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susceptibility1.pdf
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susceptibility1.tex
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@ -524,7 +524,7 @@ We calculated the second-order susceptibility surfaces at \fsumb{} by extracting
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}.
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}.
\notejg{Why do we see peaks at the vertical lines in the three fish setting but not in the RAM situation? SNR? Discussion?}
\begin{figure*}[ht!]
\includegraphics[width=\columnwidth]{data_overview_mod}
@ -627,8 +627,8 @@ On the other hand in previous literature the encoding of social envelopes was at
%This small percentage of the low-CV cells would be in line with no P-units found in the work.
\subsection{More fish would decrease second-order susceptibility}%
When using noise stimulation strong nonlinearity was demonstrated to appear for small noise stimuli but to decrease for stronger noise stimuli (\figrefb{cells_suscept}). A white noise stimulus is a proxy of many fish being present simultaneously. When the noise amplitude is small, those fish are distant and the nonlinearity is maintained. When the stimulus amplitude increases, many fish close to the receiver are mimicked and a decrease of nonlinear effects can be observed. These findings imply that the nonlinear effects arising in the presence of three fish decline the more fish join. \eigen{} can usually be found in groups of three to four fish \citealp{Tan2005} and \lepto{} in groups of two \citealp{Stamper2010}. Thus the here described second-order susceptibility might still be behaviorally relevant for both species. The decline of nonlinear effects when several fish are present might be adaptive for the receiver, reducing the number of frequencies represented in its primary sensory afferents to a minimum. Such representation would still leave room to create nonlinear effects at later processing steps in higher-order neurons. How nonlinear effects might influence the three-fish setting known as the electrosensory cocktail party (\citealp{Henninger2018}) will be addressed in the next chapter.
When using noise stimulation strong nonlinearity was demonstrated to appear for small noise stimuli but to decrease for stronger noise stimuli (\figrefb{cells_suscept}). A white noise stimulus is a proxy of many fish being present simultaneously. When the noise amplitude is small, those fish are distant and the nonlinearity is maintained. When the stimulus amplitude increases, many fish close to the receiver are mimicked and a decrease of nonlinear effects can be observed. These findings imply that the nonlinear effects arising in the presence of three fish decline the more fish join. \eigen{} can usually be found in groups of three to four fish \citealp{Tan2005} and \lepto{} in groups of two \citealp{Stamper2010}. Thus the here described second-order susceptibility might still be behaviorally relevant for both species. The decline of nonlinear effects when several fish are present might be adaptive for the receiver, reducing the number of frequencies represented in its primary sensory afferents to a minimum. Such representation would still leave room to create nonlinear effects at later processing steps in higher-order neurons. How nonlinear effects might influence the three-fish setting known as the electrosensory cocktail party (\citealp{Henninger2018}) will be addressed in the next chapter.
\notejg{Why do we see peaks at the vertical lines in the three fish setting but not in the RAM situation? SNR? Discussion?}
\subsection{Conclusion} In this work, noise stimulation was confirmed as a method to access the second-order susceptibility in P-unit responses when at least three fish or two beats were present. It was demonstrated that the theory of weakly nonlinear interactions \citealp{Voronenko2017} is valid in P-units where the stimulus is an amplitude modulation of the carrier and not the whole signal. Nonlinear effects were identified in experimentally recorded low-CV cells primary sensory afferents, the P-units and the ampullary cells. P-units share several features with mammalian
auditory nerve fibers and such nonlinear effects might also be expected in the auditory system during the encoding of amplitude modulations \citealp{Joris2004}.