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cite.bib
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@ -178,7 +178,8 @@
volume={11},
pages={20130857},
year={2014},
}
}# Cited
@article{michelsen1971physiology,
title={{The physiology of the locust ear: I. Frequency sensitivity of single cells in the isolated ear}},
author={Michelsen, Axel},
@ -194,7 +195,8 @@
volume={71},
pages={63--101},
year={1971},
}
}# Cited
@article{neuhofer2008evolutionarily,
title={Evolutionarily conserved coding properties of auditory neurons across grasshopper species},
author={Neuhofer, Daniela and Wohlgemuth, Sandra and Stumpner, Andreas and Ronacher, Bernhard},
@ -368,4 +370,4 @@
volume={5},
pages={1435--1443},
year={2008},
}
}# Cited

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@ -1,12 +1,22 @@
\documentclass[a4paper, 12pt]{article}
\usepackage[left=2.5cm,right=2.5cm,top=2cm,bottom=2cm,includeheadfoot]{geometry}
\usepackage{graphicx}
\usepackage{svg}
\usepackage{import}
\usepackage{float}
\usepackage{placeins}
\usepackage{parskip}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage[separate-uncertainty=true, locale=DE]{siunitx}
\sisetup{output-exponent-marker=\ensuremath{\mathrm{e}}}
\usepackage[
backend=biber,
style=authoryear,
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backend=biber,
style=authoryear,
mincitenames=1,
maxcitenames=2
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\addbibresource{cite.bib}
\title{Emergent intensity invariance in a physiologically inspired model of the grasshopper auditory system}
@ -103,9 +113,35 @@ $\rightarrow$ More general, simpler, unfitted formalized Gabor filter bank
\section{Developing a functional model of\\the grasshopper auditory pathway}
\begin{figure}[!ht]
\centering
\def\svgwidth{\textwidth}
\import{figures/}{fig_auditory_pathway.pdf_tex}
\caption[Grasshopper auditory system]{\textbf{The auditory system of
grasshoppers.}}
\label{fig:pathway}
\end{figure}
\FloatBarrier
\subsection{Population-driven signal pre-processing}
Grasshoppers receive airborne sound waves by a tympanal organ at each side of
the thorax. The tympanal membrane~(Fig.\,\ref{fig:pathway}) vibrates in
response to incoming sound waves in a frequency-dependent manner: Vibrations of
specific frequencies are focused on different membrane areas, while other
frequencies are attenuated~(\mbox{\cite{michelsen1971frequency}};
\mbox{\cite{windmill2008time}}; \mbox{\cite{malkin2014energy}}). This
mechanical resonance filter can be modelled by an initial bandpass filter
\begin{equation}
\filt(t)\,=\,\raw(t)\,*\,\bp, \qquad \fc\,=\,5\,\text{kHz},\,30\,\text{kHz}
\label{eq:bandpass}
\end{equation}
applied to the acoustic input signal $\raw(t)$.
"Pre-split portion" of the auditory pathway:\\
Tympanal membrane $\rightarrow$ Receptor neurons $\rightarrow$ Local interneurons
@ -118,12 +154,6 @@ Initial: Continuous acoustic input signal $x(t)$
Filtering of behaviorally relevant frequencies by tympanal membrane\\
$\rightarrow$ Bandpass filter 5-30 kHz
%
\begin{equation}
\filt(t)\,=\,\raw(t)\,*\,\bp, \qquad \fc\,=\,5\,\text{kHz},\,30\,\text{kHz}
\label{eq:bandpass}
\end{equation}
%
Extraction of signal envelope (AM encoding) by receptor population\\
$\rightarrow$ Full-wave rectification, then lowpass filter 500 Hz
%
@ -303,7 +333,7 @@ approximated as temporal averaging over a suitable time interval $\tlp$ ($\tlp >
\label{eq:feat_avg}
\end{equation}
%
$\rightarrow$ Temporal averaging over $\bi(t)\in[0,1]$ (Eq.\ref{eq:binary}) gives
$\rightarrow$ Temporal averaging over $\bi(t)\in[0,1]$ (Eq.\,\ref{eq:binary}) gives
ratio of time $T_1$ where $c_i(t)>\thr$ to total averaging interval $\tlp$\\
$\rightarrow$ Feature $\feat(t)$ approximately represents supra-threshold fraction of $\tlp$