Added newly processed species to fig_features_cross_species.pdf.
Wrote more of the results.
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\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces \textbf {Intensity invariance through logarithmic compression and adaptation is restricted by the noise floor and decreases SNR.} Input $x_{\text {filt}}(t)$ consists of song component $s(t)$ scaled by $\alpha $ with optional noise component $\eta (t)$ and is successively transformed into envelope $x_{\text {env}}(t)$, logarithmically compressed envelope $x_{\text {log}}(t)$, and intensity-adapted envelope $x_{\text {adapt}}(t)$. \textbf {Top}:~Example representations of $x_{\text {env}}(t)$, $x_{\text {log}}(t)$, and $x_{\text {adapt}}(t)$ for different $\alpha $. \textbf {a}:~Noiseless case. \textbf {b}:~Noisy case. \textbf {Bottom}:~Intensity metrics over a range of $\alpha $. \textbf {c}:~Noiseless case: Standard deviations $\sigma _x$ of $x_{\text {env}}(t)$, $x_{\text {log}}(t)$, and $x_{\text {adapt}}(t)$. \textbf {d}:~Noisy case: Ratios of $\sigma _x$ of $x_{\text {env}}(t)$, $x_{\text {log}}(t)$, and $x_{\text {adapt}}(t)$ to the respective reference standard deviation $\sigma _{\eta }$ for input $x_{\text {filt}}(t)=\eta (t)$. Shaded areas indicate $5\,\%$ (dark grey) and $95\,\%$ (light grey) curve span for $x_{\text {adapt}}(t)$. \textbf {e}:~Ratios of $\sigma _x$ to $\sigma _{\eta }$ of $x_{\text {adapt}}(t)$ as in \textbf {d} for different species (averaged over songs and recordings, see appendix Fig\,\ref {fig:app_log-hp_curves}). Dots indicate $95\,\%$ curve span per species. }}{15}{}\protected@file@percent }
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\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces \textbf {Intensity invariance through thresholding and temporal averaging is mediated by the interaction of threshold value and noise floor.} Input $x_{\text {adapt}}(t)$ consists of song component $s(t)$ scaled by $\alpha $ with optional noise component $\eta (t)$ and is transformed into single kernel response $c(t)$, binary response $b(t)$, and feature $f(t)$. Different color shades indicate different threshold values $\Theta $ (multiples of reference standard deviation $\sigma _{\eta }$ of $c(t)$ for input $x_{\text {adapt}}(t)=\eta (t)$, with darker colors for higher $\Theta $). \textbf {Left}:~Noisy case: Example representations of $x_{\text {adapt}}(t)$ as well as $c(t)$, $b(t)$, and $f(t)$ for different $\alpha $. \textbf {a}:~$x_{\text {adapt}}(t)$ with kernel $k(t)$ in black. \textbf {b\,-\,d}: $c(t)$, $b(t)$, and $f(t)$ based on the same $x_{\text {adapt}}(t)$ from \textbf {a} but with different $\Theta $. \textbf {Right}:~Average value $\mu _f$ of $f(t)$ for each $\Theta $ from \textbf {b\,-\,d}, once for the noisy case (solid lines) and once for the noiseless case (dotted lines). Dots indicate $95\,\%$ curve span (noisy case). \textbf {e}:~$\mu _f$ over a range of $\alpha $. \textbf {f}:~$\mu _f$ over the standard deviation of noisy input $x_{\text {adapt}}$ corresponding to the values of $\alpha $ shown in \textbf {e}. }}{17}{}\protected@file@percent }
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\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces \textbf {Feature representation of different species-specific songs 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 threshold value $\Theta _i=0.5\cdot \sigma _{\eta _i}$. \textbf {a}:~Examples of species-specific grasshopper songs. \textbf {Middle}:~Average value $\mu _{f_i}$ of each feature $f_i(t)$ over $\alpha $ per species (averaged over songs and recordings, see appendix Figs.\,\ref {fig:app_thresh-lp_pure} and \ref {fig:app_thresh-lp_noise}). Different color shades indicate different kernels $k_i$. Dots indicate $95\,\%$ 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 with $\alpha $ (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 species. \textbf {d}:~Noiseless case. \textbf {e}:~Noisy case. Shaded areas indicate the average minimum $\mu _{f_i}$ across all species-specific trajectories. }}{18}{}\protected@file@percent }
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\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces \textbf {Step-wise emergence of intensity-invariant song representation along the full model pathway.} Input $x_{\text {raw}}(t)$ consists of song component $s(t)$ scaled by $\alpha $ with added noise component $\eta (t)$ and is processed up to the feature set $f_i(t)$. Different color shades indicate different types of Gabor kernels with specific lobe number $n$ and either $+$ or $-$ sign, sorted (dark to light) first by increasing $n$ and then by sign~($1\,\leq \,n\,\leq \,4$; first $+$, then $-$ for each $n$; five kernel widths $\sigma $ of 1, 2, 4, 8, and $16\,$ms per type; 8 types, 40 kernels in total). \textbf {a}:~Example representations of $x_{\text {filt}}(t)$, $x_{\text {env}}(t)$, $x_{\text {log}}(t)$, $x_{\text {adapt}}(t)$, $c_i(t)$, and $f_i(t)$ for different $\alpha $. \textbf {b}:~Intensity metrics over $\alpha $. For $c_i(t)$ and $f_i(t)$, the median over kernels is shown. Dots indicate $95\,\%$ curve span for $x_{\text {log}}(t)$, $x_{\text {adapt}}(t)$, $c_i(t)$, and $f_i(t)$. \textbf {c}:~Average value $\mu _{f_i}$ of each feature $f_i(t)$ over $\alpha $. \textbf {d}:~Ratios of intensity metrics to the respective reference value for input $x_{\text {raw}}(t)=\eta (t)$. For $c_i(t)$ and $f_i(t)$, the median over kernel-specific ratios is shown. \textbf {e}:~Ratios of standard deviation $\sigma _{c_i}$ of each $c_i(t)$. \textbf {f}:~Ratios of $\mu _{f_i}$. \textbf {g}:~Distributions of kernel-specific $\alpha $ that correspond to $95\,\%$ curve span for $c_i(t)$ and $f_i(t)$. Dots indicate the values from \textbf {b}. }}{19}{}\protected@file@percent }
