updated dots in full_model
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model_full.pdf
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model_full.pdf
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@ -22,8 +22,8 @@ def model_full():
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f2 = 139
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#embed()
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ax.plot(fr_noise * f1/fr_waves, fr_noise*f2/fr_waves, 'o', ms = 5, markeredgecolor = 'white', markerfacecolor="None")
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ax.plot(fr_noise * f1 / fr_waves, -fr_noise * f2 / fr_waves, 'o', ms = 5, markeredgecolor='white', markerfacecolor="None")
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ax.plot(fr_noise * f1/fr_waves, fr_noise*f2/fr_waves, 'o', ms = 5, markeredgecolor = 'orange', markerfacecolor="None")
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ax.plot(-fr_noise * f1 / fr_waves, fr_noise * f2 / fr_waves, 'o', ms = 5, markeredgecolor='pink', markerfacecolor="None")
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# if len(cbar) > 0:
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###############################
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motivation.pdf
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@ -312,7 +312,7 @@ def motivation_all_small(ylim=[-1.25, 1.25], c1=10, dfs=['m1', 'm2'], mult_type=
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array_chosen=array_chosen,
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color0_burst=color0_burst, mean_types=[mean_type],
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color01=color01, color02=color02,
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color012=color012,
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color012=color012,color012_minus = 'pink',
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color01_2=color01_2)
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##########################################################################
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susceptibility1.pdf
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susceptibility1.pdf
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@ -516,16 +516,15 @@ In a high-CV P-unit we could not find such nonlinear structures, neither in the
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\end{figure*}
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\subsection{Second-order susceptibility can explain nonlinear peaks in pure sinewave stimulation}
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We calculated the second-order susceptibility surfaces at \fsumb{} by extracting the respective spectral component of the P-unit responses to RAM stimuli. How does this relate to the pure sinewave situation that approximates the interference of real animals? The relevant signals are the the beat frequencies \fone{} and \ftwo{} that arise from the interference of the receiving fish's own and either of the foreign EODs \figref{motivation}. The response power spectrum showed peaks from nonlinear interaction at the sum of the two beat frequencies (orange marker, \subfigrefb{motivation}{D}) and at the difference between the two beat frequencies (purple marker, \subfigrefb{motivation}{D}). In the example $\Delta f_{1}$ was similar to \fbase{}, corresponding to the vertical line in the RAM-based second-order susceptibility matrix in \subfigrefb{model_and_data}\,\panel[iii]{B}. In the three-fish example, there was a second, less prominent, nonlinearity at the difference between the two beat frequencies (purple circle, \subfigrefb{motivation}{D}), that cannot be explained with the second-order susceptibility matrix in \subfigrefb{model_and_data}\,\panel[iv]{B}, in which only the nonlinearity at \fsum{} in the response is addressed (\eqnref{eq:crosshigh}).
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We calculated the second-order susceptibility surfaces at \fsumb{} by extracting the respective spectral component of the P-unit responses to RAM stimuli. How does this relate to the pure sinewave situation that approximates the interference of real animals? The relevant signals are the the beat frequencies \fone{} and \ftwo{} that arise from the interference of the receiving fish's own and either of the foreign EODs \figref{motivation}. The response power spectrum showed peaks from nonlinear interaction at the sum of the two beat frequencies (orange marker, \subfigrefb{motivation}{D}) and at the difference between the two beat frequencies (rosa marker, \subfigrefb{motivation}{D}). In the example $\Delta f_{2}$ was similar to \fbase{}, corresponding to the horizontal line in the RAM-based second-order susceptibility matrix in \subfigrefb{model_and_data}\,\panel[iii]{B}. In the three-fish example, there was a second, less prominent, nonlinearity at the difference between the two beat frequencies (rosa circle, \subfigrefb{motivation}{D}), that cannot be explained with the second-order susceptibility matrix in \subfigrefb{model_and_data}\,\panel[iv]{B}, in which only the nonlinearity at \fsum{} in the response is addressed (\eqnref{eq:crosshigh}).
