptf{} was estimated from $N=10^6$ trials of model simulations in the noise-split condition (cell 2012-07-03-ak, see table~\ref{modelparams} for model parameters). White lines indicate zero frequencies. Nonlinear responses at \fsum{} are quantified in the upper right and lower left quadrants.  Nonlinear responses at \fdiff{} are quantified in the upper left and lower right quadrants. Baseline firing rate of this cell was at $\fbase=120$\,Hz. The position of the orange/red letters correspond to the beat frequencies used for the stimulation with pure sine-waves in the subsequent panels and indicate the sum/difference of those beat frequencies.  \figitem[]{B} Absolute value of the first-order susceptibility. \figitem{C--F} Black line -- power spectral density of model simulations in response to stimulation with two pure sine waves, \fone{} and \ftwo, in addition to the receiving fish's own EOD (three fish scenario). The contrasts of beat beats is 0.0065.  Colored circles highlight the height of selected peaks in the power spectrum. Black circles highlight the peak height that can be predicted from \panel{A, B}. Grey line -- power spectral density of model in the baseline condition. \figitem{B} The sum of the two beat frequencies match \fbase{}. \figitem{C} The difference of \fone{} and \ftwo{} match \fbase{}. \figitem{D} Only the first beat frequency matches \fbase{}. \figitem{C} None of the two beat frequencies matches \fbase{}.}
 \end{figure*}
 
 However, the second-order susceptibility \Eqnref{eq:susceptibility} is a spectral measure that is based on Fourier transforms and thus is also defined for negative stimulus frequencies. The full \susceptf{} matrix is symmetric with respect to the origin. In the upper-right and lower-left quadrants of \susceptf{}, stimulus-evoked responses at \fsum{} are shown, whereas in the lower-right and upper-left quadrants nonlinear responses at the difference \fdiff{} are shown (\figref{fig:model_full}). The vertical and horizontal lines at \foneb{} and \ftwob{} are very pronounced in the upper-right quadrant of \subfigrefb{fig:model_full}{A} for nonlinear responses at \fsum{} and extend into the upper-left quadrant (representing \fdiff) where they fade out towards more negative $f_1$ frequencies. The peak in the response power-spectrum at \fdiff{} evoked by pure sine-wave stimulation (\subfigrefb{fig:motivation}{D}) is predicted by the horizontal line in the upper-left quadrant (\subfigrefb{fig:model_full}{A}, \cite{Schlungbaum2023}). 
-Is it possible based on the second-order susceptibility estimated by means of RAM stimuli (\subfigrefb{fig:model_full}{A}) to predict nonlinear responses in a three-fish setting? We can test this by stimulating the same model with two beats with weak amplitudes \notejb{specify the contrast at least in the figure legend!} (\subfigrefb{fig:model_full}{B--E}). If we choose a frequency combination where the sum of the two beat frequencies is equal to the model's baseline firing rate \fbase{}, a peak at the sum of the two beat frequencies appears in the power spectrum of the response (\subfigrefb{fig:model_full}{B}), as expected from \suscept. If instead we choose two beat frequencies that differ by \fbase{}, a peak is present at the difference frequency (\subfigrefb{fig:model_full}{C}). If only one beat frequency is equal to \fbase{}, both a peak at the sum and at the difference frequency is present in the P-unit response (\subfigrefb{fig:model_full}{D}). And if none of these conditions are met, neither a peak at the sum nor at the difference of the two beat frequencies appears (\subfigrefb{fig:model_full}{E}).
+Is it possible based on the second-order susceptibility estimated by means of RAM stimuli (\subfigrefb{fig:model_full}{A}) to predict nonlinear responses in a three-fish setting? We can test this by stimulating the same model with two beats with weak amplitudes (\subfigrefb{fig:model_full}{C--F}). If we choose a frequency combination where the sum of the two beat frequencies is equal to the model's baseline firing rate \fbase{}, a peak at the sum of the two beat frequencies appears in the power spectrum of the response (\subfigrefb{fig:model_full}{C}), as expected from \suscept. If instead we choose two beat frequencies that differ by \fbase{}, a peak is present at the difference frequency (\subfigrefb{fig:model_full}{D}). If only one beat frequency is equal to \fbase{}, both a peak at the sum and at the difference frequency is present in the P-unit response (\subfigrefb{fig:model_full}{E}). And if none of these conditions are met, neither a peak at the sum nor at the difference of the two beat frequencies appears (\subfigrefb{fig:model_full}{F}).
 