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\@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces \textbf {Interspecific and intraspecific feature variability.} Average value $\mu _{f_i}$ of each feature $f_i(t)$ against its counterpart from a 2nd feature set based on a different input $x_{\text {raw}}(t)$. Each dot within a subplot represents a single feature $f_i(t)$. Different color shades indicate different types of Gabor kernels with specific lobe number $n$ and either $+$ or $-$ sign, sorted (dark to light) first by increasing $n$ and then by sign~($1\,\leq \,n\,\leq \,4$; first $+$, then $-$ for each $n$; five kernel widths $\sigma $ of 1, 2, 4, 8, and $16\,$ms per type; 8 types, 40 kernels in total). Data is 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 between different songs of a single species (\textit {O. rufipes}). \textbf {Lower left}:~Distribution of correlation coefficients $\rho $ for each interspecific and intraspecific comparison. Dots indicate single $\rho $ values. }}{21}{}\protected@file@percent }
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\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces \textbf {Intensity invariance through thresholding and temporal averaging is mediated by the interaction of threshold value and noise floor.} Input $x_{\text {adapt}}(t)$ consists of song component $s(t)$ scaled by $\alpha $ with optional noise component $\eta (t)$ and is transformed into single kernel response $c(t)$, binary response $b(t)$, and feature $f(t)$. Different color shades indicate different threshold values $\Theta $ (multiples of reference standard deviation $\sigma _{\eta }$ of $c(t)$ for input $x_{\text {adapt}}(t)=\eta (t)$, with darker colors for higher $\Theta $). \textbf {Left}:~Noisy case: Example representations of $x_{\text {adapt}}(t)$ as well as $c(t)$, $b(t)$, and $f(t)$ for different $\alpha $. \textbf {a}:~$x_{\text {adapt}}(t)$ with kernel $k(t)$ in black. \textbf {b\,-\,d}: $c(t)$, $b(t)$, and $f(t)$ based on the same $x_{\text {adapt}}(t)$ from \textbf {a} but with different $\Theta $. \textbf {Right}:~Average value $\mu _f$ of $f(t)$ for each $\Theta $ from \textbf {b\,-\,d}, once for the noisy case (solid lines) and once for the noiseless case (dotted lines). Dots indicate $95\,\%$ curve span (noisy case). \textbf {e}:~$\mu _f$ over a range of $\alpha $. \textbf {f}:~$\mu _f$ over the standard deviation of noisy input $x_{\text {adapt}}$ corresponding to the values of $\alpha $ shown in \textbf {e}. }}{18}{}\protected@file@percent }
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[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 21, warning: 6 characters of junk seen at toplevel
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||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 38, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 49, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 58, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 73, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 82, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 91, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 100, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 109, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 118, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 127, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 136, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 157, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 178, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 187, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 196, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 207, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 218, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 229, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 240, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 249, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 258, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 269, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 278, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 289, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 300, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 309, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 328, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 337, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 400, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 419, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 428, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 437, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 456, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 491, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 526, warning: 6 characters of junk seen at toplevel
|
||||
[331] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 535, warning: 6 characters of junk seen at toplevel
|
||||
[332] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 556, warning: 6 characters of junk seen at toplevel
|
||||
