Captioned appendix figures.

Polished some figures.
Shortened existing figure captions.

main.tex

@@ -228,6 +228,7 @@ intensity-invariant song representations, the interaction between these
 mechanisms, the overall capacity for intensity invariance in the system, and
 the ethological implications of our findings.
 
+\newpage
 \section{Methods}
 % This maybe does not quite fit here, but it is the most general part of the
 % methods and applies throughout the whole section, so I put it here for now.
@@ -289,8 +290,8 @@ the following sections.
                      representations~(boxes) and transformations~(arrows) along
                      the model pathway. All representations are time-varying.
                      1st half: Preprocessing stage~(one-dimensional
-                     representation). 2nd half: Feature extraction
+                     representations). 2nd half: Feature extraction
-                     stage~(high-dimensional representation). }
+                     stage~(high-dimensional representations). }
     \label{fig:pathway}
 \end{figure}
 
@@ -347,8 +348,8 @@ the following feature extraction stage.
 \begin{figure}[!ht]
     \centering
     \includegraphics[width=\textwidth]{figures/fig_pre_stages.pdf}
-    \caption{\textbf{Representations of a song of \textit{O. rufipes} during
+    \caption{\textbf{Song representations during the preprocessing stage.}
-                     the preprocessing stage.}
+                     Example song of \textit{O. rufipes}.
                      \textbf{a}:~Bandpass filtered tympanal signal $\filt(t)$.
                      \textbf{b}:~Signal envelope $\env(t)$.
                      \textbf{c}:~Logarithmically compressed envelope $\db(t)$.
@@ -483,14 +484,15 @@ or a simple linear classifier.
 \begin{figure}[!ht]
     \centering
     \includegraphics[width=\textwidth]{figures/fig_feat_stages.pdf}
-    \caption{\textbf{Representations of a song of \textit{O. rufipes} during
+    \caption{\textbf{Song representations during the feature extraction stage.}
-                     the feature extraction stage.}
+                     Example song of \textit{O. rufipes}.
                      Different color shades indicate different types of Gabor
-                     kernels with specific lobe number $\kn$ and either $+$ or
+                     kernels with specific lobe number $\kni$ and either $+$ or
-                     $-$ sign, sorted (dark to light) first by increasing $\kn$
+                     $-$ sign, sorted (dark to light) first by increasing
-                     and then by sign~($1\,\leq\,\kn\,\leq\,4$; first $+$, then
+                     $\kni$ and then by sign~($1\,\leq\,\kni\,\leq\,4$; first
-                     $-$ for each $\kn$; two kernel widths $\kw$ of $4\,$ms and
+                     $+$, then $-$ for each $\kni$; two kernel widths $\kwi$ of
-                     $32\,$ms per type; 8 types, 16 kernels in total).
+                     $4\,$ms and $32\,$ms per type; 8 types, 16 kernels in
+                     total).
                      \textbf{a}:~Kernel-specific filter responses $c_i(t)$.
                      \textbf{b}:~Binary responses $b_i(t)$.
                      \textbf{c}:~Finalized features $f_i(t)$.}
@@ -653,12 +655,13 @@ which is a reasonable assumption for the raw $\soc(t)$ and $\noc(t)$. However,
 the dependency of the ratio on $\sca$ is not necessarily the same for
 representations that are transformed from $x(t)$ by nonlinear operations, since
 these change the relationship of $\soc(t)$ and $\noc(t)$ in an unpredictable
-fashion. Furthermore, the ratio is not a proper SNR of the representation
+fashion~(see appendix Fig.\,\ref{fig:app_env-sd}). Furthermore, the ratio is
-because it does not relate $\soc(t)$ to $\noc(t)$ within the representation but
+not a proper SNR of the representation because it does not relate $\soc(t)$ to
-rather the entire representation to $\noc(t)$ alone. However, it still provides
+$\noc(t)$ within the representation but rather the entire representation to
-a useful measure of the relative intensity of a representation with and without
+$\noc(t)$ alone. However, it still provides a useful measure of the relative
-$\soc(t)$, which is the closest we can get to the SNR of the representation. As
+intensity of a representation with and without $\soc(t)$, which is the closest
-such, the ratio of intensity measures is referred to as SNR in the following.
+we can get to the SNR of the representation. As such, the ratio of intensity
+measures is referred to as SNR in the following.
 % Is this legal? "SNR" is much shorter than "ratio of intensity measure to the pure-noise reference measure".
 % Haven't used it much yet, sticked to "ratio" in most cases.
 
@@ -694,9 +697,10 @@ $\thr$ has been specified as a multiple of the pure-noise reference standard
 deviation $\sigma_{c_i}$ for input $x(t)=\noc(t)$. This ensures that $\thr$ as
 well as the resulting $b_i(t)$ and $f_i(t)$ are comparable across different
 $k_i(t)$ because each pure-noise $c_i(t)$ approximately follows a normal
-distribution~(see appendix
+distribution around zero~(see appendix
 Figs.\,\ref{fig:app_thresh-lp_kern-sd}-\ref{fig:app_field_kern-sd}).
 