 \notejb{Note in the discussion that \suscept{} predicts stimulus evoked responses whereas in the power spectrum we see peaks even if they are unrelated to the stimulus. Like the baseline firing rate.}
 

trialnr.py

@@ -140,11 +140,11 @@ def trialnr(nffts=['whole'], powers=[1], contrasts=[0], noises_added=[''], D_ext
                     model_show, stack_plot, stack_plot_wo_norm = get_stack(cell, stack)
                     stacks.append(stack_plot)
                     perc95.append(np.percentile(stack_plot,99.99))
-                    perc05.append(np.percentile(stack_plot, 0))
+                    perc05.append(np.percentile(stack_plot, 10))
                     median.append(np.percentile(stack_plot, 50))
                     stacks_wo_norm.append(stack_plot_wo_norm)
                     perc95_wo_norm.append(np.percentile(stack_plot_wo_norm,99.99))
-                    perc05_wo_norm.append(np.percentile(stack_plot_wo_norm, 0))
+                    perc05_wo_norm.append(np.percentile(stack_plot_wo_norm, 10))
                     median_wo_norm.append(np.percentile(stack_plot_wo_norm, 50))
 
                 else:
@@ -158,19 +158,27 @@ def trialnr(nffts=['whole'], powers=[1], contrasts=[0], noises_added=[''], D_ext
                     perc05_wo_norm.append(float('nan'))
                     median_wo_norm.append(float('nan'))
 
-        fig, ax = plt.subplots(1,1)
+        fig, ax = plt.subplots(1,2)
         #ax.plot(trial_nrs_here, perc05, color = 'grey')
-        ax.plot(trial_nrs_here, perc95, color = 'grey', clip_on = False)
+        ax[0].plot(trial_nrs_here, perc95, color = 'grey', clip_on = False, label = '99.99th percentile')
         #ax.plot(trial_nrs_here, median, color = 'black', label = 'median')
         #ax.scatter(trial_nrs_here, perc05, color = 'grey')
-        ax.scatter(trial_nrs_here, perc95, color = 'black', clip_on = False)
+        ax[0].scatter(trial_nrs_here, perc95, color = 'black', clip_on = False)
+        ax[0].set_xscale('log')
+        ax[0].set_yscale('log')
+        ax[0].set_xlabel('Trials [$N$]')
+        ax[0].set_ylabel('$\chi_{2}$\,[Hz]')
+        ax[0].legend()
+
+        ############################################
+        ax[1].plot(trial_nrs_here, perc05, color='grey', clip_on=False, label = '10th percentile')
+        ax[1].scatter(trial_nrs_here, perc05, color='black', clip_on=False)
+        ax[1].set_xscale('log')
+        ax[1].set_yscale('log')
+        ax[1].set_xlabel('Trials [$N$]')
+        ax[1].set_ylabel('$\chi_{2}$\,[Hz]')
+        ax[1].legend()
 
-
-        #embed()
-        ax.set_xscale('log')
-        ax.set_yscale('log')
-        ax.set_xlabel('Trials [$N$]')
-        ax.set_ylabel('$\chi_{2}$\,[Hz]')
         '''        ax = plt.subplot(1,3,2)
         ax.plot(trial_nrs_here, perc05_wo_norm, color = 'grey')
         ax.plot(trial_nrs_here, perc95_wo_norm, color = 'grey')