[332] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 565, warning: 6 characters of junk seen at toplevel
|
||||
[332] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 576, warning: 6 characters of junk seen at toplevel
|
||||
[332] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 587, warning: 6 characters of junk seen at toplevel
|
||||
[332] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 619, warning: 6 characters of junk seen at toplevel
|
||||
[332] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 648, warning: 6 characters of junk seen at toplevel
|
||||
[332] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 658, warning: 6 characters of junk seen at toplevel
|
||||
[332] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 667, warning: 6 characters of junk seen at toplevel
|
||||
[332] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 688, warning: 6 characters of junk seen at toplevel
|
||||
[332] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 709, warning: 6 characters of junk seen at toplevel
|
||||
[332] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 720, warning: 6 characters of junk seen at toplevel
|
||||
[332] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 729, warning: 6 characters of junk seen at toplevel
|
||||
[332] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 749, warning: 6 characters of junk seen at toplevel
|
||||
[332] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 766, warning: 6 characters of junk seen at toplevel
|
||||
[332] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 775, warning: 6 characters of junk seen at toplevel
|
||||
[332] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 800, warning: 6 characters of junk seen at toplevel
|
||||
[332] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_vMHw/347c261ec4135a5723bef5c751f5078f_55959.utf8, line 817, warning: 6 characters of junk seen at toplevel
|
||||
[332] Biber.pm:133> INFO - WARNINGS: 55
|
||||
[76] Biber.pm:979> INFO - Found 55 citekeys in bib section 0
|
||||
[82] Biber.pm:4419> INFO - Processing section 0
|
||||
[87] Biber.pm:4610> INFO - Looking for bibtex file 'cite.bib' for section 0
|
||||
[88] bibtex.pm:1713> INFO - LaTeX decoding ...
|
||||
[119] bibtex.pm:1519> INFO - Found BibTeX data source 'cite.bib'
|
||||
[302] UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'variable = shifted' with 'variable = non-ignorable'
|
||||
[302] UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'normalization = NFD' with 'normalization = prenormalized'
|
||||
[302] Biber.pm:4239> INFO - Sorting list 'nyt/global//global/global' of type 'entry' with template 'nyt' and locale 'en-US'
|
||||
[302] Biber.pm:4245> INFO - No sort tailoring available for locale 'en-US'
|
||||
[327] bbl.pm:660> INFO - Writing 'main.bbl' with encoding 'UTF-8'
|
||||
[338] bbl.pm:763> INFO - Output to main.bbl
|
||||
[338] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 10, warning: 6 characters of junk seen at toplevel
|
||||
[338] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 21, warning: 6 characters of junk seen at toplevel
|
||||
[338] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 38, warning: 6 characters of junk seen at toplevel
|
||||
[338] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 49, warning: 6 characters of junk seen at toplevel
|
||||
[338] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 58, warning: 6 characters of junk seen at toplevel
|
||||
[338] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 73, warning: 6 characters of junk seen at toplevel
|
||||
[338] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 82, warning: 6 characters of junk seen at toplevel
|
||||
[338] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 91, warning: 6 characters of junk seen at toplevel
|
||||
[338] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 100, warning: 6 characters of junk seen at toplevel
|
||||
[338] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 109, warning: 6 characters of junk seen at toplevel
|
||||
[338] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 118, warning: 6 characters of junk seen at toplevel
|
||||
[338] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 127, warning: 6 characters of junk seen at toplevel
|
||||
[338] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 136, warning: 6 characters of junk seen at toplevel
|
||||
[338] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 157, warning: 6 characters of junk seen at toplevel
|
||||
[338] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 178, warning: 6 characters of junk seen at toplevel
|
||||
[338] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 187, warning: 6 characters of junk seen at toplevel
|
||||
[338] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 196, warning: 6 characters of junk seen at toplevel
|
||||
[338] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 207, warning: 6 characters of junk seen at toplevel
|
||||
[338] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 218, warning: 6 characters of junk seen at toplevel
|
||||
[338] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 229, warning: 6 characters of junk seen at toplevel
|
||||
[338] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 240, warning: 6 characters of junk seen at toplevel
|
||||
[338] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 249, warning: 6 characters of junk seen at toplevel
|
||||