+\newpage
 \section{Results}
 
 \subsection{Mechanisms driving the emergence of intensity invariance}
@@ -767,25 +771,23 @@ more robust input representation and higher input SNR.
     \includegraphics[width=\textwidth]{figures/fig_invariance_rect_lp.pdf}
 \caption{\textbf{Rectification and lowpass filtering improves SNR
                  but does not contribute to intensity invariance.}
-                 Input $\raw(t)$ consists of song component $\soc(t)$ scaled by
+                 Input $\raw(t)$ consists of $\soc(t)$ scaled by $\sca$ with
-                 $\sca$ with optional noise component $\noc(t)$ and is
+                 optional $\noc(t)$ and is successively transformed into
-                 successively transformed into tympanal signal $\filt(t)$ and
+                 tympanal signal $\filt(t)$ and envelope $\env(t)$.
-                 envelope $\env(t)$. Different line styles indicate different
+                 \textbf{Top}:~Examples of $\filt(t)$ and $\env(t)$ for
-                 cutoff frequencies $\fc$ of the lowpass filter extracting
+                 different $\sca$.
-                 $\env(t)$.
-                 \textbf{Top}:~Example representations of $\filt(t)$ and
-                 $\env(t)$ for different $\sca$.
                  \textbf{a}:~Noiseless case.
                  \textbf{b}:~Noisy case.
-                 \textbf{Bottom}:~Intensity measures over a range of $\sca$.
+                 \textbf{Bottom}:~Intensity measures over $\sca$. Different
-                 \textbf{c}:~Noiseless case: Standard deviations $\sigma_x$ of
+                 line styles indicate different cutoff frequencies $\fc$ of the
-                 $\filt(t)$ and $\env(t)$.
+                 lowpass filter extracting $\env(t)$.
-                 \textbf{d}:~Noisy case: Ratios of $\sigma_x$ of $\filt(t)$ and
+                 \textbf{c}:~Noiseless case: Standard deviation $\sigma_x$ of
-                 $\env(t)$ to the respective reference standard deviation
+                 $\filt(t)$ and $\env(t)$, respectively.
-                 $\sigma_{\eta}$ for input $\raw(t)=\noc(t)$.
+                 \textbf{d}:~Noisy case: Ratio of $\sigma_x$ to the respective
-                 \textbf{e}:~Ratios of $\sigma_x$ to $\sigma_{\eta}$ of
+                 pure-noise reference $\sigma_{\eta}$ for $\sca=0$.
+                 \textbf{e}:~Ratio of $\sigma_x$ to $\sigma_{\eta}$ of
                  $\env(t)$ as in \textbf{d} for different species (averaged
-                 over songs and recordings, see appendix
+                 over songs and recordings, appendix
                  Fig.\,\ref{fig:app_rect-lp}).
                 }
     \label{fig:rect-lp}
@@ -907,28 +909,26 @@ is a recurring phenomenon that is further addressed in the following sections.
     \caption{\textbf{Intensity invariance through logarithmic compression and
                      adaptation is restricted by the noise floor and decreases
                      SNR.}
-                     Input $\filt(t)$ consists of song component $\soc(t)$
+                     Input $\filt(t)$ consists of $\soc(t)$
-                     scaled by $\sca$ with optional noise component $\noc(t)$
+                     scaled by $\sca$ with optional $\noc(t)$
                      and is successively transformed into envelope $\env(t)$,
                      logarithmically compressed envelope $\db(t)$, and
                      intensity-adapted envelope $\adapt(t)$.
-                     \textbf{Top}:~Example representations of $\env(t)$,
+                     \textbf{Top}:~Examples of $\env(t)$, $\db(t)$, and
-                     $\db(t)$, and $\adapt(t)$ for different $\sca$.
+                     $\adapt(t)$ for different $\sca$.
                      \textbf{a}:~Noiseless case.
                      \textbf{b}:~Noisy case.
-                     \textbf{Bottom}:~Intensity measures over a range of $\sca$.
+                     \textbf{Bottom}:~Intensity measures over $\sca$.
-                     \textbf{c}:~Noiseless case: Standard deviations $\sigma_x$
+                     \textbf{c}:~Noiseless case: Standard deviation $\sigma_x$
-                     of $\env(t)$, $\db(t)$, and $\adapt(t)$.
+                     of $\env(t)$, $\db(t)$, and $\adapt(t)$, respectively.
-                     \textbf{d}:~Noisy case: Ratios of $\sigma_x$ of $\env(t)$,
+                     \textbf{d}:~Noisy case: Ratio of $\sigma_x$ to the
-                     $\db(t)$, and $\adapt(t)$ to the respective reference
+                     respective pure-noise reference $\sigma_{\eta}$ for
-                     standard deviation $\sigma_{\eta}$ for input
+                     $\sca=0$. Shaded areas indicate $5\,\%$ (dark grey) and
-                     $\filt(t)=\noc(t)$. Shaded areas indicate $5\,\%$ (dark
+                     $95\,\%$ (light grey) curve span for $\adapt(t)$.
-                     grey) and $95\,\%$ (light grey) curve span for
+                     \textbf{e}:~Ratio of $\sigma_x$ to $\sigma_{\eta}$ of
-                     $\adapt(t)$.
-                     \textbf{e}:~Ratios of $\sigma_x$ to $\sigma_{\eta}$ of
                      $\adapt(t)$ as in \textbf{d} for different species
-                     (averaged over songs and recordings, see appendix
+                     (averaged over songs and recordings, appendix
-                     Fig\,\ref{fig:app_log-hp_curves}). Dots indicate $95\,\%$
+                     Fig.\,\ref{fig:app_log-hp_curves}). Dots indicate $95\,\%$
                      curve span per species.
                      }
     \label{fig:log-hp}
@@ -1043,33 +1043,32 @@ intensity invariance are further explored in a later section.
     \caption{\textbf{Intensity invariance through thresholding and temporal
                      averaging is mediated by the interaction of threshold
                      value and noise floor.}
-                     Input $\adapt(t)$ consists of song component $\soc(t)$
+                     Input $\adapt(t)$ consists $\soc(t)$ scaled by $\sca$ with
-                     scaled by $\sca$ with optional noise component $\noc(t)$
+                     optional $\noc(t)$ and is transformed into single kernel
-                     and is transformed into single kernel response $c(t)$,
+                     response $c(t)$, binary response $b(t)$, and feature
-                     binary response $b(t)$, and feature $f(t)$. Different
+                     $f(t)$. Different color shades indicate different
-                     color shades indicate different threshold values $\Theta$
+                     threshold values $\Theta$ (multiples of pure-noise
-                     (multiples of reference standard deviation $\sigma_{\eta}$
+                     standard deviation $\sigma_{\eta}$ of $c(t)$ for $\sca=0$,
-                     of $c(t)$ for input $\adapt(t)=\noc(t)$, with darker
+                     with darker colors for higher $\Theta$. See also appendix
-                     colors for higher $\Theta$).
+                     Fig.\,\ref{fig:app_thresh-lp_kern-sd}).
-                     \textbf{Left}:~Noisy case: Example representations of
+                     \textbf{Left}:~Noisy case: Examples of $\adapt(t)$ as well
-                     $\adapt(t)$ as well as $c(t)$, $b(t)$, and $f(t)$ for
+                     as $c(t)$, $b(t)$, and $f(t)$ for different $\sca$.
-                     different $\sca$.
                      \textbf{a}:~$\adapt(t)$ with kernel $k(t)$ in black.
                      \textbf{b\,-\,d}: $c(t)$, $b(t)$, and $f(t)$ based on the
-                     same $\adapt(t)$ from \textbf{a} but with different
+                     same $\adapt(t)$ from \textbf{a} but for different
                      $\Theta$.
                      \textbf{Right}:~Average value $\mu_f$ of $f(t)$ for each
                      $\Theta$ from \textbf{b\,-\,d}. Dots indicate $95\,\%$
                      curve span (noisy case).
-                     \textbf{e}:~$\mu_f$ over a range of $\sca$, once for the
+                     \textbf{e}:~$\mu_f$ over $\sca$, once for the noisy case
-                     noisy case (solid lines) and once for the noiseless case
+                     (solid lines) and once for the noiseless case (dotted
-                     (dotted lines).
+                     lines).
-                     \textbf{f}:~Noisy case: $\mu_f$ over the standard
+                     \textbf{f}:~Noisy case: $\mu_f$ over standard deviation
-                     deviation of input $\adapt$ corresponding to the values of
+                     $\sigma_{\text{adapt}}$ of input $\adapt$ corresponding to
-                     $\sca$ shown in \textbf{e}. Shaded area indicates standard
+                     $\sca$ shown in \textbf{e}. Shaded area indicates values
-                     deviations that would be capped in the output $\adapt(t)$
+                     of $\sigma_{\text{adapt}}$ that are capped in the output
-                     of the previous transformation pair (see
+                     $\adapt(t)$ of the previous transformation pair
-                     Fig.\,\ref{fig:log-hp}cd).
+                     (Fig.\,\ref{fig:log-hp}cd).
                      }
     \label{fig:thresh-lp_single}
 \end{figure}
@@ -1148,29 +1147,29 @@ point of $f_i(t)$ less relevant.
                      saturates at different points in feature space.}
                      Same input and processing as in
                      Fig.\,\ref{fig:thresh-lp_single} but with three different
-                     kernels $k_i$, each with a single kernel-specific
+                     kernels $k_i$ and a single kernel-specific threshold value
-                     threshold value $\thr=0.5\cdot\sigma_{\eta_i}$.
+                     $\thr=0.5\cdot\sigma_{\eta_i}$ (appendix
+                     Fig.\,\ref{fig:app_thresh-lp_kern-sd}).
                      \textbf{a}:~Examples of species-specific grasshopper
                      songs.
-                     \textbf{Middle}:~Average value $\mu_{f_i}$ of each feature
+                     \textbf{Middle}:~Average value $\muf$ of each feature
                      $f_i(t)$ over $\sca$ per species (averaged over songs and
-                     recordings, see appendix
+                     recordings, appendix Figs.\,\ref{fig:app_thresh-lp_pure}
-                     Figs.\,\ref{fig:app_thresh-lp_pure} and
+                     and \ref{fig:app_thresh-lp_noise}). Different color shades
-                     \ref{fig:app_thresh-lp_noise}). Different color shades
+                     indicate different $k_i$. Dots indicate $95\,\%$ curve
-                     indicate different kernels $k_i$. Dots indicate $95\,\%$
+                     span per $k_i$.
-                     curve span per $k_i$.
                      \textbf{b}:~Noiseless case.
                      \textbf{c}:~Noisy case.
                      \textbf{Bottom}:~2D feature spaces spanned by each pair of
                      $f_i(t)$. Each trajectory corresponds to a
-                     species-specific combination of $\mu_{f_i}$ that develops
+                     species-specific combination of $\muf$ that develops
                      with $\sca$ (colorbars). Horizontal dashes in the colorbar
                      indicate $5\,\%$ (dark grey) and $95\,\%$ (light grey)
-                     curve span of the norm across all three $\mu_{f_i}$ per
+                     curve span of the norm across all three $\muf$ per
                      species.
                      \textbf{d}:~Noiseless case.
                      \textbf{e}:~Noisy case. Shaded areas indicate the average
-                     minimum $\mu_{f_i}$ across all species-specific trajectories.
+                     minimum $\muf$ across all species-specific trajectories.
                      }
     \label{fig:thresh-lp_species}
 \end{figure}
@@ -1255,34 +1254,34 @@ in principle, work together towards an intensity-invariant song representation.
     \includegraphics[width=\textwidth]{figures/fig_invariance_full_Omocestus_rufipes.pdf}
     \caption{\textbf{Step-wise emergence of intensity-invariant song
                      representations along the model pathway.}
-                     Input $\raw(t)$ consists of song component $\soc(t)$
+                     Input $\raw(t)$ consists of $\soc(t)$ scaled by $\sca$
-                     scaled by $\sca$ with added noise component $\noc(t)$ and
+                     with added $\noc(t)$ and is processed up to the feature
-                     is processed up to the feature set $f_i(t)$. Different
+                     set $f_i(t)$ using kernel-specific threshold values
