From d9fb7d3e5d89a95f7a8eb66202c609255e05f2e4 Mon Sep 17 00:00:00 2001 From: j-hartling Date: Thu, 6 Nov 2025 09:27:17 +0100 Subject: [PATCH] Formalizing stuff (WIP). --- cite.bib | 8 + main.aux | 23 +- main.bbl | 53 + main.bbl-SAVE-ERROR | 53 + main.bcf | 2398 +++++++++++++++++++++++++++++++++++++++++++ main.fdb_latexmk | 53 +- main.fls | 79 ++ main.log | 402 +++++++- main.pdf | Bin 58581 -> 129427 bytes main.run.xml | 85 ++ main.synctex.gz | Bin 10952 -> 17705 bytes main.tex | 121 ++- 12 files changed, 3195 insertions(+), 80 deletions(-) create mode 100644 main.bbl create mode 100644 main.bbl-SAVE-ERROR create mode 100644 main.bcf create mode 100644 main.run.xml diff --git a/cite.bib b/cite.bib index e69de29..4a1beb9 100644 --- a/cite.bib +++ b/cite.bib @@ -0,0 +1,8 @@ +@article{clemens2011, + author = "Jan Clemens, Olaf Kutzki; Bernd Ronacher; Susanne Schreiber; Sandra Wohlgemuth", + journal = "PNAS", + volume = "108", + number = "33", + year = "2011", + DOI = "https://doi.org/10.1073/pnas.1104506108", +} diff --git a/main.aux b/main.aux index af21313..294a3bd 100644 --- a/main.aux +++ b/main.aux @@ -1,8 +1,19 @@ \relax +\abx@aux@refcontext{nyt/global//global/global} \@writefile{toc}{\contentsline {section}{\numberline {1}The sensory world of a grasshopper}{1}{}\protected@file@percent } -\@writefile{toc}{\contentsline {section}{\numberline {2}Pre-split pathway: Population pre-processing}{2}{}\protected@file@percent } -\@writefile{toc}{\contentsline {section}{\numberline {3}Post-split pathway: Feature extraction}{2}{}\protected@file@percent } -\@writefile{toc}{\contentsline {section}{\numberline {4}Pre-split intensity invariance:\\Logarithm-highpass mechanism}{3}{}\protected@file@percent } -\@writefile{toc}{\contentsline {section}{\numberline {5}Post-split intensity invariance:\\Threshold-lowpass mechanism}{3}{}\protected@file@percent } -\@writefile{toc}{\contentsline {section}{\numberline {6}Conclusion and outlook}{3}{}\protected@file@percent } -\gdef \@abspage@last{3} +\abx@aux@cite{0}{clemens2011} +\abx@aux@segm{0}{0}{clemens2011} +\@writefile{toc}{\contentsline {section}{\numberline {2}Developing a functional model of\\the grasshopper auditory pathway}{2}{}\protected@file@percent } +\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Population-driven signal pre-processing}{2}{}\protected@file@percent } +\abx@aux@page{1}{2} +\abx@aux@cite{0}{clemens2011} +\abx@aux@segm{0}{0}{clemens2011} +\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Feature extraction by individual neurons}{3}{}\protected@file@percent } +\abx@aux@page{2}{3} +\@writefile{toc}{\contentsline {section}{\numberline {3}Two mechanisms driving the emergence of intensity-invariant song representation}{4}{}\protected@file@percent } +\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Logarithmic scaling \& spike-frequency adaptation}{4}{}\protected@file@percent } +\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Threshold nonlinearity \& temporal averaging}{4}{}\protected@file@percent } +\@writefile{toc}{\contentsline {section}{\numberline {4}Discriminating species-specific song\\patterns in feature space}{4}{}\protected@file@percent } +\@writefile{toc}{\contentsline {section}{\numberline {5}Conclusions \& outlook}{4}{}\protected@file@percent } +\abx@aux@read@bbl@mdfivesum{D9585839A1478809D4C6E9E5BFFC8FE4} +\gdef \@abspage@last{4} diff --git a/main.bbl b/main.bbl new file mode 100644 index 0000000..43be07f --- /dev/null +++ b/main.bbl @@ -0,0 +1,53 @@ +% $ 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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+\newcommand{\bi}{b_\theta} +\newcommand{\feat}{f_\theta} + \section{The sensory world of a grasshopper} Strong dependence on acoustic signals for ranged communication\\ @@ -53,39 +67,108 @@ How can a human observer conceive a grasshopper's auditory percepts?\\ - How to integrate the available knowledge on anatomy, physiology, ethology?