[338] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 258, warning: 6 characters of junk seen at toplevel
|
||||
[338] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 269, warning: 6 characters of junk seen at toplevel
|
||||
[339] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 278, warning: 6 characters of junk seen at toplevel
|
||||
[339] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 289, warning: 6 characters of junk seen at toplevel
|
||||
[339] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 300, warning: 6 characters of junk seen at toplevel
|
||||
[339] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 309, warning: 6 characters of junk seen at toplevel
|
||||
[339] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 328, warning: 6 characters of junk seen at toplevel
|
||||
[339] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 337, warning: 6 characters of junk seen at toplevel
|
||||
[339] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 400, warning: 6 characters of junk seen at toplevel
|
||||
[339] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 419, warning: 6 characters of junk seen at toplevel
|
||||
[339] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 428, warning: 6 characters of junk seen at toplevel
|
||||
[339] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 437, warning: 6 characters of junk seen at toplevel
|
||||
[339] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 456, warning: 6 characters of junk seen at toplevel
|
||||
[339] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 491, warning: 6 characters of junk seen at toplevel
|
||||
[339] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 526, warning: 6 characters of junk seen at toplevel
|
||||
[339] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 535, warning: 6 characters of junk seen at toplevel
|
||||
[339] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 556, warning: 6 characters of junk seen at toplevel
|
||||
[339] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 565, warning: 6 characters of junk seen at toplevel
|
||||
[339] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 576, warning: 6 characters of junk seen at toplevel
|
||||
[339] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 587, warning: 6 characters of junk seen at toplevel
|
||||
[339] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 619, warning: 6 characters of junk seen at toplevel
|
||||
[339] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 648, warning: 6 characters of junk seen at toplevel
|
||||
[339] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 658, warning: 6 characters of junk seen at toplevel
|
||||
[339] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 667, warning: 6 characters of junk seen at toplevel
|
||||
[339] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 688, warning: 6 characters of junk seen at toplevel
|
||||
[339] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_MhxB/347c261ec4135a5723bef5c751f5078f_14936.utf8, line 709, warning: 6 characters of junk seen at toplevel
|
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File: figures/fig_invariance_cross_species_thresh_appendix.pdf Graphic file (type pdf)
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||||
<use figures/fig_invariance_cross_species_thresh_appendix.pdf>
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||||
Package pdftex.def Info: figures/fig_invariance_cross_species_thresh_appendix.pdf used on input line 1248.
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[30 <./figures/fig_kernel_sd_perc_short_appendix.pdf> <./figures/fig_kernel_sd_perc_field_appendix.pdf>] [31 <./figures/fig_invariance_cross_species_thresh_appendix.pdf>] (./main.aux)
|
||||
[29 <./figures/fig_kernel_sd_perc_short_appendix.pdf> <./figures/fig_kernel_sd_perc_field_appendix.pdf>] [30 <./figures/fig_invariance_cross_species_thresh_appendix.pdf>] (./main.aux)
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L3 programming layer <2024-01-22>
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main.tex
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main.tex
@@ -103,8 +103,8 @@
|
||||
\newcommand{\xvar}{\sigma_{x}^{2}} % Variance of synthetic mixture
|
||||
\newcommand{\svar}{\sigma_{\text{s}}^{2}} % Song component variance
|
||||
\newcommand{\nvar}{\sigma_{\eta}^{2}} % Noise component variance
|
||||
\newcommand{\pc}{p(c_i,\,T)} % Probability density (general interval)
|
||||
\newcommand{\pclp}{p(c_i,\,\tlp)} % Probability density (lowpass interval)
|
||||
\newcommand{\pc}{p(c,\,T)} % Probability density (general interval)
|
||||
\newcommand{\pclp}{p(c,\,\tlp)} % Probability density (lowpass interval)
|
||||
|
||||
\section{Exploring a grasshopper's sensory world}
|
||||
|
||||
@@ -758,8 +758,7 @@ saturation regime is, of course, desirable in the context of intensity
|
||||
invariance, but it also means to pass up on the higher SNR values that are
|
||||
achieved by $\env(t)$ for the same $\sca$ (up to several orders of magnitude,
|
||||
Fig.\,\ref{fig:log-hp}d). This trade-off between intensity invariance and SNR
|
||||
--- and the consequences it has further downstream along the pathway --- are
|
||||
adressed in the following sections.
|
||||
is a recurring phenomenon that is further addressed in the following sections.
|
||||
|
||||
\begin{figure}[!ht]
|
||||
\centering
|
||||
@@ -797,6 +796,92 @@ adressed in the following sections.