-                     color shades indicate different types of Gabor kernels
+                     $\thr=2\cdot\sigma_{\eta_i}$ (appendix
-                     with specific lobe number $\kn$ and either $+$ or $-$
+                     Fig.\,\ref{fig:app_full_kern-sd}). Different color shades
-                     sign, sorted (dark to light) first by increasing $\kn$ and
+                     indicate different types of Gabor kernels with specific
-                     then by sign~($1\,\leq\,\kn\,\leq\,4$; first $+$, then $-$
+                     lobe number $\kn$ and either $+$ or $-$ sign, sorted (dark
-                     for each $\kn$; five kernel widths $\kw$ of 1, 2, 4, 8,
+                     to light) first by increasing $\kn$ and then by
-                     and $16\,$ms per type; 8 types, 40 kernels in total).
+                     sign~($1\,\leq\,\kn\,\leq\,4$; first $+$, then $-$ for
-                     \textbf{a}:~Example representations of $\filt(t)$,
+                     each $\kn$; five kernel widths $\kw$ of 1, 2, 4, 8, and
-                     $\env(t)$, $\db(t)$, $\adapt(t)$, $c_i(t)$, and $f_i(t)$
+                     $16\,$ms per type; 8 types, 40 $k_i(t)$ in total).
-                     for different $\sca$.
+                     \textbf{a}:~Examples of $\filt(t)$, $\env(t)$, $\db(t)$,
-                     \textbf{b}:~Intensity measures over $\sca$. For $c_i(t)$
+                     $\adapt(t)$, $c_i(t)$, and $f_i(t)$ for different $\sca$.
-                     and $f_i(t)$, the median over kernels is shown. Dots
+                     \textbf{b}:~Intensity measures over $\sca$. The median
+                     over $k_i(t)$ is shown for $c_i(t)$ and $f_i(t)$. Dots
                      indicate $95\,\%$ curve span for $\db(t)$, $\adapt(t)$,
                      $c_i(t)$, and $f_i(t)$.
-                     \textbf{c}:~Average value $\mu_{f_i}$ of each feature
+                     \textbf{c}:~Average value $\muf$ of each $f_i(t)$
-                     $f_i(t)$ over $\sca$.
+                     over $\sca$.
-                     \textbf{d}:~Ratios of intensity measures to the respective
+                     \textbf{d}:~Ratio of intensity measures from \textbf{b} to
-                     reference value for input $\raw(t)=\noc(t)$. For $c_i(t)$
+                     the respective pure-noise reference for $\sca=0$.
-                     and $f_i(t)$, the median over kernel-specific ratios is
+                     \textbf{e}:~Ratio of standard deviation $\sigma_{c_i}$ of
-                     shown.
-                     \textbf{e}:~Ratios of standard deviation $\sigma_{c_i}$ of
                      each $c_i(t)$.
-                     \textbf{f}:~Ratios of $\mu_{f_i}$.
+                     \textbf{f}:~Ratio of $\muf$.
                      \textbf{g}:~Distributions of kernel-specific $\sca$ that
                      correspond to $95\,\%$ curve span for $c_i(t)$ and
-                     $f_i(t)$. Dots indicate the values from \textbf{b}.
+                     $f_i(t)$. Dots indicate values based on the median from
+                     \textbf{b}.
                      }
     \label{fig:pipeline_full}
 \end{figure}
@@ -1337,32 +1336,24 @@ guaranteed simply by disabling logarithmic compression.
     \includegraphics[width=\textwidth]{figures/fig_invariance_short_Omocestus_rufipes.pdf}
     \caption{\textbf{Effects of disabling logarithmic compression on intensity
                      invariance along the model pathway.}
-                     Input $\raw(t)$ consists of song component $\soc(t)$
+                     Same input and processing as in
-                     scaled by $\sca$ with added noise component $\noc(t)$ and
+                     Fig.\,\ref{fig:pipeline_full}, using kernel-specific
-                     is processed up to the feature set $f_i(t)$, skipping
+                     threshold values $\thr=2\cdot\sigma_{\eta_i}$ (appendix
-                     $\db(t)$. Different color shades indicate different types
+                     Fig.\,\ref{fig:app_short_kern-sd}), except that
-                     of Gabor kernels with specific lobe number $\kn$ and
+                     logarithmic compression and hence $\db(t)$ are skipped.
-                     either $+$ or $-$ sign, sorted (dark to light) first by
+                     \textbf{a}:~Examples of $\filt(t)$, $\env(t)$,
-                     increasing $\kn$ and then by
+                     $\adapt(t)$, $c_i(t)$, and $f_i(t)$ for different $\sca$.
-                     sign~($1\,\leq\,\kn\,\leq\,4$; first $+$, then $-$ for
+                     \textbf{b}:~Intensity measures over $\sca$. The median
-                     each $\kn$; five kernel widths $\kw$ of 1, 2, 4, 8, and
+                     over $k_i(t)$ is shown for $c_i(t)$ and $f_i(t)$. Dot
-                     $16\,$ms per type; 8 types, 40 kernels in total).
+                     indicates $95\,\%$ curve span for $f_i(t)$.
-                     \textbf{a}:~Example representations of $\filt(t)$,
+                     \textbf{c}:~Average value $\muf$ of each $f_i(t)$
-                     $\env(t)$, $\adapt(t)$, $c_i(t)$, and $f_i(t)$ for
+                     over $\sca$.
-                     different $\sca$.
+                     \textbf{d}:~Ratio of intensity measures from \textbf{b} to
-                     \textbf{b}:~Intensity measures over $\sca$. For $c_i(t)$
+                     the respective pure-noise reference for $\sca=0$.
-                     and $f_i(t)$, the median over kernels is shown. Dots
+                     \textbf{e}:~Ratio of $\muf$.
-                     indicate $95\,\%$ curve span for $f_i(t)$.
-                     \textbf{c}:~Average value $\mu_{f_i}$ of each feature
-                     $f_i(t)$ over $\sca$.
-                     \textbf{d}:~Ratios of intensity measures to the respective
-                     reference value for input $\raw(t)=\noc(t)$. For $c_i(t)$
-                     and $f_i(t)$, the median over kernel-specific ratios is
-                     shown.
-                     \textbf{e}:~Ratios of $\mu_{f_i}$.
                      \textbf{f}:~Distribution of kernel-specific $\sca$ that
-                     correspond to $95\,\%$ curve span for $f_i(t)$. Dots
+                     correspond to $95\,\%$ curve span for $f_i(t)$. Dot
-                     indicate the value from \textbf{b}.
+                     indicates value based on the median from \textbf{b}.
                      }
     \label{fig:pipeline_short}
 \end{figure}
@@ -1426,26 +1417,27 @@ distances~(Fig.\,\ref{fig:pipeline_field}a, bottom row).
                      Input $\raw(t)$ consists of a song of \textit{P.
                      parallelus} recorded in the field at eight different
                      distances $d$ and is processed up to the feature set
-                     $f_i(t)$. Different color shades indicate different types
+                     $f_i(t)$ using kernel-specific threshold values
-                     of Gabor kernels with specific lobe number $\kn$ and
+                     $\thr=2\cdot\sigma_{\eta_i}$ (appendix
-                     either $+$ or $-$ sign, sorted (dark to light) first by
+                     Fig.\,\ref{fig:app_field_kern-sd}). Different color shades
-                     increasing $\kn$ and then by
+                     indicate different types of Gabor kernels with specific
+                     lobe number $\kn$ and either $+$ or $-$ sign, sorted (dark
+                     to light) first by increasing $\kn$ and then by
                      sign~($1\,\leq\,\kn\,\leq\,4$; first $+$, then $-$ for
                      each $\kn$; five kernel widths $\kw$ of 1, 2, 4, 8, and
-                     $16\,$ms per type; 8 types, 40 kernels in total).
+                     $16\,$ms per type; 8 types, 40 $k_i(t)$ in total).
                      \textbf{a}:~$\filt(t)$, $\env(t)$, $\db(t)$, $\adapt(t)$,
                      $c_i(t)$, and $f_i(t)$ at each $d$. A noise segment from
                      the same recording is shown for reference.
-                     \textbf{b}:~Intensity measures over $d$. For $c_i(t)$
+                     \textbf{b}:~Intensity measures over $d$. The median over
-                     and $f_i(t)$, the median over kernels is shown.
+                     $k_i(t)$ is shown for $c_i(t)$ and $f_i(t)$.
-                     \textbf{c}:~Average value $\mu_{f_i}$ of each feature
+                     \textbf{c}:~Average value $\muf$ of each $f_i(t)$ over
-                     $f_i(t)$ over $d$.
+                     $d$.
-                     \textbf{d}:~Ratios of intensity measures to the respective
+                     \textbf{d}:~Ratio of intensity measures from \textbf{b} to
-                     value obtained from the noise reference. For $c_i(t)$ and
+                     the respective value obtained from the noise reference.
-                     $f_i(t)$, the median over kernel-specific ratios is shown.
+                     \textbf{e}:~Ratio of standard deviation $\sigma_{c_i}$ of
-                     \textbf{e}:~Ratios of standard deviation $\sigma_{c_i}$ of
                      each $c_i(t)$.
-                     \textbf{f}:~Ratios of $\mu_{f_i}$.
+                     \textbf{f}:~Ratios of $\muf$.
                      }
     \label{fig:pipeline_field}
 \end{figure}
@@ -1470,8 +1462,8 @@ song, so that each dot within a subplot corresponds to a single feature
 $f_i(t)$. For the intraspecific
 comparisons~(Fig.\,\ref{fig:feat_cross_species}, upper triangular), the pairs
 of $\muf$ are distributed closely around the diagonal, with a minimum
-correlation coefficient of $\rho=0.85$, a maximum of $\rho=0.99$, and a median
+correlation coefficient of $\rho=0.82$, a maximum of $\rho=0.99$, and a median
-of $\rho=0.92$. A given $f_i(t)$ thus tends to have a similar $\muf$ across
+of $\rho=0.91$. A given $f_i(t)$ thus tends to have a similar $\muf$ across
 different songs of the same species. In contrast, the pairs of $\muf$ for the
 interspecific comparisons~(Fig.\,\ref{fig:feat_cross_species}, lower
 triangular) are distributed in a variety of different ways, most in broader
@@ -1479,7 +1471,7 @@ clouds (e.g. \textit{C. biguttulus} vs. \textit{C. mollis}) but some more
 narrowly around the diagonal (e.g. \textit{P. parallelus} vs. \textit{C.
 dispar}). The correlation coefficients $\rho$ vary widely between different
 interspecific comparisons, with a minimum of $\rho=-0.1$, a maximum of
-$\rho=0.92$, and a median of $\rho=0.53$. A given $f_i(t)$ therefore tends to
+$\rho=0.91$, and a median of $\rho=0.40$. A given $f_i(t)$ therefore tends to
 have a less similar $\muf$ across different species than within the same
 species, although certain exeptions exist~(Fig.\,\ref{fig:feat_cross_species},
 lower right). Accordingly, the feature representation that is generated by the
@@ -1498,18 +1490,17 @@ natural song variation.
     \centering
     \includegraphics[width=\textwidth]{figures/fig_features_cross_species.pdf}
     \caption{\textbf{Interspecific and intraspecific feature variability.}
-                     Average value $\mu_{f_i}$ of each feature $f_i(t)$ against
+                     Average value $\muf$ of each feature $f_i(t)$ against its
-                     its counterpart from a 2nd feature set based on a
+                     counterpart from a 2nd feature set based on a different
-                     different input $\raw(t)$. Each dot within a subplot
+                     input $\raw(t)$. Data is based on the saturated $\muf$
-                     represents a single feature $f_i(t)$. Different color
+                     from Fig.\,\ref{fig:pipeline_full}. Each dot within a
+                     subplot represents a single $f_i(t)$. Different color
                      shades indicate different types of Gabor kernels with
                      specific lobe number $\kn$ and either $+$ or $-$ sign,
                      sorted (dark to light) first by increasing $\kn$ and then
                      by sign~($1\,\leq\,\kn\,\leq\,4$; first $+$, then $-$ for
                      each $\kn$; five kernel widths $\kw$ of 1, 2, 4, 8, and
-                     $16\,$ms per type; 8 types, 40 kernels in total). Data is
+                     $16\,$ms per type; 8 types, 40 kernels in total).
-                     based on the analysis underlying
-                     Fig\,\ref{fig:pipeline_full}.
                      \textbf{Lower triangular}:~Interspecific comparisons
                      between single songs of different species.
                      \textbf{Upper triangular}:~Intraspecific comparisons
@@ -1524,7 +1515,8 @@ natural song variation.
 \end{figure}
 \FloatBarrier
 
