Syncing to wörk.

main.tex

@@ -1236,31 +1236,30 @@ guaranteed simply by disabling logarithmic compression.
 
 \subsubsection{Intensity invariance in a naturalistic setting}
 
-% This one appears...meh.
-% Also, subplot "a" is currently not cited.
+% This one appears...meh?
 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 $\sca$. 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})
+pathway performs under more naturalistic conditions. The previous analysis of
+the full model pathway~(Fig.\,\ref{fig:pipeline_full}) was hence repeated,
 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
+reference. 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 value of $\sca$ that corresponds to a
+given $d$ cannot be determined in a straightforward manner, 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
+over $1/d$ on a double-logarithmic scale, which is insofar comparable to
+previous analyses that a decade on the $1/d$ axis corresponds to a decade on
+the $\sca$ axis. To complicate matters further, the $1/d$ axis is sampled too
+sparsely to determine saturation points as before based on the $95\,\%$ curve
+span. Instead, one has to rely on the slope of the curve to assess if, and at
+which $1/d$, a given representation reaches a saturation regime. 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
@@ -1268,16 +1267,22 @@ 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
+set~(Fig.\,\ref{fig:pipeline_field}c). Saturation of $f_i(t)$ without
+saturation of $c_i(t)$ suggests that the input $\raw(t)$ at the smallest
+$d=10\,$cm corresponds to a value of $\sca$ between 10 and 20 based on
+comparison with the simulation-based analysis~(Fig.\,\ref{fig:pipeline_full}b).
+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
-
+kernels~(Fig.\,\ref{fig:pipeline_field}ef) but serve to consolidate the
+previous observation that only $f_i(t)$ exhibits some degree of intensity
+invariance within the available range of $1/d$. Based on the current results,
+this intensity invariance of $f_i(t)$ in the field holds up to a distance of
+around $40\,$cm from the sender, decays steadily between $40\,$cm and
+$130\,$cm, and is substantially dimished for larger
+distances~(Fig.\,\ref{fig:pipeline_field}a, bottom row).
 
 \begin{figure}[!ht]
     \centering