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susceptibility1.tex.bak
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@ -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*}
@ -561,7 +561,7 @@ 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, 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.''}
\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*}
@ -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*}
@ -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*}