-\section{Conclusions \& outlook}
+\newpage
+\section{Discussion}
 
 % RIPPED FROM INTRODUCTION:
 
@@ -1677,105 +1669,189 @@ $\rightarrow$ Graded again but highly decorrelated from the acoustic stimulus\\
 $\rightarrow$ Parameters of a behavioral response may be graded (e.g. approach speed),
 initiation of one behavior over another is categorical (e.g. approach/stay)
 
+\newpage
+\section{Appendix}
 
+% Not sure if we really need this one. Might raise more questions than it
+% provides answers. The noise component is not stable throughout nonlinear
+% transformations, that is all the reader needs to know, i believe.
 \begin{figure}[!ht]
     \centering
     \includegraphics[width=\textwidth]{figures/fig_noise_env_sd_conversion_appendix.pdf}
-    \caption{\textbf{}
+    \caption{\textbf{Conversion of the noise component by envelope extraction.}
-                     }
+                     Standard deviation $\sigma_{\eta}$ of noise component
+                     $\noc(t)$ within the signal envelope $\env(t)$ over scale
+                     $\sca$. Based on input $\raw(t)$ with $\sigma_{\eta}=1$
+                     (corresponding to the analysis underlying
+                     Fig.\,\ref{fig:rect-lp}), using 100 realizations of
+                     $\noc(t)$.}
     \label{fig:app_env-sd}
-\end{figure}
+\end{figure}% Referenced.
 \FloatBarrier
 
 \begin{figure}[!ht]
     \centering
     \includegraphics[width=\textwidth]{figures/fig_invariance_rect-lp_appendix.pdf}
-    \caption{\textbf{}
+    \caption{\textbf{Species-specific data underlying Fig.\,\ref{fig:rect-lp}e.}
-                     }
+                     Ratio of the standard deviation $\sigma_{\text{env}}$ to
+                     the pure-noise reference $\sigma_{\eta}$ of the signal
+                     envelope $\env(t)$ over scale $\sca$ for different cutoff
+                     frequencies $\fc$ of the lowpass filter extracting
+                     $\env(t)$. Solid lines and shaded areas indicate mean
+                     $\pm$ standard deviation across songs per recording.
+                     Dashed lines indicate mean across recordings (shown in
+                     Fig.\,\ref{fig:rect-lp}e).}
     \label{fig:app_rect-lp}
-\end{figure}
+\end{figure}% Referenced.
 \FloatBarrier
 
 \begin{figure}[!ht]
     \centering
     \includegraphics[width=\textwidth]{figures/fig_invariance_log-hp_appendix.pdf}
-    \caption{\textbf{}
+    \caption{\textbf{Species-specific data underlying Fig.\,\ref{fig:log-hp}e.}
-                     }
+                     Ratio of the standard deviation $\sigma_{\text{adapt}}$ to
+                     the pure-noise reference $\sigma_{\eta}$ of the
+                     intensity-adapted envelope $\adapt(t)$ over scale $\sca$.
+                     Solid lines and shaded areas indicate mean $\pm$ standard
+                     deviation across songs per recording. Dashed lines
+                     indicate mean across recordings (shown in
+                     Fig.\,\ref{fig:log-hp}e).}
     \label{fig:app_log-hp_curves}
-\end{figure}
+\end{figure}% Referenced.
 \FloatBarrier
 
 \begin{figure}[!ht]
    \centering
    \includegraphics[width=\textwidth]{figures/fig_saturation_log-hp_appendix.pdf}
-   \caption{\textbf{}
+   \caption{\textbf{Species-specific saturation points underlying
-                    }
+                    Fig.\,\ref{fig:log-hp}e.}
+                    Distribution of saturation points ($95\,\%$ curve span) of
+                    ratio $\sigma_{\text{adapt}} / \sigma_{\eta}$ of the
+                    intensity-adapted envelope $\adapt(t)$ over scale $\sca$
+                    across all available songs. Dots indicate the saturation
+                    point of the mean curve across songs and recordings (shown
+                    in Fig.\,\ref{fig:log-hp}e, see also appendix
+                    Fig.\,\ref{fig:app_log-hp_curves}).}
    \label{fig:app_log-hp_saturation}
-\end{figure}
+\end{figure}% Referenced.
 \FloatBarrier
 
 \begin{figure}[!ht]
     \centering
     \includegraphics[width=\textwidth]{figures/fig_invariance_thresh-lp_pure_appendix.pdf}
-    \caption{\textbf{}
+    \caption{\textbf{Species-specific data underlying Fig.\,\ref{fig:thresh-lp_species}bd.}
-                     }
+                     Average value $\muf$ of each of the three features
+                     $f_i(t)$ over scale $\sca$ in the noiseless case. Solid
+                     lines and shaded areas indicate mean $\pm$ standard
+                     deviation across songs per recording. Dashed lines
+                     indicate mean across recordings (shown in
+                     Fig.\,\ref{fig:thresh-lp_species}bd).}
     \label{fig:app_thresh-lp_pure}
-\end{figure}
+\end{figure}% Referenced.
 \FloatBarrier
 
 \begin{figure}[!ht]
     \centering
     \includegraphics[width=\textwidth]{figures/fig_invariance_thresh-lp_noise_appendix.pdf}
-    \caption{\textbf{}
+    \caption{\textbf{Species-specific data underlying Fig.\,\ref{fig:thresh-lp_species}ce.}
-                     }
+                     Average value $\muf$ of each of the three features
+                     $f_i(t)$ over scale $\sca$ in the noisy case. Solid lines
+                     and shaded areas indicate mean $\pm$ standard deviation
+                     across songs per recording. Dashed lines indicate mean
+                     across recordings (shown in
+                     Fig.\,\ref{fig:thresh-lp_species}ce).}
     \label{fig:app_thresh-lp_noise}
-\end{figure}
+\end{figure}% Referenced.
 \FloatBarrier
 
 \begin{figure}[!ht]
     \centering
     \includegraphics[width=\textwidth]{figures/fig_kernel_sd_perc_thresh_lp_appendix.pdf}
-    \caption{\textbf{}
+    \caption{\textbf{Relation between threshold value and pure-noise feature
+                     value for Fig.\,\ref{fig:thresh-lp_single} and
+                     Fig.\,\ref{fig:thresh-lp_species}.}
+                     Proportion of pure-noise kernel response $c_i(t)$ that
+                     exceeds threshold value $\thr$ --- which determines the
+                     average value $\muf$ of feature $f_i(t)$ --- over $\thr$
+                     in multiples of standard deviation $\sigma_{c_i}$.
+                     Corresponds to a "reverse" cumulative distribution
+                     function of $c_i(t)$. Black solid lines indicate rCDF per
+                     kernel $k_i(t)$. Red dashed line indicates rCDF for a
+                     normal distribution with $\mu=0$ and $\sigma=1$.
                      }
     \label{fig:app_thresh-lp_kern-sd}
-\end{figure}
+\end{figure}% Referenced.
 \FloatBarrier
 
