From cc701a09f8f18e456a59393e0d4c538251e23554 Mon Sep 17 00:00:00 2001 From: j-hartling Date: Wed, 25 Feb 2026 16:53:49 +0100 Subject: [PATCH] Managed 1st half of results text, began with 2nd half. --- main.aux | 15 +- main.bbl-SAVE-ERROR | 2207 ------------------------------------------- main.blg | 130 +-- main.fdb_latexmk | 16 +- main.log | 66 +- main.pdf | Bin 10362545 -> 10361972 bytes main.synctex.gz | Bin 109642 -> 111485 bytes main.tex | 205 ++-- 8 files changed, 216 insertions(+), 2423 deletions(-) delete mode 100644 main.bbl-SAVE-ERROR diff --git a/main.aux b/main.aux index c20f48f..daf29e3 100644 --- a/main.aux +++ b/main.aux @@ -242,17 +242,16 @@ \newlabel{eq:lowpass}{{10}{9}{}{}{}} \@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces \textbf {Representations of a song of \textit {O. rufipes} during the feature extraction stage.} Different colors indicate Gabor kernels with different lobe number $n$ and sign, with lighter colors for higher $n$~($1\,\leq \,n\,\leq \,4$; both $+$ and $-$ per $n$; two kernel widths $\sigma $ of $4\,$ms and $32\,$ms per sign). \textbf {a}:~Kernel-specific filter responses. \textbf {b}:~Binary responses. \textbf {c}:~Finalized features. }}{10}{}\protected@file@percent } \newlabel{fig:stages_feat}{{3}{10}{}{}{}} -\@writefile{toc}{\contentsline {section}{\numberline {3}Two mechanisms driving the emergence of intensity-invariant song representations}{10}{}\protected@file@percent } +\@writefile{toc}{\contentsline {section}{\numberline {3}Two mechanisms driving the emergence of intensity-invariant song representation}{10}{}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Logarithmic compression \& spike-frequency adaptation}{10}{}\protected@file@percent } \newlabel{eq:toy_env}{{11}{10}{}{}{}} -\newlabel{eq:toy_snr}{{12}{11}{}{}{}} -\newlabel{eq:toy_log}{{13}{11}{}{}{}} -\newlabel{eq:toy_highpass}{{14}{11}{}{}{}} -\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Threshold nonlinearity \& temporal averaging}{12}{}\protected@file@percent } +\newlabel{eq:toy_log}{{12}{11}{}{}{}} +\newlabel{eq:toy_highpass}{{13}{11}{}{}{}} +\newlabel{eq:toy_snr}{{14}{11}{}{}{}} +\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Thresholding nonlinearity \& temporal averaging}{11}{}\protected@file@percent } \newlabel{eq:pdf_split}{{15}{12}{}{}{}} -\newlabel{eq:pdf}{{16}{12}{}{}{}} -\newlabel{eq:feat_avg}{{17}{12}{}{}{}} -\newlabel{eq:feat_prop}{{18}{13}{}{}{}} +\newlabel{eq:feat_avg}{{16}{12}{}{}{}} +\newlabel{eq:feat_prop}{{17}{12}{}{}{}} \abx@aux@cite{0}{stumpner1991auditory} \abx@aux@segm{0}{0}{stumpner1991auditory} \@writefile{toc}{\contentsline {section}{\numberline {4}Discriminating species-specific song\\patterns in feature space}{14}{}\protected@file@percent } diff --git a/main.bbl-SAVE-ERROR b/main.bbl-SAVE-ERROR deleted file mode 100644 index 3536320..0000000 --- a/main.bbl-SAVE-ERROR +++ /dev/null @@ -1,2207 +0,0 @@ -% $ biblatex auxiliary file $ -% $ biblatex bbl format version 3.2 $ -% Do not modify the above lines! -% -% This is an auxiliary file used by the 'biblatex' package. -% This file may safely be deleted. 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BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 21, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 38, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 49, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 58, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 73, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 82, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 91, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 100, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 109, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 118, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 127, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 136, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 157, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 178, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 187, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 196, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 207, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 218, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 229, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 240, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 249, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 258, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 269, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 278, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 289, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 300, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 309, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 328, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 337, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 400, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 419, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 428, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 437, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 456, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 491, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 526, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 535, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 556, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 565, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 576, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 587, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 619, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 648, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 658, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 667, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 688, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 709, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 720, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 729, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 749, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 766, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 775, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 800, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_DBXa/347c261ec4135a5723bef5c751f5078f_38197.utf8, line 817, warning: 6 characters of junk seen at toplevel -[310] Biber.pm:133> INFO - WARNINGS: 55 +[120] bibtex.pm:1519> INFO - Found BibTeX data source 'cite.bib' +[297] UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'variable = shifted' with 'variable = non-ignorable' +[297] UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'normalization = NFD' with 'normalization = prenormalized' +[297] Biber.pm:4239> INFO - Sorting list 'nyt/global//global/global' of type 'entry' with template 'nyt' and locale 'en-US' +[297] Biber.pm:4245> INFO - No sort tailoring available for locale 'en-US' +[322] bbl.pm:660> INFO - Writing 'main.bbl' with encoding 'UTF-8' +[333] bbl.pm:763> INFO - Output to main.bbl +[333] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 10, warning: 6 characters of junk seen at toplevel +[333] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 21, warning: 6 characters of junk seen at toplevel +[333] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 38, warning: 6 characters of junk seen at toplevel +[333] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 49, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 58, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 73, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 82, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 91, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 100, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 109, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 118, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 127, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 136, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 157, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 178, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 187, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 196, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 207, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 218, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 229, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 240, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 249, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 258, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 269, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 278, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 289, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 300, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 309, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 328, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 337, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 400, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 419, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 428, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 437, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 456, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 491, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 526, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 535, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 556, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 565, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 576, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 587, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 619, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 648, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 658, warning: 6 characters of junk seen at toplevel +[334] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 667, warning: 6 characters of junk seen at toplevel +[335] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 688, warning: 6 characters of junk seen at toplevel +[335] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 709, warning: 6 characters of junk seen at toplevel +[335] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 720, warning: 6 characters of junk seen at toplevel +[335] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 729, warning: 6 characters of junk seen at toplevel +[335] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 749, warning: 6 characters of junk seen at toplevel +[335] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 766, warning: 6 characters of junk seen at toplevel +[335] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 775, warning: 6 characters of junk seen at toplevel +[335] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 800, warning: 6 characters of junk seen at toplevel +[335] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_E030/347c261ec4135a5723bef5c751f5078f_66584.utf8, line 817, warning: 6 characters of junk seen at toplevel +[335] Biber.pm:133> INFO - WARNINGS: 55 diff --git a/main.fdb_latexmk b/main.fdb_latexmk index d3ce154..beb530b 100644 --- a/main.fdb_latexmk +++ b/main.fdb_latexmk @@ -1,14 +1,14 @@ # Fdb version 4 -["biber main"] 1771861690.00046 "main.bcf" "main.bbl" "main" 1771861692.33072 0 +["biber main"] 1772034264.18198 "main.bcf" "main.bbl" "main" 1772034759.24472 0 "cite.bib" 1770904753.08918 27483 4290db0c91f7b5055e25472ef913f6b4 "" - 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z7C7j5x2&;&jwL${Y>3hgBI*^eArf2Cqt z7jccpw!8qsNx(6uuss*xpG>=h*Fc(Hoz=-jjUg4jLb(Df?&Ey&r}=yVRyZ)W6r7yz z5MaG$$}mzn*q`Mrap60-t;1~|58AUx)^HxLN4>%4&gwR`CXg3QK%H(pAB zlOW%`E(%ZhS}_nE_k7VnkWL(i&-|9W?O`1#AX&#yO7r#$=^3QKu6 diff --git a/main.tex b/main.tex index 9328699..faaeb0e 100644 --- a/main.tex +++ b/main.tex @@ -29,6 +29,9 @@ mincitenames=1 ]{biblatex} \addbibresource{cite.bib} +%\bibdata +%\bibstyle +%\citation \title{Emergent intensity invariance in a physiologically inspired model of the grasshopper auditory system} \author{Jona Hartling, Jan Benda} @@ -82,7 +85,7 @@ \newcommand{\fwrh}{\text{FWRH}} % Gaussian full-width at relative height \newcommand{\off}{\beta_0} % Offset for linear frequency approximation -% Math shorthands - Threshold nonlinearity: +% Math shorthands - Thresholding nonlinearity: \newcommand{\thr}{\Theta_i} % Step function threshold value \newcommand{\nl}{H(c_i\,-\,\thr)} % Shifted Heaviside step function @@ -90,6 +93,7 @@ \newcommand{\soc}{s} % Song component of synthetic mixture \newcommand{\noc}{\eta} % Noise component of synthetic mixture \newcommand{\sca}{\alpha} % Multiplicative scale of song component +\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) @@ -509,7 +513,7 @@ threshold value $\thr$ to obtain a binary response \label{eq:binary} \end{equation} which can be thought of as a categorization into "relevant" and "irrelevant" -response values. In the grasshopper, these threshold nonlinearities might +response values. In the grasshopper, these thresholding nonlinearities might either be part of the processing within the ascending neurons or take place further downstream~(SOURCE). Finally, the responses of the ascending neurons are assumed to be integrated somewhere