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main.tex

@@ -1236,10 +1236,48 @@ guaranteed simply by disabling logarithmic compression.
 
 \subsubsection{Intensity invariance in a naturalistic setting}
 
+% This one appears...meh.
+% Also, subplot "a" is currently not cited.
 So far, the analyses on intensity invariance were based on synthetically
-generated input signals, since these allow for a systematic manipulation of
-the mixture of song component $\soc(t)$ and noise component $\noc(t)$ over
-an arbitrary range of scales $\sca$.
+generated input signals, since these allow for a systematic manipulation of the
+mixture of song component $\soc(t)$ and noise component $\noc(t)$ over an
+arbitrary range of scales $\sca$. Now, the question remains how the model
+pathway performs under more naturalistic conditions. We therefore repeated the
+previous analysis of the full model pathway~(Fig.\,\ref{fig:pipeline_full})
+using field recordings of a song of \textit{P. parallelus} as input $\raw(t)$
+and a segment of background noise from the same recordings as pure-noise
+reference $\raw(t)=\noc(t)$. Recordings were taken simultaneously at eight
+different distances $d$ from the sender, ranging from $10\,$cm to $220\,$cm
+with intervals of $30\,$cm between microphones. The precise values of $\sca$
+that correspond to the different $d$ cannot be determined, but $\sca$ is
+expected to be inversely proportional to $d$ based on the inverse-square law of
+sound propagation. All intensity metrics and ratios thereof were hence plotted
+over $1/d\sim\sca$ on a double-logarithmic scale to resemble the previous
+analyses as closely as possible. One decade on the $1/d$ axis is comparable to
+one decade on the $\sca$ axis, even if direct conversion is not possible. To
+complicate matters, it is also not possible to quantify potential saturation
+points due to the small number of $d$ values, so that one can only refer to the
+slopes of each curve to assess whether one representation is more stable than
+another across $d$. Bearing these limitations in mind, the intensity metrics of
+each representation over $1/d$~(Fig.\,\ref{fig:pipeline_field}b) follow a
+pattern that is consistent with the results of the previous simulation-based
+analysis~(Fig.\,\ref{fig:pipeline_full}b): The standard deviations of
+$\filt(t)$ and $\env(t)$ increase linearly with $1/d$, respectively. The
+standard deviations of $\db(t)$, $\adapt(t)$, and $c_i(t)$ show a weaker
+increase with $1/d$ and appear to approach, but not reach, a saturation regime
+for larger $1/d$. The average feature values $\muf$ of $f_i(t)$ show an even
+weaker increase with $1/d$ and appear to reach a saturation regime for
+$d=40\,$cm and $d=10\,$cm, which is consistent across most $f_i(t)$ in the
+set~(Fig.\,\ref{fig:pipeline_field}c). The saturated $\muf$ are distributed
+over a comparably narrow range of values, which could in parts be a property of
+the songs of \textit{P. parallelus}~(see also
+Fig.\,\ref{fig:thresh-lp_species}bc). The ratios of each intensity metric to
+the respective pure-noise reference value are not aligned across
+representations~(Fig.\,\ref{fig:pipeline_field}d) or
+kernels~(Fig.\,\ref{fig:pipeline_field}ef) but still serve to consolidate the
+previous observation that only $f_i(t)$ appears to reach a saturation regime
+across the available $d$. This implies
+
 
 \begin{figure}[!ht]
     \centering