 \begin{figure}[!ht]
     \centering
     \includegraphics[width=\textwidth]{figures/fig_kernel_sd_perc_full_appendix.pdf}
-    \caption{\textbf{}
+    \caption{\textbf{Relation between threshold value and pure-noise feature
+                     value for Fig.\,\ref{fig:pipeline_full}.}
+                     Proportion of pure-noise kernel response $c_i(t)$ that
+                     exceeds threshold value $\thr$ --- which determines the
+                     average value $\muf$ of feature $f_i(t)$ --- over $\thr$
+                     in multiples of standard deviation $\sigma_{c_i}$.
+                     Corresponds to a "reverse" cumulative distribution
+                     function of $c_i(t)$. Black solid lines indicate rCDF per
+                     kernel $k_i(t)$. Red dashed line indicates rCDF for a
+                     normal distribution with $\mu=0$ and $\sigma=1$.
                      }
     \label{fig:app_full_kern-sd}
-\end{figure}
+\end{figure}% Referenced.
 \FloatBarrier
 
 \begin{figure}[!ht]
     \centering
     \includegraphics[width=\textwidth]{figures/fig_kernel_sd_perc_short_appendix.pdf}
-    \caption{\textbf{}
+    \caption{\textbf{Relation between threshold value and pure-noise feature
+                     value for Fig.\,\ref{fig:pipeline_short}.}
+                     Proportion of pure-noise kernel response $c_i(t)$ that
+                     exceeds threshold value $\thr$ --- which determines the
+                     average value $\muf$ of feature $f_i(t)$ --- over $\thr$
+                     in multiples of standard deviation $\sigma_{c_i}$.
+                     Corresponds to a "reverse" cumulative distribution
+                     function of $c_i(t)$. Black solid lines indicate rCDF per
+                     kernel $k_i(t)$. Red dashed line indicates rCDF for a
+                     normal distribution with $\mu=0$ and $\sigma=1$.
                      }
     \label{fig:app_short_kern-sd}
-\end{figure}
+\end{figure}% Referenced.
 \FloatBarrier
 
 \begin{figure}[!ht]
     \centering
     \includegraphics[width=\textwidth]{figures/fig_kernel_sd_perc_field_appendix.pdf}
-    \caption{\textbf{}
+    \caption{\textbf{Relation between threshold value and pure-noise feature
+                     value for Fig.\,\ref{fig:pipeline_field}.}
+                     Proportion of pure-noise kernel response $c_i(t)$ that
+                     exceeds threshold value $\thr$ --- which determines the
+                     average value $\muf$ of feature $f_i(t)$ --- over $\thr$
+                     in multiples of standard deviation $\sigma_{c_i}$.
+                     Corresponds to a "reverse" cumulative distribution
+                     function of $c_i(t)$. Black solid lines indicate rCDF per
+                     kernel $k_i(t)$. Red dashed line indicates rCDF for a
+                     normal distribution with $\mu=0$ and $\sigma=1$.
                      }
     \label{fig:app_field_kern-sd}
-\end{figure}
+\end{figure}% Referenced.
 \FloatBarrier
 
-
 \begin{figure}[!ht]
     \centering
     \includegraphics[width=\textwidth]{figures/fig_invariance_cross_species_thresh_appendix.pdf}
-    \caption{\textbf{}
+    \caption{\textbf{Threshold-dependent intensity invariance of
+                     species-specific feature sets.}
+                     Same input and processing as in
+                     Fig.\,\ref{fig:pipeline_full}, using different
+                     kernel-specific threshold values $\thr$ (multiples of
+                     pure-noise standard deviation $\sigma_{\eta_i}$ of
+                     $c_i(t)$ for $\sca=0$. See also appendix
+                     Fig.\,\ref{fig:app_full_kern-sd}). Average value $\muf$ of
+                     each feature $f_i(t)$ over $\sca$.
                      }
     \label{fig:app_cross_species_thresh}
-\end{figure}
+\end{figure}% Reference this one!
 \FloatBarrier
 
 \end{document}

python/fig_env_sd_conversion_appendix.py

@@ -1,7 +1,7 @@
 import plotstyle_plt
 import numpy as np
 import matplotlib.pyplot as plt
-from plot_functions import xlabel, ylabel, strip_zeros, letter_subplots
+from plot_functions import xlabel, ylabel
 
 # GENERAL SETTINGS:
 data_path = '../data/inv/noise_env/sd_conversion.npz'
@@ -10,16 +10,14 @@ save_path = '../figures/fig_noise_env_sd_conversion_appendix.pdf'
 # PLOT SETTINGS:
 fig_kwargs = dict(
     figsize=(32/2.54, 16/2.54),
-    nrows=2,
+    nrows=1,
     ncols=1,
-    sharex=True,
-    sharey=True,
     gridspec_kw=dict(
         wspace=0,
-        hspace=0.1,
+        hspace=0,
-        left=0.09,
+        left=0.08,
         right=0.98,
-        bottom=0.08,
+        bottom=0.1,
         top=0.95,
     )
 )
@@ -30,81 +28,41 @@ grid_line_kwargs = dict(
     color='k',
     lw=0.5,
 )
-trial_kwargs = dict(
-    color='k',
-    alpha=0.5,
-    lw=0.5,
-)
 line_kwargs = dict(
-    color='black',
+    c='k',
-    lw=1,
+    lw=0.5,
-)
-fill_kwargs = dict(
-    color='k',
     alpha=0.5,
 )
-xlabels = dict(
+xlab = '$\\text{scale }\\alpha$'
-    bottom='$\\text{scale }\\alpha$',
-)
-ylabels = dict(
-    top='$\\sigma_{\\eta}\\,(PLACEHOLDER \\,\\text{realizations})$',
-    bottom='$\\sigma_{\\eta}\\,(\\text{mean}\\,\\pm\\,\\text{SD})$',
-)
 xlab_kwargs = dict(
     y=0,
     fontsize=20,
     ha='center',
     va='bottom',
 )
+ylab = '$\\sigma_{\\eta}$'
 ylab_kwargs = dict(
     x=0,
     fontsize=20,
     ha='center',
     va='top',
 )
-title_kwargs = dict(
-    t='$\\sigma_{\\text{filt}}\\,=$',
-    x=0.5,
-    y=1,
-    ha='center',
-    va='top',
-    fontsize=20,
-)
-letter_kwargs = dict(
-    x=0.005,
-    y=0.99,
-    fontsize=22,
-    ha='left',
-    va='top',
-)
 
 # Fetch data:
 data = dict(np.load('../data/inv/noise_env/sd_conversion.npz'))
-n = data['n_trials']
-
-# Adjust parameters:
-ylabels['top'] = f'$\\sigma_{{\\eta}}\\,({data["n_trials"]}\\text{{ realizations}})$'
-title_kwargs['t'] += f'$\\,{strip_zeros(data["sd_factor"])}$'
 
 # Prepare graph:
-fig, (ax1, ax2) = plt.subplots(**fig_kwargs)
+fig, ax = plt.subplots(**fig_kwargs)
-fig.suptitle(**title_kwargs)
+ax.grid(**grid_line_kwargs)
-ax1.grid(**grid_line_kwargs)
+ax.set_xlim(data['scales'][0], data['scales'][-1])
-ax1.set_xlim(data['scales'][0], data['scales'][-1])
+ax.set_xscale('symlog', linthresh=data['scales'][1], linscale=0.5)
-ax1.set_xscale('symlog', linthresh=data['scales'][1], linscale=0.5)
+ax.set_ylim(0, 0.08)
-ax1.set_ylim(0, 0.1)
+ax.yaxis.set_major_locator(plt.MultipleLocator(0.02))
-ylabel(ax1, ylabels['top'], transform=fig.transFigure, **ylab_kwargs)
+xlabel(ax, xlab, transform=fig.transFigure, **xlab_kwargs)
-ax2.grid(**grid_line_kwargs)
+ylabel(ax, ylab, transform=fig.transFigure, **ylab_kwargs)
-xlabel(ax2, xlabels['bottom'], transform=fig.transFigure, **xlab_kwargs)
-ylabel(ax2, ylabels['bottom'], transform=fig.transFigure, **ylab_kwargs)
-letter_subplots((ax1, ax2), **letter_kwargs)
 
 # Plot individual trials:
-ax1.plot(data['scales'], data['trials'], **trial_kwargs)
+ax.plot(data['scales'], data['sd_noise'][..., 0], **line_kwargs)
-
-# Plot mean and spread across trials:
-ax2.plot(data['scales'], data['mean'], **line_kwargs)
-ax2.fill_between(data['scales'], data['mean'] - data['spread'], data['mean'] + data['spread'], **fill_kwargs)
 
 if save_path is not None:
     fig.savefig(save_path)

python/fig_features_cross_species.py

@@ -45,7 +45,7 @@ save_path = '../figures/fig_features_cross_species.pdf'
 
 
 # ANALYSIS SETTINGS:
-thresh_rel = np.array([0, 0.5, 1, 1.5, 2, 2.5, 3])[5]
+thresh_rel = np.array([0, 0.5, 1, 1.5, 2, 2.5, 3])[4]
 single_spec_file = True # Only use example files for cross-species comparison
 equalize_spec_files = False # Prune to minimum available across species
 n_song = n_spec#None # Limit to n first songs of in-species dataset (None for all)

python/fig_inv_cross_spec-thresh_appendix.py

@@ -13,9 +13,9 @@ from IPython import embed
 
 # GENERAL SETTINGS:
 target_species = [
-    # 'Chorthippus_biguttulus',
+    'Chorthippus_biguttulus',
-    # 'Chorthippus_mollis',
+    'Chorthippus_mollis',
-    # 'Chrysochraon_dispar',
+    'Chrysochraon_dispar',
     # 'Euchorthippus_declivus',
     'Gomphocerippus_rufus',
     'Omocestus_rufipes',
@@ -35,7 +35,15 @@ save_path = '../figures/fig_invariance_cross_species_thresh_appendix.pdf'
 