\\ $\rightarrow$ Abstract, simplify, formalize $\rightarrow$ Functional model framework -\section{Pre-split pathway: Population pre-processing} + +\section{Developing a functional model of\\the grasshopper auditory pathway} + + +\subsection{Population-driven signal pre-processing} + +"Pre-split portion" of the auditory pathway:\\ +Tympanal membrane $\rightarrow$ Receptor neurons $\rightarrow$ Local interneurons + +Similar response/filter properties within receptor/interneuron populations (\cite{clemens2011})\\ +$\rightarrow$ One population-wide response trace per stage (no "single-cell resolution") + +\textbf{Stage-specific processing steps and functional approximations:} + +Initial: Continuous acoustic input signal $x(t)$ + Filtering of behaviorally relevant frequencies by tympanal membrane\\ -- Bandpass 5-30 kHz +$\rightarrow$ Bandpass filter 5-30 kHz +\begin{equation} + x(t)\,*\,\bp; \quad\quad \fc\,=\,5\,\text{kHz},\,30\,\text{kHz} +\end{equation} Extraction of signal envelope (AM encoding) by receptor population\\ -- Full-wave rectification + lowpass 500 Hz +$\rightarrow$ Full-wave rectification, then lowpass filter 500 Hz +\begin{equation} + |x(t)|\,*\,\lp; \quad\quad \fc\,=\,500\,\text{Hz} +\end{equation} Logarithmically compressed intensity tuning curve of receptors\\ -- Decibel transformation +$\rightarrow$ Decibel transformation +\begin{equation} + 20\,\cdot\,\log_{10} \frac{x(t)}{x_{\text{max}}} +\end{equation} Spike-frequency adaptation in receptor and interneuron populations\\ -- Highpass 10 Hz +$\rightarrow$ Highpass filter 10 Hz +\begin{equation} + x(t)\,*\,\hp; \quad\quad \fc\,=\,10\,\text{Hz} +\end{equation} -\section{Post-split pathway: Feature extraction} -Template matching by individual ascending neurons\\ -- Separate convolution with each of a set of Gabor kernels\\ -- Pathway splitting: Single population response into several separate branches -- Expansion into a higher-dimensional sound representation +\subsection{Feature extraction by individual neurons} + +"Post-split portion" of the auditory pathway:\\ +Ascending neurons (AN) $\rightarrow$ Central brain neurons + +Diverse response/filter properties within AN population (\cite{clemens2011})\\ +- Pathway splitting into several parallel branches\\ +- Expansion into a decorrelated higher-dimensional sound representation\\ +$\rightarrow$ Individual neuron-specific response traces from this stage onwards + +\textbf{Stage-specific processing steps and functional approximations:} + +Template matching by individual ANs\\ +- Filter base (STA approximations): Set of Gabor kernels\\ +- Gabor parameters: $\sigma, \phi, f$ $\rightarrow$ Determines kernel sign and lobe number +\begin{equation} + k(t)\,=\,e^{-\frac{t^{2}}{2\sigma^{2}}}\,\cdot\,\sin(2\pi f t\,+\,\phi) +\end{equation} +$\rightarrow$ Separate convolution with each member of the kernel set +\begin{equation} + c_i(t)\,=\,x(t)\,*\,k_i(t) + = \infint x(\tau)\,\cdot\,k_i(t\,-\,\tau)\,d\tau +\end{equation} Thresholding nonlinearity in ascending neurons (or further downstream)\\ -- Step-function (or sigmoid) threshold\\ -- Binarization of response values into "relevant" vs. "irrelevant" +- Binarization of AN response traces into "relevant" vs. "irrelevant"\\ +$\rightarrow$ Heaviside step-function $H(c\,-\,\theta)$ (or steep sigmoid threshold?) +\begin{equation} + \bi(t)\,=\,\begin{cases} + \;1, \quad c(t)\,\geq\,\theta\\ + \;0, \quad c(t)\,<\,\theta + \end{cases} +\end{equation} Temporal averaging by neurons of the central brain\\ -- Lowpass 1 Hz\\ -- Finalized set of slowly changing kernel-specific features\\ -- Different (species-specific) songs are characterized by a distinct combination of feature values +- Finalized set of slowly changing kernel-specific features (one per AN)\\ +- Different species-specific song patterns are characterized by a distinct combination +of feature values $\rightarrow$ Clusters in high-dimensional feature space\\ +$\rightarrow$ Lowpass filter 1 Hz +\begin{equation} + \feat(t)\,=\,\bi(t)\,*\,\lp; \quad\quad \fc\,=\,1\,\text{Hz} +\end{equation} -\section{Pre-split intensity invariance:\\Logarithm-highpass mechanism} -\section{Post-split intensity invariance:\\Threshold-lowpass mechanism} +\section{Two mechanisms driving the emergence of intensity-invariant song representation} -\section{Conclusion and outlook} + +\subsection{Logarithmic scaling \& spike-frequency adaptation} + +Song signal $s(t)$ with variable scale $\alpha$ and fixed-scale additive noise $\eta(t)$ +\begin{equation} + \alpha\,\cdot\,s(t)\,+\,\eta(t) +\end{equation} + + +\subsection{Threshold nonlinearity \& temporal averaging} + + +\section{Discriminating species-specific song\\patterns in feature space} + + +\section{Conclusions \& outlook} \end{document} \ No newline at end of file