in the supraesophageal @@ -543,47 +547,38 @@ can be read out by a simple linear classifier. \end{figure} \FloatBarrier -\section{Two mechanisms driving the emergence of intensity-invariant song representations} +\section{Two mechanisms driving the emergence of intensity-invariant song representation} % Still missing the SNR analysis. Should be able to write around it for now. The robustness of song recognition is tied to the degree of intensity invariance of the finalized feature representation. Ideally, the values of each feature should depend only on the relative amplitude dynamics of the song -pattern but not on the overall intensity level of the song. In the grasshopper, -the emergence of intensity-invariant representations along the song recognition +pattern but not on the overall intensity of the song. In the grasshopper, the +emergence of intensity-invariant representations along the song recognition pathway likely is a distributed process that involves different neuronal populations, which raises the question of what the essential computational mechanisms are that drive this process. Within the model pathway, we identified two key mechanisms that render the song representation more invariant to -variations in baseline intensity. The two mechanisms each comprise a nonlinear -signal transformation followed by a linear signal transformation but differ in -the specific operations and the neural substrate involved, as outlined in the -following sections. +intensity variations. The two mechanisms each comprise a nonlinear signal +transformation followed by a linear signal transformation but differ in the +specific operations involved, as outlined in the following sections. \subsection{Logarithmic compression \& spike-frequency adaptation} -The first emergence of intensity invariance along the model pathway occurs -during the preprocessing stage, in the transition from the signal envelope -$\env(t)$ to the logarithmically scaled envelope $\db(t)$ and then to the -intensity-adapted envelope $\adapt(t)$. In order to disentangle the interplay -of logarithmic compression and adaptation, we can rewrite -$\env(t)$~(Eq.\,\ref{eq:env}) as synthetic mixture +The first notable emergence of intensity invariance along the model pathway +occurs during the transformation of the signal envelope $\env(t)$ into the +logarithmically scaled envelope $\db(t)$ and then into the intensity-adapted +envelope $\adapt(t)$. In order to disentangle the interplay of logarithmic +compression and adaptation, $\env(t)$ can be rewritten as a synthetic mixture \begin{equation} \env(t)\,=\,\sca\,\cdot\,\soc(t)\,+\,\noc(t), \qquad \env(t)\,>\,0\enspace\forall\enspace t\,\in\,\mathbb{R} \label{eq:toy_env} \end{equation} of a song component $\soc(t)$ with variable multiplicative scale $\sca\geq0$ and a fixed-scale noise component $\noc(t)$. Both $\soc(t)$ and $\noc(t)$ are -assumed to have unit variance~($\svar=\nvar=1$). If $\soc(t)$ and $\noc(t)$ are -uncorrelated~($\soc(t)\perp\noc(t)$), the signal-to-noise ratio (SNR) of the -synthetic $\env(t)$ with ($\sca>0$) and without ($\sca=0$) song component -$\soc(t)$ is given by -\begin{equation} - \text{SNR}\,=\,\frac{\sigma_{s+\eta}^{2}}{\nvar}\,=\,\frac{\alpha^{2}\,\cdot\,\svar\,+\,\nvar}{\nvar}\,=\,\alpha^{2}\,+\,1 - \label{eq:toy_snr} -\end{equation} -When simplifying the decibel transformation~(Eq.\,\ref{eq:log}), the logarithmically -scaled envelope $\db(t)$ can be expressed as a sum of two logarithmic terms +assumed to have unit variance. By conversion of $\env(t)$ to decibel +scale~(Eq.\,\ref{eq:log}), $\sca$ turns from a multiplicative scale in linear +space into an additive term, or offset, in logarithmic space \begin{equation} \begin{split} \db(t)\,&=\,\log \frac{\alpha\,\cdot\,s(t)\,+\,\eta(t)}{\dbref}\\ @@ -591,99 +586,90 @@ scaled envelope $\db(t)$ can be expressed as a sum of two logarithmic terms \end{split} \label{eq:toy_log} \end{equation} - - - - -\textbf{Logarithmic component:}\\ -- Simplify decibel transformation (Eq.\,\ref{eq:log}) and apply to synthetic $\env(t)$\\ -- Isolate scale $\alpha$ and reference $\dbref$ using logarithm product/quotient laws - -$\rightarrow$ In log-space, a multiplicative scaling factor becomes additive\\ -$\rightarrow$ Allows for the separation of song signal $s(t)$ and its scale $\alpha$\\ -$\rightarrow$ Introduces scaling of noise term $\eta(t)$ by the inverse of $\alpha$\\ -$\rightarrow$ Normalization by $\dbref$ applies equally to all terms (no individual effects) - -\textbf{Adaptation component:}\\ -- Highpass filter over $\db(t)$ (Eq.