|
||||
|
||||
\subsection{Thresholding nonlinearity \& temporal averaging}
|
||||
|
||||
The third nonlinear transformation along the model pathway is the thresholding
|
||||
nonlinearity $\nl$ that transforms each kernel response $c_i(t)$ into a binary
|
||||
binary response $b_i(t)$, Eq.\,\ref{eq:binary}. This transformation takes place
|
||||
after the convolutional filtering of $\adapt(t)$ with kernel $k_i(t)$,
|
||||
Eq.\,\ref{eq:conv}, and is followed by the temporal averaging of $b_i(t)$ into
|
||||
the feature set $f_i(t)$ by a lowpass filter, Eq.\,\ref{eq:lowpass}. The
|
||||
effects of thresholding and temporal averaging are best illustrated based on a
|
||||
single kernel~(Fig.\,\ref{fig:thresh-lp_single}) instead of the full set. For
|
||||
this analysis, input $\adapt(t)$ was
|
||||
rescaled~(Fig.\,\ref{fig:thresh-lp_single}a) and convolved with kernel $k(t)$.
|
||||
The resulting kernel response $c(t)$ was passed through $H(c\,-\,\Theta)$ with
|
||||
three different threshold values
|
||||
$\Theta$~(Fig.\,\ref{fig:thresh-lp_single}b-d). Each resulting binary response
|
||||
$b(t)$ was transformed into $f(t)$, whose average feature value serves as a
|
||||
measure of intensity~(Fig.\,\ref{fig:thresh-lp_single}ef). The thresholding
|
||||
nonlinearity $H(c\,-\,\Theta)$ categorizes the values of $c(t)$ into "relevant"
|
||||
($c(t)>\Theta$, $b(t)=1$) and "irrelevant" ($c(t)\leq\Theta$, $b(t)=0$)
|
||||
response values. It thereby splits the probability density $\pc$ of $c(t)$
|
||||
within some observed time interval $T$ into two complementary parts around
|
||||
$\Theta$:
|
||||
\begin{equation}
|
||||
\int_{\Theta}^{+\infty} \pc\,dc\,=\,1\,-\,\int_{-\infty}^{\Theta} \pc\,dc\,=\,\frac{T_1}{T}, \qquad \infint \pc\,dc\,=\,1
|
||||
\label{eq:pdf_split}
|
||||
\end{equation}
|
||||
The right-sided part of the split $\pc$ corresponds to time $T_1$ where
|
||||
$c(t)>\Theta$, while the left-sided part corresponds to time $T_0=T-T_1$ where
|
||||
$c(t)\leq\Theta$. The semi-definite integral over the right-sided part of $\pc$
|
||||
represents the ratio of time $T_1$ to total time $T$ because the indefinite
|
||||
integral of a probability density is normalized to 1. The lowpass filtering of
|
||||
$b(t)$ can be approximated as temporal averaging over a suitable time interval
|
||||
$\tlp>\frac{1}{\fc}$ in order to express $f(t)$ as a similar temporal ratio
|
||||
\begin{equation}
|
||||
f(t)\,\approx\,\frac{1}{\tlp} \int_{t}^{t\,+\,\tlp} b(\tau)\,d\tau\,=\,\frac{T_1}{\tlp}, \qquad b(t)\,\in\,\{0,\,1\}
|
||||
\label{eq:feat_avg}
|
||||
\end{equation}
|
||||
of time $T_1$ during which $b(t)$ is 1 within the averaging interval $\tlp$.
|
||||
Therefore, the value of $f(t)$ at every time point $t$ approximately signifies
|
||||
the cumulative probability that $c(t)$ exceeds $\Theta$ during the
|
||||
corresponding averaging interval $\tlp$:
|
||||
\begin{equation}
|
||||
f(t)\,\approx\,\int_{\Theta}^{+\infty} \pclp\,dc\,=\,P(c\,>\,\Theta,\,\tlp)
|
||||
\label{eq:feat_prop}
|
||||
\end{equation}
|
||||
In a sense, $f(t)$ can be interpreted as some sort of duty cycle with respect
|
||||
to $\Theta$. For example, a feature value of $f(t)=0.4$ means that $c(t)$
|
||||
exceeds $\Theta$ for approximately 40\,\% of the time within $\tlp$ around $t$.
|
||||
In the most extreme cases, $\Theta$ lays either above the maximum of $c(t)$ or
|
||||
below the minimum of $c(t)$, which results in a minimum or maximum possible
|
||||
feature value of $f(t)=0$~(Fig.\,\ref{fig:thresh-lp_single}d, left column) or
|
||||
$f(t)=1$, respectively.
