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Seriously, no idea. Wild amount of changes. Good luck.

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j-hartling
2026-04-17 17:19:30 +02:00
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main.tex
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@@ -393,7 +393,7 @@ signal~(\bcite{machens2001discrimination}), which likely involves a rectifying
nonlinearity~(\bcite{machens2001representation}). This can be modelled as
full-wave rectification followed by lowpass filtering
\begin{equation}
\env(t)\,=\,|\filt(t)|\,*\,\lp, \qquad \fc\,=\,500\,\text{Hz}
\env(t)\,=\,|\filt(t)|\,*\,\lp, \qquad \fc\,=\,250\,\text{Hz}
\label{eq:env}
\end{equation}
of the tympanal signal $\filt(t)$. Furthermore, the receptors exhibit a
@@ -401,7 +401,7 @@ sigmoidal response curve over logarithmically compressed intensity
levels~(\bcite{suga1960peripheral}; \bcite{gollisch2002energy}). In the model
pathway, logarithmic compression is achieved by conversion to decibel scale
\begin{equation}
\db(t)\,=\,10\,\cdot\,\dec \frac{\env(t)}{\dbref}, \qquad \dbref\,=\,\max\big[\env(t)\big]
\db(t)\,=\,20\,\cdot\,\dec \frac{\env(t)}{\dbref}, \qquad \dbref\,=\,1
\label{eq:log}
\end{equation}
relative to the maximum intensity $\dbref$ of the signal envelope $\env(t)$.
@@ -586,10 +586,17 @@ and a fixed-scale noise component $\noc(t)$. Both $\soc(t)$ and $\noc(t)$ are
assumed to have unit variance. By conversion of $\env(t)$ to decibel
scale~(Eq.\,\ref{eq:log}), $\sca$ turns from a multiplicative scale in linear
space into an additive term, or offset, in logarithmic space
% \begin{equation}
% \begin{split}
% \db(t)\,&=\,\dec \frac{\alpha\,\cdot\,s(t)\,+\,\eta(t)}{\dbref}\\
% &=\,\dec \frac{\alpha}{\dbref}\,+\,\dec \left[s(t)\,+\,\frac{\eta(t)}{\alpha}\right], \qquad \sca\,>\,0
% \end{split}
% \label{eq:toy_log}
% \end{equation}
\begin{equation}
\begin{split}
\db(t)\,&=\,\log \frac{\alpha\,\cdot\,s(t)\,+\,\eta(t)}{\dbref}\\
&=\,\log \frac{\alpha}{\dbref}\,+\,\log \left[s(t)\,+\,\frac{\eta(t)}{\alpha}\right]
\db(t)\,&=\,20\,\cdot\,\dec \left[\,\sca\,\cdot\,s(t)\,+\,\eta(t)\,\right]\\
&=\,20\,\cdot\,\left(\dec \sca\,+\,\dec \left[s(t)\,+\,\frac{\eta(t)}{\sca}\right]\right), \qquad \sca\,>\,0
\end{split}
\label{eq:toy_log}
\end{equation}
@@ -598,9 +605,15 @@ $\noc(t)$ by the inverse of $\sca$. The subsequent
highpass-filtering~(Eq.\,\ref{eq:highpass}) of $\db(t)$ can then be
approximated as a subtraction of the local offset within a suitable time
interval $0 \ll \thp < \frac{1}{\fc}$:
% \begin{equation}
% \begin{split}
% \adapt(t)\,\approx\,\db(t)\,-\,\dec \frac{\sca}{\dbref}\,=\,\dec\left[s(t)\,+\,\frac{\eta(t)}{\sca}\right], \qquad \sca\,>\,0
% \end{split}
% \label{eq:toy_highpass}
% \end{equation}
\begin{equation}
\begin{split}
\adapt(t)\,\approx\,\db(t)\,-\,\log \frac{\alpha}{\dbref}\,=\,\log\left[s(t)\,+\,\frac{\eta(t)}{\alpha}\right]
\adapt(t)\,\approx\,\db(t)\,-\,20\,\cdot\,\dec \sca\,=\,20\,\cdot\,\dec\left[s(t)\,+\,\frac{\eta(t)}{\sca}\right], \qquad \sca\,>\,0
\end{split}
\label{eq:toy_highpass}
\end{equation}
@@ -859,7 +872,7 @@ initiation of one behavior over another is categorical (e.g. approach/stay)
\begin{figure}[!ht]
\centering
\includegraphics[width=\textwidth]{figures/fig_noise_env_sd_conversion.pdf}
\includegraphics[width=\textwidth]{figures/fig_noise_env_sd_conversion_appendix.pdf}
\caption{\textbf{}
}
\label{}
@@ -868,7 +881,16 @@ initiation of one behavior over another is categorical (e.g. approach/stay)
\begin{figure}[!ht]
\centering
\includegraphics[width=\textwidth]{figures/fig_invariance_log-hp_species.pdf}
\includegraphics[width=\textwidth]{figures/fig_invariance_log-hp_appendix.pdf}
\caption{\textbf{}
}
\label{}
\end{figure}
\FloatBarrier
\begin{figure}[!ht]
\centering
\includegraphics[width=\textwidth]{figures/fig_invariance_thresh-lp_appendix.pdf}
\caption{\textbf{}
}
\label{}