 # ANALYSIS SETTINGS:
 exclude_zero = True
-thresh_rel = np.array([0, 0.5, 1, 1.5, 2, 2.5, 3])
+thresh_rel = np.array([
+    # 0,
+    0.5,
+    1,
+    # 1.5,
+    2,
+    # 2.5,
+    3,
+])
 
 # SUBSET SETTINGS:
 types = np.array([1, -1, 2, -2, 3, -3, 4, -4])
@@ -53,15 +61,15 @@ fig_kwargs = dict(
     sharex=True,
     sharey=True,
     gridspec_kw=dict(
-        wspace=0.2,
+        wspace=0.3,
-        hspace=0.75,
+        hspace=0.5,
         left=0.1,
-        right=0.95,
+        right=0.97,
-        bottom=0.08,
+        bottom=0.1,
         top=0.98,
     )
 )
-inset_x_bounds = [0, -0.5, 1, 0.4]
+inset_x_bounds = [0, -0.3, 1, 0.25]
 inset_y_bounds = [1.01, 0, 0.1, 1]
 
 # PLOT SETTINGS:
@@ -162,6 +170,7 @@ y_dist_kwargs = dict(
 fig, axes = plt.subplots(**fig_kwargs)
 axes[0, 0].set_ylim(0, 1)
 axes[0, 0].yaxis.set_major_locator(plt.MultipleLocator(yloc))
+axes[0, 0].xaxis.set_major_locator(plt.LogLocator(base=10, subs=(1,)))
 super_xlabel(xlab, fig, axes[-1, 0], axes[-1, -1], **xlab_kwargs)
 super_ylabel(ylab, fig, axes[0, 0], axes[-1, 0], **ylab_super_kwargs)
 for ax, species in zip(axes[0, :], target_species):
@@ -197,25 +206,27 @@ for i, species in enumerate(target_species):
         symlog_kwargs = dict(linthresh=scales[scales > 0][0], linscale=0.5)
 
     # Run through thresholds:
-    for j in range(thresh_rel.size):
+    for j, thresh in enumerate(thresh_rel):
         ax = axes[j, i]
+        ind = np.nonzero(data['thresh_rel'] == thresh)[0][0]
+
         # Plot swarm of feature-specific intensity curves:
-        handles = ax.plot(scales, measure[:, :, j], lw=lw['swarm'])
+        handles = ax.plot(scales, measure[:, :, ind], lw=lw['swarm'])
         assign_colors(handles, config['k_specs'][:, 0], kern_colors)
-        reorder_by_sd(handles, measure[:, :, j])
+        reorder_by_sd(handles, measure[:, :, ind])
 
         # Plot single compressed intensity curve:
-        compressed = np.median(measure[:, :, j], axis=1)
+        compressed = np.median(measure[:, :, ind], axis=1)
         ax.plot(scales, compressed, **median_kwargs)
 
         # Plot distribution of saturation levels:
         inset = ax.inset_axes(inset_y_bounds)
         inset.set_ylim(0, 1)
         inset.axis('off')
-        y_dist(inset, measure[-1, :, j], **y_dist_kwargs)
+        y_dist(inset, measure[-1, :, ind], **y_dist_kwargs)
 
         # Plot distribution of saturation points:
-        crit_inds = np.array(get_saturation(measure[:, :, j], **plateau_settings)[1])
+        crit_inds = np.array(get_saturation(measure[:, :, ind], **plateau_settings)[1])
         if np.isnan(crit_inds).sum():
             print(f'WARNING: No saturation points found for {species} at threshold {thresh_rel[j]}')
             crit_inds = crit_inds[~np.isnan(crit_inds)].astype(int)
@@ -223,12 +234,13 @@ for i, species in enumerate(target_species):
         inset = ax.inset_axes(inset_x_bounds)
         inset.set_xlim(scales[0], scales[-1])
         inset.set_xscale('symlog', **symlog_kwargs)
+        inset.xaxis.set_major_locator(plt.LogLocator(base=10, subs=(1,)))
         hide_axis(inset, 'left')
         if j < thresh_rel.size - 1:
             hide_ticks(inset, 'bottom')
         x_dist(inset, crit_scales, **x_dist_kwargs)
 
-        if j > 0:
+        if thresh > 0:
             # Plot single saturation point:
             crit_ind = get_saturation(compressed, **plateau_settings)[1]
             crit_scale = scales[crit_ind]
@@ -237,6 +249,7 @@ for i, species in enumerate(target_species):
 # Posthocs:
 axes[0, 0].set_xscale('symlog', **symlog_kwargs)
 axes[0, 0].set_xlim(scales[0], scales[-1])
+axes[0, 0].xaxis.set_major_locator(plt.LogLocator(base=10, subs=(1,)))
 
 if save_path is not None:
     fig.savefig(save_path)

python/fig_kernel_sd_perc_appendix.py

@@ -6,13 +6,13 @@ from plot_functions import xlabel, ylabel
 from IPython import embed
 
 # Analysis settings:
-mode = ['thresh_lp', 'full', 'short', 'field'][3]
+mode = ['thresh_lp', 'full', 'short', 'field'][0]
 thresh_path = f'../data/inv/{mode}/thresholds.npz'
 save_path = f'../figures/fig_kernel_sd_perc_{mode}_appendix.pdf'
 
 # Plot settings:
 fig_kwargs = dict(
-    figsize=(32/2.54, 16/2.54),
+    figsize=(32/2.54, 15/2.54),
     nrows=1,
     ncols=1,
     gridspec_kw=dict(
@@ -41,8 +41,8 @@ grid_line_kwargs = dict(
     color='k',
     lw=0.5,
 )
-xlab = '$\\text{multiple of }\\sigma_{k_i}$'
+xlab = '$\\Theta_i\\,[\\text{multiples of }\\sigma_{c_i}]$'
-ylab = '$P\\,(c_i > \\Theta_i)$'
+ylab = '$\\mu_{f_i}\\,\\approx\\,P\\,(c_i > \\Theta_i)$'
 xlab_kwargs = dict(
     y=0,
     fontsize=20,
@@ -55,6 +55,8 @@ ylab_kwargs = dict(
     ha='center',
     va='top',
 )
+xloc = 1
+yloc = 0.25
 
 # Load threshold data:
 data = dict(np.load(thresh_path))
@@ -69,6 +71,8 @@ fig, ax = plt.subplots(**fig_kwargs)
 ax.grid(**grid_line_kwargs)
 ax.set_xlim(factors[0], factors[-1])
 ax.set_ylim(-0.01, 1.01)
+ax.xaxis.set_major_locator(plt.MultipleLocator(xloc))
+ax.yaxis.set_major_locator(plt.MultipleLocator(yloc))
 ylabel(ax, ylab, transform=fig.transFigure, **ylab_kwargs)
 xlabel(ax, xlab, transform=fig.transFigure, **xlab_kwargs)
 

python/fig_pathway_stages.py

@@ -17,7 +17,7 @@ stages = ['filt', 'env', 'log', 'inv', 'conv', 'bi', 'feat']
 save_path = '../figures/'
 
 # GRAPH SETTINGS:
-fig_kwargs = dict(
+fig_pre_kwargs = dict(
     figsize=(32/2.54, 16/2.54),
     sharex='col',
     subplot_kw=dict(
@@ -28,10 +28,17 @@ fig_kwargs = dict(
         hspace=0.3,
         left=0.12,
         right=0.99,
-        bottom=0.08,
+        bottom=0.09,
-        top=0.95
+        top=0.97
     ),
 )
+fig_feat_kwargs = fig_pre_kwargs.copy()
+fig_feat_kwargs['gridspec_kw'] = fig_pre_kwargs['gridspec_kw'].copy()
+fig_feat_kwargs['gridspec_kw'].update(dict(
+    left=0.09,
+    wspace=0.15,
+    hspace=0.2,
+))
 