|
||||
|
||||
Importantly, $f(t)$ neither retains information about the timing of individual
|
||||
threshold crossings nor the precise values of $c(t)$ apart from their relation
|
||||
to $\Theta$. Accordingly, for a given $\Theta$, different $\sca$ can still
|
||||
result in similar $T_1$ segments (and hence similar feature values) depending
|
||||
on the magnitude of the derivative of $c(t)$ in temporal proximity to time
|
||||
points at which $c(t)$ crosses $\Theta$: The steeper the slope of $c(t)$, the
|
||||
less $T_1$ changes with variations in $\sca$. The most reliable way of
|
||||
exploiting this invariant porperty of $f(t)$ is to set $\Theta$ to a value near
|
||||
0, because these values are least affected by different scales of $c(t)$. For
|
||||
sufficiently large $\sca$, $f(t)$ then approaches the same constant value in
|
||||
both the noiseless and the noisy case~(Fig.\,\ref{fig:thresh-lp_single}e,
|
||||
saturation regime).
|
||||
|
||||
The value of $f(t)$ in the saturation regime is independent of the precise
|
||||
value of $\Theta$, but the value of $\sca$ at which the saturation regime is
|
||||
reached decreses with $\Theta$~(Fig.\,\ref{fig:thresh-lp_single}e). Therefore,
|
||||
a threshold value of $\Theta=0$ would be the optimal choice for achieving
|
||||
intensity invariance at the lowest possible $\sca$. In stark contrast, the
|
||||
closer $\Theta$ is to 0, the higher the pure-noise response of $f(t)$ and the
|
||||
lower the resulting SNR of $f(t)$ between noise regime and saturation
|
||||
regime~(Fig.\,\ref{fig:thresh-lp_single}b-d, left column, and
|
||||
Fig.\,\ref{fig:thresh-lp_single}e). It is even possible to achieve an
|
||||
"unlimited" SNR of $f(t)$ by setting $\Theta$ above the maximum of the
|
||||
pure-noise $c(t)$, so that any value of $f(t)$ greater than 0 indicates the
|
||||
presence of the song component $\soc(t)$ in input $\adapt(t)$ at the cost of
|
||||
requiring a higher $\sca$ to reach the saturation regime. This trade-off
|
||||
between intensity invariance and SNR has already been observed during the
|
||||
previous analysis on logarithmic compression and
|
||||
adaptation~(Fig.\,\ref{fig:log-hp}d). However, the parameters that determine
|
||||
the SNR of $\adapt(t)$ are much less understood and likely relate to properties
|
||||
of the signal, whereas the SNR of $f(t)$ depends on the choice of $\Theta$ and
|
||||
can be more directly manipulated by the system.
|
||||
|
||||
Finally,
|
||||
|
||||
\begin{figure}[!ht]
|
||||
\centering
|
||||
\includegraphics[width=\textwidth]{figures/fig_invariance_thresh_lp_single.pdf}
|
||||
@@ -1003,96 +1088,6 @@ adressed in the following sections.
|
||||
\end{figure}
|
||||
\FloatBarrier
|
||||
|
||||
The second key mechanism for the emergence of intensity invariance along the
|
||||
model pathway takes place during the transformation of the kernel responses
|
||||
$c_i(t)$ over the binary responses $b_i(t)$ into the finalized features
|
||||
$f_i(t)$. Kernel response $c_i(t)$ quantifies the degree of similarity between
|
||||
kernel $k_i(t)$ and the preprocessed signal $\adapt(t)$. The thresholding
|
||||
nonlinearity $\nl$ categorizes the value of $c_i(t)$ at every time point $t$
|
||||
into "relevant" ($c_i(t)>\thr$, $b_i(t)=1$) and "irrelevant" ($c_i(t)\leq\thr$,
|
||||
$b_i(t)=0$) response values
|
||||
|
||||
By passing $c_i(t)$ through the thresholding
|
||||
nonlinearity $\nl$, its amplitude values are binned
|
||||
into one of two categories~(Eq.\,\ref{eq:binary}).
