Alsmost finished introduction.
Few more papers.
This commit is contained in:
j-hartling
31
cite.bib
31
cite.bib
@@ -55,6 +55,17 @@
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year={2017},
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}# Cited
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@article{bolding2018recurrent,
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title={Recurrent cortical circuits implement concentration-invariant odor coding},
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author={Bolding, Kevin A and Franks, Kevin M},
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journal={Science},
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volume={361},
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number={6407},
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pages={eaat6904},
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year={2018},
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publisher={American Association for the Advancement of Science}
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}# Cited
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@article{breckow1985mechanics,
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title={Mechanics of the transduction of sound in the tympanal organ of adults and larvae of locusts},
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author={Breckow, Joachim and Sippel, Martin},
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@@ -388,6 +399,17 @@
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year={1978},
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publisher={Springer}
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}
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@article{ketkar2023multifaceted,
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title={Multifaceted luminance gain control beyond photoreceptors in Drosophila},
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author={Ketkar, Madhura D and Shao, Shuai and Gjorgjieva, Julijana and Silies, Marion},
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journal={Current Biology},
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volume={33},
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number={13},
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pages={2632--2645},
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year={2023},
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publisher={Elsevier}
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}# Cited
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@article{kohler2017morphological,
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title={{Morphological and colour morph clines along an altitudinal gradient in the meadow grasshopper Pseudochorthippus parallelus}},
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author={K{\"o}hler, G{\"u}nter and Samietz, J{\"o}rg and Schielzeth, Holger},
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@@ -453,6 +475,15 @@
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year={2014},
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}# Cited
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@article{mann2025resonant,
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title={Resonant song recognition and the evolution of acoustic communication in crickets},
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author={Mann, Winston and Erregger, Bettina and Hennig, Ralf Matthias and Clemens, Jan},
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journal={iScience},
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volume={28},
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number={2},
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year={2025},
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publisher={Elsevier}
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}
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@article{meyer1996well,
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title={How well are frequency sensitivities of grasshopper ears tuned to species-specific song spectra?},
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author={Meyer, Jens and Elsner, Norbert},
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literature/Mann_Erregger_Hennig_Clemens_2025.pdf
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399
main.tex
399
main.tex
@@ -107,25 +107,42 @@
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\newcommand{\muf}{\mu_{f_i}} % Average feature value
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\section{Introduction}
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% % Drosophila/visual/article:
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% \bcite{ketkar2023multifaceted}
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% Why functional models of sensory systems?
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Our scientific understanding of sensory processing systems is based on the
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distributed accumulation of specific anatomical, physiological, and ethological
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evidence. This leaves us with the challenge of integrating the available
|
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knowledge fragments into a coherent whole in order to address more and more
|
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far-reaching questions, from the interaction between individual processing
|
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steps to comparisons between similar systems across different species. One way
|
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to deal with this challenge is to build a unified framework that captures the
|
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essential functional aspects of a sensory system. However, building such a
|
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framework is a challenging task in itself. It requires a wealth of existing
|
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knowledge of the system and the stimuli it operates on, a clearly defined
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scope, and careful abstraction of the underlying structures and mechanisms.
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% % Drosophila/auditory/article:
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% \bcite{ozeri2018fast}
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% % Primate/auditory/review:
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% \bcite{barbour2011intensity}
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% % Cricket/auditory/article:
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% \bcite{benda2008spike}
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% % Locust/auditory/article:
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% \bcite{clemens2010intensity}
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% % Rodent/olfactory/article:
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% \bcite{bolding2018recurrent}
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% Introduction to intensity invariance:
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Intensity invariance is a fundamental property of sensory systems across
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modalities and species, from fruit flies~(\bcite{ozeri2018fast};
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\bcite{ketkar2023multifaceted}) over crickets~(\bcite{benda2008spike}) and
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grasshoppers~(\bcite{clemens2010intensity}) to
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rodents~(\bcite{bolding2018recurrent}) and
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primates~(\bcite{barbour2011intensity}). It allows for the robust recognition
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of behaviorally relevant stimuli despite variations in stimulus intensity.
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However, the computational mechanisms underlying intensity invariance are often
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difficult to disentangle. Here, we use a physiologically inspired functional
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model of the grasshopper song recognition pathway to investigate the emergence
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of intensity invariance throughout the auditory processing stream.