 # PLOT SETTINGS:
 fs = dict(
@@ -76,13 +83,15 @@ xlab_kwargs = dict(
     va='bottom',
     fontsize=fs['lab_norm'],
 )
-ylab_kwargs = dict(
+ylab_pre_kwargs = dict(
     x=0.03,
     rotation=0,
     ha='center',
     va='center',
     fontsize=fs['lab_tex'],
 )
+ylab_feat_kwargs = ylab_pre_kwargs.copy()
+ylab_feat_kwargs['x'] = 0.02
 xloc = dict(
     full=2,
     zoom=0.2
@@ -98,42 +107,28 @@ yloc_full = dict(
 yloc_zoom = dict(
     filt=0.1,
     env=0.02,
-    log=50,
+    log=25,
     inv=10,
     conv=0.5,
     feat=1
 )
 letter_kwargs = dict(
-    x=0,
+    xref=0,
     y=1,
     ha='left',
-    va='bottom',
+    va='center',
     fontsize=fs['letter'],
 )
-zoom_rel = np.array([0.3, 0.4])
+zoom_rel = np.array([0.295, 0.4])
 zoom_kwargs = dict(
     color=3 * (0.85,),
     zorder=0,
     linewidth=0
 )
-# kernels = np.array([
+types = np.array([1, -1, 2, -2, 3, -3, 4, -4])
-#     [1, 0.002],
+# types = [1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 7, -7, 8, -8, 9, -9, 10, -10]
-#     [1, 0.016],
+sigmas = np.array([0.004, 0.032])
-#     [-1, 0.004],
+# sigmas = [0.001, 0.002, 0.004, 0.008, 0.016, 0.032]
-#     [-1, 0.032],
-#     [2, 0.004],
-#     [2, 0.016],
-#     [-2, 0.002],
-#     [-2, 0.032],
-#     [3, 0.008],
-#     [3, 0.032],
-#     [-3, 0.008],
-#     [-3, 0.032],
-#     [4, 0.004],
-#     [4, 0.032],
-#     [-4, 0.004],
-#     [-4, 0.032]
-# ])
 t = [1, -1, 2, -2, 3, -3, 4, -4]
 s = [0.004, 0.032]
 kernels = np.array([[i, j] for i in t for j in s])
@@ -162,31 +157,31 @@ for data_path in data_paths:
 
 
     # PART I: PREPROCESSING STAGE
-    fig, axes = plt.subplots(4, 2, **fig_kwargs)
+    fig, axes = plt.subplots(4, 2, **fig_pre_kwargs)
     super_xlabel(xlabels['super'], fig, axes[0, 0], axes[0, -1], **xlab_kwargs)
     [hide_axis(ax, 'bottom') for ax in axes[:-1, :].ravel()]
 
     # Bandpass-filtered signal:
     ax_full, ax_zoom = axes[0, :]
-    ylabel(ax_full, ylabels['filt'], transform=fig.transFigure, **ylab_kwargs)
+    ylabel(ax_full, ylabels['filt'], transform=fig.transFigure, **ylab_pre_kwargs)
     plot_line(ax_full, t_full, data['filt'], c=colors['filt'], lw=lw_full['filt'], yloc=yloc_full['filt'])
     plot_line(ax_zoom, t_zoom, data['filt'][zoom_mask], c=colors['filt'], lw=lw_zoom['filt'], yloc=yloc_zoom['filt'])
 
     # Signal envelope:
     ax_full, ax_zoom = axes[1, :]
-    ylabel(ax_full, ylabels['env'], transform=fig.transFigure, **ylab_kwargs)
+    ylabel(ax_full, ylabels['env'], transform=fig.transFigure, **ylab_pre_kwargs)
     plot_line(ax_full, t_full, data['env'], ymin=0, c=colors['env'], lw=lw_full['env'], yloc=yloc_full['env'])
     plot_line(ax_zoom, t_zoom, data['env'][zoom_mask], ymin=0, c=colors['env'], lw=lw_zoom['env'], yloc=yloc_zoom['env'])
 
     # Logarithmic envelope:
     ax_full, ax_zoom = axes[2, :]
-    ylabel(ax_full, ylabels['log'], transform=fig.transFigure, **ylab_kwargs)
+    ylabel(ax_full, ylabels['log'], transform=fig.transFigure, **ylab_pre_kwargs)
     plot_line(ax_full, t_full, data['log'], ymax=0, c=colors['log'], lw=lw_full['log'], yloc=yloc_full['log'])
-    plot_line(ax_zoom, t_zoom, data['log'][zoom_mask], ymax=0, c=colors['log'], lw=lw_zoom['log'], yloc=yloc_zoom['log'])
+    plot_line(ax_zoom, t_zoom, data['log'][zoom_mask], c=colors['log'], lw=lw_zoom['log'], yloc=yloc_zoom['log'])
 
     # Adapted envelope:
     ax_full, ax_zoom = axes[3, :]
-    ylabel(ax_full, ylabels['inv'], transform=fig.transFigure, **ylab_kwargs)
+    ylabel(ax_full, ylabels['inv'], transform=fig.transFigure, **ylab_pre_kwargs)
     plot_line(ax_full, t_full, data['inv'], c=colors['inv'], lw=lw_full['inv'], yloc=yloc_full['inv'])
     plot_line(ax_zoom, t_zoom, data['inv'][zoom_mask], c=colors['inv'], lw=lw_zoom['inv'], yloc=yloc_zoom['inv'])
 
@@ -197,25 +192,17 @@ for data_path in data_paths:
     ax_zoom.xaxis.set_major_locator(plt.MultipleLocator(xloc['zoom']))
     indicate_zoom(fig, axes[0, 0], axes[-1, 0], zoom_abs, **zoom_kwargs)
     indicate_zoom(fig, axes[0, 1], axes[-1, 1], zoom_abs, **zoom_kwargs)
-    letter_subplots(axes[:, 0], **letter_kwargs)
+    letter_subplots(axes[:, 0], ref=fig.transFigure, **letter_kwargs)
     if save_path is not None:
         fig.savefig(f'{save_path}fig_pre_stages.pdf')
 
-    # Update parameters:
-    fig_kwargs['gridspec_kw'].update(
-        left=0.09,
-    )
-    ylab_kwargs.update(
-        x=0.02,
-    )
-
     # PART II: FEATURE EXTRACTION STAGE:
-    fig, axes = plt.subplots(3, 2, **fig_kwargs)
+    fig, axes = plt.subplots(3, 2, **fig_feat_kwargs)
     super_xlabel(xlabels['super'], fig, axes[0, 0], axes[0, -1], **xlab_kwargs)
 
     # Convolutional filter responses:
     ax_full, ax_zoom = axes[0, :]
-    ylabel(ax_full, ylabels['conv'], transform=fig.transFigure, **ylab_kwargs)
+    ylabel(ax_full, ylabels['conv'], transform=fig.transFigure, **ylab_feat_kwargs)
     signal = data['conv'][:, kern_inds]
     handles = plot_line(ax_full, t_full, signal, lw=lw_full['conv'], yloc=yloc_full['conv'])
     assign_colors(handles, kern_specs[:, 0], conv_colors)
@@ -228,7 +215,7 @@ for data_path in data_paths:
 
     # Binary responses:
     ax_full, ax_zoom = axes[1, :]
-    ylabel(ax_full, ylabels['bi'], transform=fig.transFigure, **ylab_kwargs)
+    ylabel(ax_full, ylabels['bi'], transform=fig.transFigure, **ylab_feat_kwargs)
     signal = data['bi'][:, kern_inds]
     handles = plot_barcode(ax_full, t_full, signal, lw=lw_full['bi'])
     assign_colors(handles, kern_specs[:, 0], bi_colors)
@@ -237,7 +224,7 @@ for data_path in data_paths:
 
     # Finalized features:
     ax_full, ax_zoom = axes[2, :]
-    ylabel(ax_full, ylabels['feat'], transform=fig.transFigure, **ylab_kwargs)
+    ylabel(ax_full, ylabels['feat'], transform=fig.transFigure, **ylab_feat_kwargs)
     signal = data['feat'][:, kern_inds]
     handles = plot_line(ax_full, t_full, signal, ymin=0, ymax=1, c=colors['feat'], lw=lw_full['feat'], yloc=yloc_full['feat'])
     assign_colors(handles, kern_specs[:, 0], feat_colors)
@@ -251,7 +238,7 @@ for data_path in data_paths:
     ax_zoom.xaxis.set_major_locator(plt.MultipleLocator(xloc['zoom']))
     indicate_zoom(fig, axes[0, 0], axes[-1, 0], zoom_abs, **zoom_kwargs)
     indicate_zoom(fig, axes[0, 1], axes[-1, 1], zoom_abs, **zoom_kwargs)
-    letter_subplots(axes[:, 0], **letter_kwargs)
+    letter_subplots(axes[:, 0], ref=fig.transFigure, **letter_kwargs)
     if save_path is not None:
         fig.savefig(f'{save_path}fig_feat_stages.pdf')
     plt.show()

python/fig_saturation_log-hp_appendix.py

@@ -90,6 +90,12 @@ text_kwargs = dict(
     ha='right',
     va='top',
 )
+plateau_dot_kwargs = dict(
+    marker='o',
+    markersize=8,
+    markeredgewidth=1,
+    clip_on=False,
+)
 
 # Prepare graph:
 fig, axes = plt.subplots(**fig_kwargs)
@@ -111,12 +117,22 @@ for species, ax in zip(target_species, axes):
     # Plot distribution of saturation points:
     handles.append(ax.bar(bins, hist, width=bins[1] - bins[0], fc=color, **bar_kwargs))
     ax.set_ylim(0, hist.max() * 1.05)
+    if species == 'Gomphocerippus_rufus':
+        ax.yaxis.set_major_locator(plt.MultipleLocator(0.05))
+    else:
+        ax.yaxis.set_major_locator(plt.MultipleLocator(0.03))
 
     # Indicate mean of distribution:
-    ax.axvline(data['crit_scales'].mean(), **mean_kwargs)
+    # ax.axvline(data['crit_scales'].mean(), **mean_kwargs)
 