\,\ref{eq:highpass}) can -be approximated as subtraction of the local signal offset within a suitable time -interval $\thp$ ($0 \ll \thp < \frac{1}{\fc}$) -% +which allows for its separation from $\soc(t)$ but introduces a scaling of +$\noc(t)$ by the inverse of $\sca$. The subsequent +highpass-filtering~(Eq.\,\ref{eq:highpass}) of $\db(t)$ can then be +approximated as a subtraction of the local offset within a suitable time +interval $0 \ll \thp < \frac{1}{\fc}$: \begin{equation} \begin{split} \adapt(t)\,\approx\,\db(t)\,-\,\log \frac{\alpha}{\dbref}\,=\,\log\left[s(t)\,+\,\frac{\eta(t)}{\alpha}\right] \end{split} \label{eq:toy_highpass} \end{equation} -% -\textbf{Implication for intensity invariance:}\\ -- Logarithmic scaling is essential for equalizing different song intensities\\ -$\rightarrow$ Intensity information can be manipulated more easily when in form -of a signal offset in log-space than a multiplicative scale in linear space - -- Scale $\alpha$ can only be redistributed, not entirely eliminated from $\adapt(t)$\\ -$\rightarrow$ Turn initial scaling of song $s(t)$ by $\alpha$ into scaling of noise $\eta(t)$ by $\frac{1}{\alpha}$ - -- Capability to compensate for intensity variations, i.e. selective amplification -of output $\adapt(t)$ relative to input $\env(t)$, is limited by input SNR (Eq.\,\ref{eq:toy_snr}):\\ -$\alpha\gg1$: Attenuation of $\eta(t)$ term $\rightarrow$ $s(t)$ dominates $\adapt(t)$\\ -$\alpha\approx1$ Negligible effect on $\eta(t)$ term $\rightarrow$ $\adapt(t)=\log[s(t)+\eta(t)]$\\ -$\alpha\ll1$: Amplification of $\eta(t)$ term $\rightarrow$ $\eta(t)$ dominates $\adapt(t)$\\ -$\rightarrow$ Ability to equalize between different sufficiently large scales of $s(t)$\\ -$\rightarrow$ Inability to recover $s(t)$ when initially masked by noise floor $\eta(t)$ - -- Logarithmic scaling emphasizes small amplitudes (song onsets, noise floor) \\ -$\rightarrow$ Recurring trade-off: Equalizing signal intensity vs preserving initial SNR - -\subsection{Threshold nonlinearity \& temporal averaging} - -Convolved $c_i(t)$ $\xrightarrow{\nl}$ Binary $b_i(t)$ $\xrightarrow{\lp}$ Feature $f_i(t)$ - -\textbf{Thresholding component:}\\ -- Within an observed time interval $T$, $c_i(t)$ follows probability density $\pc$\\ -- Within $T$, $c_i(t)$ exceeds threshold value $\thr$ for time $T_1$ ($T_1+T_0=T$)\\ -- Threshold $\nl$ splits $\pc$ around $\thr$ in two complementary parts -% +This means that $\sca$ cannot be entirely eliminated from $\adapt(t)$, only +redistributed between $\soc(t)$ and $\noc(t)$. In consequence, if $\sca$ is +sufficiently large ($\sca\gg1$), $\noc(t)$ is attenuated to the point of being +negligible, so that $\adapt(t)$ represents $\soc(t)$ in a scale-free manner. If +$\soc(t)$ and $\noc(t)$ are at similar scales ($\sca\approx1$), $\adapt(t)$ +largely resembles $\db(t)$. However, if $\sca$ is sufficiently small +($\sca\ll1$), $\noc(t)$ masks $\soc(t)$ even after the intensity adaptation. +Therefore, the effective intensity invariance of $\adapt(t)$ relative to +$\env(t)$ is limited by the initial scaling of $\soc(t)$ relative to $\noc(t)$; +that is, the signal-to-noise ratio (SNR) of $\env(t)$ with ($\sca>0$) and +without ($\sca=0$) song component $\soc(t)$ \begin{equation} - \int_{\thr}^{+\infty} p(c_i,T)\,dc_i\,=\,1\,-\,\int_{-\infty}^{\thr} p(c_i,T)\,dc_i\,=\,\frac{T_1}{T} + \text{SNR}(\sca)\,=\,\frac{\xvar}{\nvar}\,=\,\frac{\alpha^{2}\,\cdot\,\svar\,+\,\nvar}{\nvar}\,=\,\alpha^{2}\,+\,1, \qquad \svar\,=\,\nvar\,=\,1 + \label{eq:toy_snr} +\end{equation} +which depends quadratically on $\sca$ if $\soc(t)$ and $\noc(t)$ are +uncorrelated~($\soc(t)\perp\noc(t)$). In summary, the combination of +logarithmic compression and adaptation allows for the equalization of different +sufficiently large song scales, which is essential for intensity-invariant song +representation. However, this mechanism is unable to recover songs that have +already sunken below the noise floor, which emphasizes the importance of a +sufficiently high SNR at the intial reception of the signal for reliable song +recognition. + +\subsection{Thresholding nonlinearity \& temporal averaging} + +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 +$f_i(t)$. 