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% Why the grasshopper auditory system?
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% Why focus on song recognition among other auditory functions?
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One sensory system that has been extensively studied over the years is the
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auditory system of grasshoppers~(\textit{Acrididae}). Grasshoppers rely on
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their sense of hearing for intraspecific communication --- including mate
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The auditory system of grasshoppers~(\textit{Acrididae}) has been studied
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extensively over the years. Grasshoppers rely on their sense of hearing for
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intraspecific communication --- including mate
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attraction~(\bcite{helversen1972gesang}) and
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evaluation~(\bcite{stange2012grasshopper}), sender
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localization~(\bcite{helversen1988interaural}), courtship
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@@ -143,11 +160,6 @@ represents a strong evolutionary driving force that resulted in a massive
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species diversification~(\bcite{vedenina2011speciation};
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\bcite{sevastianov2023evolution}), with over 6800 recognized species in the
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\textit{Acrididae} family~(\bcite{cigliano2024orthoptera}).
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% Could go lower to concluding part:
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% Its evolutionary significance makes the grasshopper auditory system ---
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% specifically, the pathway responsible for species-specific song recognition
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% --- an intriguing candidate for attempting to construct a functional model
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% framework.
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% What are the signals that the auditory system is supposed to recognize?
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Grasshopper songs are amplitude-modulated broad-band acoustic signals. They
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@@ -163,144 +175,163 @@ amplitude modulation of the song alone~(\bcite{helversen1997recognition}).
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% Why is intensity invariance important for song recognition?
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Grasshopper songs, like all acoustic signals, are subject to sound attenuation,
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which depends on the distance from the sender, the frequency content of the
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signal, and the vegetation of the habitat~(\bcite{michelsen1978sound}). The
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amplitude dynamics of the song pattern degrade fairly quickly, which limits the
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effective communication range of grasshoppers to~\mbox{1\,-\,2\,m} in their
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typical grassland habitats~(\bcite{lang2000acoustic}). Moreover, the intensity
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of a song at the receiver's position varies with the location of the sender,
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which should ideally not affect the recognition of the song.
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This neccessitates that the auditory system achieves a certain degree of
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intensity invariance --- a time scale-selective sensitivity to faster amplitude
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dynamics and simultaneous insensitivity to slower, more sustained amplitude
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dynamics. Intensity invariance in different auditory systems is often
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associated with neuronal adaptation~(\bcite{benda2008spike};
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\bcite{barbour2011intensity}; \bcite{ozeri2018fast}; more
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general:~\bcite{benda2021neural}). In the grasshopper auditory system, a number
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of neuron types along the processing chain exhibit spike-frequency adaptation
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in response to sustained stimulus
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intensities~(\bcite{romer1976informationsverarbeitung};
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which depends on the distance from the sound source, the frequency content of
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the signal, and the vegetation of the habitat~(\bcite{michelsen1978sound}).
|
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Sound attenuation has two major consequences for song recognition. First, the
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amplitude dynamics of the song pattern degrade with increasing distance to the
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sender, which limits the effective communication range of grasshoppers
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to~\mbox{1\,-\,2\,m} in their typical grassland
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habitats~(\bcite{lang2000acoustic}). Second, the intensity of a song at the
|
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receiver's position varies with the position of the sender, which should
|
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ideally not affect song recognition. The auditory system thus needs to achieve
|
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a certain degree of intensity invariance --- a time scale-selective sensitivity
|
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to faster amplitude dynamics and simultaneous insensitivity to more sustained
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amplitude dynamics. Intensity invariance is commonly associated with neural
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adaptation~(\bcite{benda2008spike}; \bcite{barbour2011intensity};
|
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\bcite{ozeri2018fast}; more general:~\bcite{benda2021neural}). Different neuron
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types in the grasshopper auditory system exhibit spike-frequency adaptation in
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response to sustained stimulation~(\bcite{romer1976informationsverarbeitung};
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\bcite{gollisch2004input}; \bcite{hildebrandt2009origin};
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\bcite{clemens2010intensity}; \bcite{fisch2012channel}) and thus likely
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contribute to the emergence of intensity-invariant song representations. This
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means that intensity invariance is not the result of a single processing step
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but rather a gradual process, in which different neuronal populations
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contribute to varying degrees~(\bcite{clemens2010intensity}) and by different
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mechanisms~(\bcite{hildebrandt2009origin}). Approximating this process within a
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functional model framework thus requires a considerable amount of
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simplification. In this work, we demonstrate that even a small number of basic
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physiologically inspired signal transformations --- specifically, pairs of
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nonlinear and linear operations --- is sufficient to achieve a meaningful
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degree of intensity invariance.