     # Indicate number of songs:
-    ax.text(**text_kwargs, s=f'n = {n_songs}', transform=ax.transAxes)
+    ax.text(**text_kwargs, s=f'n={n_songs}', transform=ax.transAxes)
+
+    # Indicate saturation point of condensed curve:
+    ax.plot(data['crit_scale'], 0, c='w', alpha=1, zorder=5.5,
+            transform=ax.get_xaxis_transform(), **plateau_dot_kwargs) 
+    ax.plot(data['crit_scale'], 0, mfc=color, mec='k', alpha=0.75, zorder=6,
+            transform=ax.get_xaxis_transform(), **plateau_dot_kwargs)
 
 # Posthocs:
 labels = [shorten_species(species) for species in target_species]

python/save_env_sd_conversion.py

@@ -1,26 +1,24 @@
-import glob
 import numpy as np
-import matplotlib.pyplot as plt
+from thunderhopper.filetools import search_files
 from thunderhopper.modeltools import load_data
 from thunderhopper.filters import sosfilter
 from IPython import embed
 
 # GENERAL SETTINGS:
 target = 'Omocestus_rufipes'
-data_path = glob.glob(f'../data/processed/{target}*.npz')[0]
+data_path = search_files(target, dir='../data/processed/')[0]
 save_path = '../data/inv/noise_env/'
 
 # ANALYSIS SETTINGS:
-scales = np.geomspace(0.1, 10000, 200)
+scales = np.geomspace(0.01, 1000, 100)
 sd_inputs = np.array([1.0])
-n_trials = 10
+n_trials = 100
-tol_to_one = 0.1
 
 # EXECUTION:
 
 # Load signal data:
-data, config = load_data(data_path, files='filt')
+data, config = load_data(data_path, files='raw')
-signal, rate = data['filt'], config['rate']
+signal, rate = data['raw'], config['rate']
 
 # Reduce to song segment and normalize:
 time = np.arange(signal.shape[0]) / rate
@@ -28,67 +26,60 @@ start, end = data['songs_0'].ravel()
 segment = (time >= start) & (time <= end)
 signal /= signal[segment].std()
 
-# Get rescaled signals (time, scale):
+# Rescale signal (time, scale):
 signal = signal[:, None] * scales[None, :]
 
 # Prepare storage:
-if sd_inputs.size > 1:
+sd_noise = np.zeros((scales.size, n_trials, sd_inputs.size), dtype=float)
-    current_match = 0
-    storage = dict(
-        scales=scales,
-        n_trials=n_trials,
-        sd_factor=np.array([0.]),
-        trials=np.zeros((scales.size, n_trials), dtype=float),
-        mean=np.zeros(scales.size, dtype=float),
-        spread=np.zeros(scales.size, dtype=float),
-    )
 
 # Analyze piece-wise:
 rng = np.random.default_rng()
 for i, sigma in enumerate(sd_inputs):
     print(f'Testing SD: {sigma:.3f} ...')
 
-    # Add Gaussian noise of given SD to rescaled signals (time, scale, trial):
+    # Prepare trial storage:
-    mix = signal[..., None] + rng.normal(0, sigma, (*signal.shape, n_trials))
+    sd_trials = np.zeros((segment.sum(), scales.size, n_trials), dtype=float)
 
-    # Get mixture envelopes (time, scale, trial):
+    # Run trials:
-    mix = sosfilter(np.abs(mix), rate, config['env_fcut'], 'lp',
+    for j in range(n_trials):
-                    padtype='even', padlen=config['padlen'])[segment, ...]
+        # Mix signals with white noise of target SD:
+        mix = signal + rng.normal(0, sigma, signal.shape)
+
+        # Process mixture:
+        mix = sosfilter(mix, rate, config['bp_fcut'], 'bp',
+                        padtype='fixed', padlen=config['padlen'])
+        mix = sosfilter(np.abs(mix), rate, config['env_fcut'], 'lp',
+                        padtype='even', padlen=config['padlen'])
+
+        # Log current trial:
+        sd_trials[..., j] = mix[segment, :]
 
     # Get noise remainders of mean over trials:
-    mix -= mix.mean(axis=-1, keepdims=True)
+    sd_trials -= sd_trials.mean(axis=-1, keepdims=True)
 
     # Estimate noise SD:
-    sd = mix.std(axis=0)
+    sd_noise[:, :, i] = sd_trials.std(axis=0)
-    # Average SD over trials:
-    mean_sd = sd.mean(axis=-1)
 
-    # Log single-run results:
+    # # Add Gaussian noise of given SD to rescaled signals (time, scale, trial):
-    if sd_inputs.size == 1:
+    # mix = signal[..., None] + rng.normal(0, sigma, (*signal.shape, n_trials))
-        storage = dict(
-            scales=scales,
-            n_trials=n_trials,
-            sd_factor=sigma,
-            trials=sd,
-            mean=mean_sd,
-            spread=sd.std(axis=-1),
-        )
-        break
 
-    # Update multi-run results if better than previous:
+    # # Get mixture envelopes (time, scale, trial):
-    n_match = (np.abs(1 - mean_sd) <= tol_to_one).sum()
+    # mix = sosfilter(np.abs(mix), rate, config['env_fcut'], 'lp',
-    if n_match > current_match:
+    #                 padtype='even', padlen=config['padlen'])[segment, ...]
-        print(f'Found better SD: {sigma:.3f} with {n_match} matches (previous: {current_match})')
+
-        storage['sd_factor'][0] = sigma
+    # # Get noise remainders of mean over trials:
-        storage['trials'][:, :] = sd
+    # mix -= mix.mean(axis=-1, keepdims=True)
-        storage['mean'][:] = mean_sd
+
-        storage['spread'][:] = sd.std(axis=-1)
+    # # Estimate noise SD:
-        current_match = n_match
+    # sd_noise[:, :, i] = mix.std(axis=0)
-    del mix
-del signal
 
 if save_path is not None:
-    np.savez(save_path + 'sd_conversion.npz', **storage)
+    archive = dict(
+        scales=scales,
+        sd_input=sd_inputs,
+        sd_noise=sd_noise,
+    )
+    np.savez(save_path + 'sd_conversion.npz', **archive)
 
 print('Done.')
 embed()

python/save_saturation_log-hp.py

@@ -14,7 +14,8 @@ target_species = [
     'Omocestus_rufipes',
     'Pseudochorthippus_parallelus',
 ]
-search_path = '../data/inv/log_hp/collected/'
+collect_path = '../data/inv/log_hp/collected/'
+condense_path = '../data/inv/log_hp/condensed/'
 save_path = '../data/inv/log_hp/saturation/'
 
 # ANALYSIS SETTINGS:
@@ -32,7 +33,7 @@ pad = 0.05
 # PREPARATION:
 if compute_hist:
     species_scales = []
-    min_scale, max_scale = [], []
+    min_scale, max_scale = np.inf, -np.inf
     archives = [{} for _ in target_species]
 
 # EXECUTION:
@@ -40,31 +41,48 @@ for i, species in enumerate(target_species):
     print(f'Processing {species}')
 
     # Load accumulated invariance data:
-    path = search_files(species, dir=search_path)[0]
+    path = search_files(species, dir=collect_path)[0]
     data, config = load_data(path, ['scales', 'measure_inv'])
 
     # Find upper saturation point per song file:
     crit_inds = np.array(get_saturation(data['measure_inv'], **plateau_settings)[1])
     crit_scales = data['scales'][crit_inds]
 
+    # Load condensed invariance data:
+    path = search_files(species, incl=['noise', 'norm-base'], dir=condense_path)[0]
+    data, _ = load_data(path, ['scales', 'mean_inv'])
+
+    # Find single upper saturation point of condensed curve:
+    crit_ind = get_saturation(data['mean_inv'].mean(axis=-1), **plateau_settings)[1]
+    crit_scale = data['scales'][crit_ind]
+
     # Output options:
     if not compute_hist:
         # Save species data immediately:
-        archive = dict(crit_inds=crit_inds, crit_scales=crit_scales, scales=data['scales'])
+        archive = dict(
+            scales=data['scales'],
+            crit_inds=crit_inds,
+            crit_scales=crit_scales,
+            crit_ind=crit_ind,
+            crit_scale=crit_scale,
+            )
         save_data(save_path + species, archive, config, overwrite=True)
         continue
 
     # Log but don't save data yet:
-    archives[i]['crit_inds'] = crit_inds
+    min_scale = min(crit_scales.min(), min_scale)
-    archives[i]['crit_scales'] = crit_scales
+    max_scale = max(crit_scales.max(), max_scale)
-    archives[i]['scales'] = data['scales']
+    archives[i].update(
-    min_scale.append(crit_scales.min())
+        scales=data['scales'],
-    max_scale.append(crit_scales.max())
+        crit_inds=crit_inds,
+        crit_scales=crit_scales,
+        crit_ind=crit_ind,
+        crit_scale=crit_scale,    
+    )
 
 # Optional histogram:
 if compute_hist:
-    # Generated shared histogram edges:
+    # Generated shared bin edges:
-    min_scale, max_scale = min(min_scale), max(max_scale)
     pad *= (max_scale - min_scale)
     edges = np.linspace(max(0, min_scale - pad), max_scale + pad, bins + 1)
     centers = edges[:-1] + np.diff(edges) / 2