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 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} -% -$\rightarrow$ Semi-definite integral over right-sided portion of split $\pc$ gives ratio -of time $T_1$ where $c_i(t)>\thr$ to total time $T$ due to normalization of $\pc$ -% +Due to the normalization of $\pc$, the semi-definite integral over the +right-sided part of the split $\pc$ is the ratio of time $T_1$ during which +$c_i(t)$ exceeds $\thr$ within the total time $T$. If the subsequent lowpass +filter~(Eq.\,\ref{eq:lowpass}) over $b_i(t)$ is approximated as temporal +averaging over a suitable time interval +$\tlp>\frac{1}{\fc}$ \begin{equation} - \infint \pc\,dc_i\,=\,1 - \label{eq:pdf} -\end{equation} -% -\textbf{Averaging component:}\\ -- Lowpass filter over binary response $b_i(t)$ (Eq.\,\ref{eq:lowpass}) can be -approximated as temporal averaging over a suitable time interval $\tlp$ ($\tlp > \frac{1}{\fc}$)\\ -- Within $\tlp$, $b_i(t)$ takes a value of 1 ($c_i(t)>\thr$) for time $T_1$ ($T_1+T_0=\tlp$) -% -\begin{equation} - f_i(t)\,\approx\,\frac{1}{\tlp} \int_{t}^{t\,+\,\tlp} b_i(\tau)\,d\tau\,=\,\frac{T_1}{\tlp} + 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} -% -$\rightarrow$ Temporal averaging over $b_i(t)\in[0,1]$ (Eq.\,\ref{eq:binary}) gives -ratio of time $T_1$ where $c_i(t)>\thr$ to total averaging interval $\tlp$\\ -$\rightarrow$ Feature $f_i(t)$ approximately represents supra-threshold fraction of $\tlp$ - -\textbf{Combined result:}\\ -- Feature $f_i(t)$ can be linked to the distribution of $c_i(t)$ using Eqs.\,\ref{eq:pdf_split} \& \ref{eq:feat_avg} -% +feature $f_i(t)$ likewise represents a ratio of time $T_1$ during which +$b_i(t)$ is 1 within the total averaging interval $\tlp$. Since $b_i(t)$ is 1 +where $c_i(t)>\thr$, $f_i(t)$ relates to the probability density of $c_i(t)$ by \begin{equation} f_i(t)\,\approx\,\int_{\thr}^{+\infty} \pclp\,dc_i\,=\,P(c_i\,>\,\thr,\,\tlp) \label{eq:feat_prop} \end{equation} -% -$\rightarrow$ Because the integral over a probability density is a cumulative -probability, the value of feature $f_i(t)$ (temporal compression of $b_i(t)$) -at every time point $t$ signifies the probability that convolution output -$c_i(t)$ exceeds the threshold value $\thr$ during the corresponding 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 $\tlp$. Accordingly, the combination of +thresholding nonlinearity and temporal averaging constitutes a remapping of a +quantity that encodes temporal similarity between signal $\adapt(t)$ and kernel +$k_i(t)$ into a quantity that encodes a duty cycle with respect to $\thr$. + +Accordingly, the combination of +thresholding nonlinearity and temporal averaging constitutes a remapping of the +amplitude-encoding quantity $c_i(t)$ into the duty cycle-encoding quantity +$f_i(t)$ by binning graded amplitude values into one of two categorical states. +This deliberate loss of precise amplitude information is the key to intensity +invariance of the finalized features, as different scales of $c_i(t)$ can +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 +$\thr$. + + + \textbf{Implication for intensity invariance:}\\ - Convolution output $c_i(t)$ quantifies temporal similarity between amplitudes of @@ -743,6 +729,21 @@ large-scale AM, current overall intensity level)\\ $\rightarrow$ Without time scale selectivity, any fully intensity-invariant output will be a flat line + +\textbf{Log-HP: Implication for intensity invariance:}\\ +- Logarithmic scaling is essential for equalizing different song intensities\\ +$\rightarrow$ Intensity information can be manipulated more easily when in form +of a signal offset in log-space than a multiplicative scale in linear space + +- Capability to compensate for intensity variations, i.e. selective amplification +of output $\adapt(t)$ relative to input $\env(t)$, is limited by input SNR (Eq.\,\ref{eq:toy_snr}):\\ +$\rightarrow$ Ability to equalize between different sufficiently large scales of $s(t)$\\ +$\rightarrow$ Inability to recover $s(t)$ when initially masked by noise floor $\eta(t)$ + +- Logarithmic scaling emphasizes small amplitudes (song onsets, noise floor) \\ +$\rightarrow$ Recurring trade-off: Equalizing signal intensity vs preserving initial SNR + + The model pathway includes a rather large number of Gabor kernels compared to the 15 to 20 ascending neurons in the grasshopper auditory system~(\bcite{stumpner1991auditory}).