|
||||
|
||||
: $c_i(t)>\thr$
|
||||
|
||||
|
||||
|
||||
|
||||
This mechanism is mediated by the thresholding nonlinearity $\nl$. By
|
||||
passing $c_i(t)$ through the thresholding nonlinearity~(Eq.\,\ref{eq:binary}),
|
||||
its probability density $\pc$ within some observed time interval $T$ is split
|
||||
around threshold value $\thr$ into two complementary parts:
|
||||
\begin{equation}
|
||||
\int_{\thr}^{+\infty} \pc\,dc_i\,=\,1\,-\,\int_{-\infty}^{\thr} \pc\,dc_i\,=\,\frac{T_1}{T}, \qquad \infint \pc\,dc_i\,=\,1
|
||||
\label{eq:pdf_split}
|
||||
\end{equation}
|
||||
The right-sided part of the split $\pc$ corresponds to time $T_1$ where
|
||||
$c_i(t)>\thr$, while the left-sided part corresponds to time $T_0=T-T_1$ where
|
||||
$c_i(t)\leq\thr$. The semi-definite integral over the right-sided part of $\pc$
|
||||
represents the ratio of time $T_1$ to total time $T$ because the indefinite
|
||||
integral of a probability density is normalized to 1. Following the
|
||||
thresholding nonlinearity, the resulting binary responses $b_i(t)$ are
|
||||
lowpass-filtered~(Eq.\,\ref{eq:lowpass}) to obtain $f_i(t)$, which can be
|
||||
approximated as temporal averaging over a suitable time interval
|
||||
$\tlp>\frac{1}{\fc}$
|
||||
\begin{equation}
|
||||
f_i(t)\,\approx\,\frac{1}{\tlp} \int_{t}^{t\,+\,\tlp} b_i(\tau)\,d\tau\,=\,\frac{T_1}{\tlp}, \qquad b_i(t)\,\in\,\{0,\,1\}
|
||||
\label{eq:feat_avg}
|
||||
\end{equation}
|
||||
Feature $f_i(t)$
|
||||
|
||||
If the lowpass
|
||||
filter~(Eq.\,\ref{eq:lowpass}) over $b_i(t)$ is approximated as temporal
|
||||
averaging over a suitable time interval $\tlp>\frac{1}{\fc}$, then $f_i(t)$ can
|
||||
be linked to a similar temporal ratio
|
||||
% \begin{equation}
|
||||
% f_i(t)\,\approx\,\frac{1}{\tlp} \int_{t}^{t\,+\,\tlp} b_i(\tau)\,d\tau\,=\,\frac{T_1}{\tlp}, \qquad b_i(t)\,\in\,\{0,\,1\}
|
||||
% \label{eq:feat_avg}
|
||||
% \end{equation}
|
||||
of time $T_1$ during which $b_i(t)$ is 1 within the total averaging interval
|
||||
$\tlp$. Therefore, the value of $f_i(t)$ at every time point $t$ approximately
|
||||
signifies the cumulative probability that $c_i(t)$ exceeds $\thr$ during the
|
||||
corresponding averaging interval $\tlp$:
|
||||
\begin{equation}
|
||||
f_i(t)\,\approx\,\int_{\thr}^{+\infty} \pclp\,dc_i\,=\,P(c_i\,>\,\thr,\,\tlp)
|
||||
\label{eq:feat_prop}
|
||||
\end{equation}
|
||||
In a sense, $f_i(t)$ resembles a duty cycle of some sort, which quantifies
|
||||
purely temporal relations in the structure of $c_i(t)$ with no regard for
|
||||
precise amplitude values apart from their relation to $\thr$.
|
||||
|
||||
Accordingly, a substantial amount of information about the degree of similarity
|
||||
between signal $\adapt(t)$ and kernel $k_i(t)$ that is contained in $c_i(t)$ is
|
||||
lost during its transformation into $f_i(t)$. Instead, $f_i(t)$ only retains
|
||||
information about the temporal relation of $c_i(t)$ relative to $\thr$
|
||||
|
||||
|
||||
This loss of amplitude information is the key to the intensity
|
||||
invariance of $f_i(t)$: For a given $\thr$, different scales of $c_i(t)$ can
|
||||
still result in similar $T_1$ segments depending on the magnitude of the
|
||||
derivative of $c_i(t)$ in temporal proximity to time points at which $c_i(t)$
|
||||
crosses $\thr$. The steeper the slope of $c_i(t)$ around the threshold
|
||||
crossings, the less $T_1$ changes with scale variations.
|
||||
|
||||
|
||||
|
||||
In a sense, $f_i(t)$ resembles a duty
|
||||
cycle of some sort, as it quantifies purely temporal relations in the structure
|
||||
of $c_i(t)$ with no regard for precise amplitude values apart from their
|
||||
relation to $\thr$. This near-complete loss of amplitude information is the key
|
||||
to the intensity invariance of $f_i(t)$: For a given $\thr$, different scales
|
||||
of $c_i(t)$ can still result in similar $T_1$ segments depending on the
|
||||
magnitude of the derivative of $c_i(t)$ in temporal proximity to time points at
|
||||
which $c_i(t)$ crosses $\thr$. The steeper the slope of $c_i(t)$ around the
|
||||
threshold crossings, the less $T_1$ changes with scale variations.