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\begin{figure*}[h]
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\includegraphics[width=\columnwidth]{model_full}
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\caption{\label{model_full} Second-order susceptibility of an electrophysiologically recorded P-unit and of the corresponding model (see table~\ref{modelparams} for model parameters of 2012-07-03-ak). White lines -- coordinate axis. The nonlinearity at \fsum{} in the firing rate is quantified in the upper right and lower left quadrants (\eqnref{eq:susceptibility}). The nonlinearity at \fdiff{} in the firing rate is quantified in the upper left and lower right quadrants. Mean baseline firing rate $\fbase{}=120$\,Hz. \figitem{A} Absolute value of the second-order susceptibility of an electrophysiologically recorded P-unit. RAM stimulus realizations $N=11$. Diagonal bands appear when the sum of the frequencies \fsum{} or the difference \fdiff{} is equal to \fbase{}. \figitem{B} Absolute value of the model second-order susceptibility, with $N=1$\,million stimulus realizations and the intrinsic noise split (see methods section \ref{intrinsicsplit_methods}). The diagonals, that were present in \panel{A}, are complemented by vertical and horizontal lines when \fone{} or \ftwo{} are equal to \fbase{}. 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 \panel{B}.}
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\end{figure*}
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The second-order susceptibility can also be calculated for the full matrix including negative frequency components of the respective spectra in \eqnsref{eq:crosshigh} and (\ref{eq:susceptibility}). The resulting \suscept{} matrix is symmetric with respect to the origin and shows the \suscept{} at \fsum{} in the upper-right and lower-left quadrants and \suscept{} for the differences \fdiff{} in the lower-right and upper-left quadrants\citealp{Voronenko2017} (\figref{model_full}). The vertical and horizontal lines at \foneb{} and \ftwob{} are very pronounced in the upper-right quadrant of \subfigref{model_full}{B} for the nonlinearity at \fsum{} and extend into the lower-right quadrant (representing \fdiff)fading out towards more negative $f_2$ frequencies. \suscept{} values at \fsum{} match the \fsum{} peak seen in \figref{motivation}.
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The second-order susceptibility can also be calculated for the full matrix including negative frequency components of the respective spectra in \eqnsref{eq:crosshigh} and (\ref{eq:susceptibility}). The resulting \suscept{} matrix is symmetric with respect to the origin and shows the \suscept{} at \fsum{} in the upper-right and lower-left quadrants and \suscept{} for the differences \fdiff{} in the lower-right and upper-left quadrants \citealp{Voronenko2017} (\figref{model_full}). The vertical and horizontal lines at \foneb{} and \ftwob{} are very pronounced in the upper-right quadrant of \subfigref{model_full}{B} for the nonlinearity at \fsum{} and extend into the upper-left quadrant (representing \fdiff) fading out towards more negative $f_1$ frequencies. \suscept{} values at \fsum{} match the \fsum{} peak seen in \figref{motivation}.
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The smaller \fdiff{} power spectral peak observed during pure sine-wave stimulation (\subfigrefb{motivation}{D}) can be explained by the fading out vertical line in the lower-right quadrant (\subfigrefb{model_full}{B}, \citealp{Schlungbaum2023}). Even though the second-order susceptibilities were here estimated form data and models with an modulated (EOD) carrier (\figrefb{model_full}) they are in good accordance with the second-order susceptibilities found in LIF models without a carrier\citealp{Voronenko2017, Schlungbaum2023}.
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\notejg{Only show the model?}
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The smaller \fdiff{} power spectral peak observed during pure sine-wave stimulation (\subfigrefb{motivation}{D}) can be explained by the fading out horizontal line in the upper-left quadrant (\subfigrefb{model_full}{B}, \citealp{Schlungbaum2023}). Even though the second-order susceptibilities here were estimated form data and models with an modulated (EOD) carrier (\figrefb{model_full}) they are in good accordance with the second-order susceptibilities found in LIF models without a carrier\citealp{Voronenko2017, Schlungbaum2023}.
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\notejg{Why do we see peaks at the vertical lines in the three fish setting but not in the RAM situation? SNR? Discussion?}
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\begin{figure*}[ht!]
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@ -516,7 +516,7 @@ In a high-CV P-unit we could not find such nonlinear structures, neither in the
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\end{figure*}
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\subsection{Second-order susceptibility can explain nonlinear peaks in pure sinewave stimulation}
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We calculated the second-order susceptibility surfaces at \fsumb{} by extracting the respective spectral component of the P-unit responses to RAM stimuli. How does this relate to the pure sinewave situation that approximates the interference of real animals? The relevant signals are the the beat frequencies \fone{} and \ftwo{} that arise from the interference of the receiving fish's own and either of the foreign EODs \figref{motivation}. The response power spectrum showed peaks from nonlinear interaction at the sum of the two beat frequencies (orange marker, \subfigrefb{motivation}{D}) and at the difference between the two beat frequencies (purple marker, \subfigrefb{motivation}{D}). In the example $\Delta f_{1}$ was similar to \fbase{}, corresponding to the vertical line in the RAM-based second-order susceptibility matrix in \subfigrefb{model_and_data}\,\panel[iii]{B}. In the three-fish example, there was a second, less prominent, nonlinearity at the difference between the two beat frequencies (purple circle, \subfigrefb{motivation}{D}), that cannot be explained with the second-order susceptibility matrix in \subfigrefb{model_and_data}\,\panel[iv]{B}, in which only the nonlinearity at \fsum{} in the response is addressed (\eqnref{eq:crosshigh}).