|
||||
|
||||
|
||||
|
||||
\section{Discriminating species-specific song\\patterns in feature space}
|
||||
|
||||
\section{Conclusions \& outlook}
|
||||
|
||||
\textbf{Song recognition pathway: Grasshopper vs. model:}\\
|
||||
|
||||
@@ -14,9 +14,9 @@ from IPython import embed
|
||||
|
||||
# GENERAL SETTINGS:
|
||||
cross_species = [
|
||||
# 'Chorthippus_biguttulus',
|
||||
'Chorthippus_biguttulus',
|
||||
# 'Chorthippus_mollis',
|
||||
# 'Chrysochraon_dispar',
|
||||
'Chrysochraon_dispar',
|
||||
# 'Euchorthippus_declivus',
|
||||
'Gomphocerippus_rufus',
|
||||
'Omocestus_rufipes',
|
||||
@@ -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])[4]
|
||||
thresh_rel = np.array([0, 0.5, 1, 1.5, 2, 2.5, 3])[5]
|
||||
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)
|
||||
@@ -121,7 +121,7 @@ ylab_up_kwargs = dict(
|
||||
ha='center',
|
||||
va='top',
|
||||
)
|
||||
loc = 0.5
|
||||
loc = 1
|
||||
dot_spec_kwargs = dict(
|
||||
ls='none',
|
||||
marker='o',
|
||||
@@ -171,7 +171,7 @@ text_song_kwargs = dict(
|
||||
text_spec_prefix = '$\\rho\\,=\\,$'
|
||||
text_song_prefix = ['$\\rho\\,=\\,$', ''][0]
|
||||
if test_regression:
|
||||
test_ax_side = 0.15
|
||||
test_ax_side = 0.1
|
||||
test_ax_bounds = [
|
||||
song_grid_kwargs['right'] - test_ax_side,
|
||||
spec_grid_kwargs['bottom'],
|
||||
@@ -179,7 +179,7 @@ if test_regression:
|
||||
test_ax_side
|
||||
]
|
||||
ylab_test = '$\\rho$'
|
||||
yloc_test = 0.5
|
||||
yloc_test = 1
|
||||
ylab_test_kwargs = dict(
|
||||
x=-0.3,
|
||||
fontsize=fs['lab_norm'],
|
||||
|
||||
@@ -18,7 +18,7 @@ target_species = [
|
||||
# 'Gomphocerippus_rufus',
|
||||
# 'Omocestus_rufipes',
|
||||
# 'Pseudochorthippus_parallelus',
|
||||
][0]
|
||||
][1]
|
||||
example_file = {
|
||||
'Chorthippus_biguttulus': 'Chorthippus_biguttulus_GBC_94-17s73.1ms-19s977ms',
|
||||
'Chorthippus_mollis': 'Chorthippus_mollis_DJN_41_T28C-46s4.58ms-1m15s697ms',
|
||||
@@ -28,7 +28,7 @@ example_file = {
|
||||
'Omocestus_rufipes': 'Omocestus_rufipes_DJN_32-40s724ms-48s779ms',
|
||||
'Pseudochorthippus_parallelus': 'Pseudochorthippus_parallelus_GBC_88-6s678ms-9s32.3ms'
|
||||
}[target_species]
|
||||
data_paths = search_files(target_species, dir='../data/processed/')
|
||||
data_paths = search_files(target_species, incl='GBC', dir='../data/processed/')
|
||||
noise_path = '../data/processed/white_noise_sd-1.npz'
|
||||
thresh_path = '../data/inv/full/thresholds.npz'
|
||||
stages = ['filt', 'env', 'log', 'inv', 'conv', 'feat']
|
||||
@@ -55,10 +55,13 @@ thresh_abs = thresh_rel[:, None] * thresh_data['sds'][None, :]
|
||||
for data_path, name in zip(data_paths, crop_paths(data_paths)):
|
||||
save_detailed = example_file in name
|
||||
print(f'Processing {name}')
|
||||
if 'BM04' in name:
|
||||
continue
|
||||
|
||||
# Get song recording (prior to anything):
|
||||
data, config = load_data(data_path, files='raw')
|
||||
song, rate = data['raw'], config['rate']
|
||||
print(song.shape, song.size)
|
||||
|
||||
# Reduce to kernel subset:
|
||||
if any(var is not None for var in [kernels, types, sigmas]):
|
||||
|
||||
Reference in New Issue
Block a user