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We calculated the second-order susceptibility surfaces at \fsumb{} by extracting the respective spectral component of the P-unit responses to RAM stimuli. How does this relate to the pure sinewave situation that approximates the interference of real animals? The relevant signals are the the beat frequencies \fone{} and \ftwo{} that arise from the interference of the receiving fish's own and either of the foreign EODs \figref{motivation}. The response power spectrum showed peaks from nonlinear interaction at the sum of the two beat frequencies (orange marker, \subfigrefb{motivation}{D}) and at the difference between the two beat frequencies (rosa marker, \subfigrefb{motivation}{D}). In the example $\Delta f_{1}$ was similar to \fbase{}, corresponding to the vertical line in the RAM-based second-order susceptibility matrix in \subfigrefb{model_and_data}\,\panel[iii]{B}. In the three-fish example, there was a second, less prominent, nonlinearity at the difference between the two beat frequencies (rosa circle, \subfigrefb{motivation}{D}), that cannot be explained with the second-order susceptibility matrix in \subfigrefb{model_and_data}\,\panel[iv]{B}, in which only the nonlinearity at \fsum{} in the response is addressed (\eqnref{eq:crosshigh}).
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\begin{figure*}[h]
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\includegraphics[width=\columnwidth]{model_full}
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\caption{\label{model_full} Second-order susceptibility of an electrophysiologically recorded P-unit and of the corresponding model (see table~\ref{modelparams} for model parameters of 2012-07-03-ak). White lines -- coordinate axis. The nonlinearity at \fsum{} in the firing rate is quantified in the upper right and lower left quadrants (\eqnref{eq:susceptibility}). The nonlinearity at \fdiff{} in the firing rate is quantified in the upper left and lower right quadrants. Mean baseline firing rate $\fbase{}=120$\,Hz. \figitem{A} Absolute value of the second-order susceptibility of an electrophysiologically recorded P-unit. RAM stimulus realizations $N=11$. Diagonal bands appear when the sum of the frequencies \fsum{} or the difference \fdiff{} is equal to \fbase{}. \figitem{B} Absolute value of the model second-order susceptibility, with $N=1$\,million stimulus realizations and the intrinsic noise split (see methods section \ref{intrinsicsplit_methods}). The diagonals, that were present in \panel{A}, are complemented by vertical and horizontal lines when \fone{} or \ftwo{} are equal to \fbase{}. 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 \panel{B}.}
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@ -9989,7 +9989,7 @@ def plot_arrays_ROC_psd_single3(arrays, arrays_original, spikes_pure, fr, cell,
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rocextra=False, xlim=[0, 100], row=4, subdevision_nr=3, way='absolut', datapoints=1000,
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colors=['grey'], xlim_psd=[0, 235], color0='blue', color0_burst='darkgreen',
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color01='green', ylim_log=(-15, 3), add_burst_corr=False, color02='red',
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array_chosen=1, mean_types=[], color012='orange', color01_2='purple', log='log'):
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array_chosen=1,color012_minus = 'purple', mean_types=[], color012='orange', color01_2='purple', log='log'):
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# mean_type = '_AllTrialsIndex_Min0.25sExcluded_'#'_MeanTrialsIndexPhaseSort_Min0.25sExcluded_'
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# time_array = np.arange(0, len(arrays[0][0]) / 40, 1 / 40)
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@ -10009,7 +10009,7 @@ def plot_arrays_ROC_psd_single3(arrays, arrays_original, spikes_pure, fr, cell,
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key_names = ['base_0', 'control_02', 'control_01', '012']
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names = ['0', '02', '01', '012'] # color012color0, color02, color01,
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colors = ['grey', 'grey', 'grey', 'grey', color0_burst, color0_burst, color0, color0]
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color012_minus = 'purple'
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colors_p = [color0, color02, color01, color012, color02, color01, color012_minus, color0_burst, color0_burst,
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color0, color0]
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