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\bcite{clemens2010intensity}; \bcite{fisch2012channel}). Accordingly, intensity
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invariance is not the result of a single processing step but rather a gradual
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process, in which different neuronal populations contribute to varying
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degrees~(\bcite{clemens2010intensity}) and by different
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mechanisms~(\bcite{hildebrandt2009origin}).
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% How can song recognition be modelled functionally (feat. Jan Clemens & Co.)?
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% How did we expand on the previous framework?
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% (Still can't stand some of this paragraph's structure and wording...)
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Invariance to non-informative song variations is crucial for reliable song
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recognition; however, it is not sufficient to this end. In order to recognize a
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conspecific song as such, the auditory system needs to extract sufficiently
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informative features of the song pattern and then integrate the gathered
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information into a final categorical percept. Previous authors have proposed a
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functional model framework that describes this process --- feature extraction,
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evidence accumulation, and categorical decision making --- in both
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In the current study, we leverage functional modelling to trace the emergence
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of intensity invariance through individual processing steps of the grasshopper
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song recognition pathway. The model pathway we propose here expands on a
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previous functional model framework for song recognition --- including feature
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extraction, evidence accumulation, and categorical decision making --- in both
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crickets~(\bcite{clemens2013computational}; \bcite{hennig2014time}) and
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grasshoppers~(\bcite{clemens2013feature}; review on
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both:~\bcite{ronacher2015computational}). Their framework provides a
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comprehensible and biologically plausible account of the computational
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mechanisms required for species-specific song recognition, which has served as
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the inspiration for the development of the model pathway we propose here. The
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existing framework relies on pulse trains as input signals, which were designed
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to capture the essential structural properties of natural song
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envelopes~(\bcite{clemens2013feature}). In the first step, a bank of parallel
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linear-nonlinear feature detectors is applied to the input signal. Each feature
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detector consists of a convolutional filter and a subsequent sigmoidal
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nonlinearity. The outputs of these feature detectors are temporally averaged to
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obtain a single feature value per detector, which is then assigned a specific
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weight. The linear combination of weighted feature values results in a single
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preference value, that serves as predictor for the behavioral response of the
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animal to the presented input signal. Our model pathway adopts the general
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structure of the existing framework but modifies it in several key aspects. The
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convolutional filters, which have previously been fitted to behavioral data for
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each individual species~(\bcite{clemens2013computational}), are replaced by a
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larger, generic set of unfitted Gabor basis functions in order to cover a wide
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range of possible song features across different species. Gabor functions
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approximate the general structure of the filters used in the existing framework
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as well as the filter functions found in various auditory
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neurons~(\bcite{rokem2006spike}; \bcite{clemens2011efficient};
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\bcite{clemens2012nonlinear}). The fitted sigmoidal nonlinearities in the
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existing framework consistently exhibited very steep slopes and are therefore
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replaced by shifted Heaviside step-functions, which results in a binarization
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of the feature detector outputs. Another, more substantial modification is that
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the feature detector outputs are temporally averaged in a way that does not
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condense them into single feature values but retains their time-varying
|
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structure. This is in line with the fact that songs are no discrete units but
|
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part of a continuous acoustic stream that the auditory system has to process in
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real time. Moreover, a time-varying feature representation only stabilizes
|
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after a certain delay following the onset of a song, which emphasizes the
|
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temporal dynamics of evidence accumulation towards a final categorical
|
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decision. The most notable difference between our model pathway and the
|
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existing framework, however, lays in the addition of a physiologically inspired
|
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preprocessing stage, whose starting point corresponds to the initial reception
|
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of airborne sound waves. This allows the model to operate on unmodified
|
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recordings of natural grasshopper songs instead of condensed pulse train
|
||||
approximations, which widens its scope towards more realistic, ecologically
|
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relevant scenarios. For instance, we were able to investigate the contribution
|
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of different processing stages to the emergence of intensity-invariant song
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representations based on actual field recordings of songs at different
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distances from the sender.
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% Forgive me, it's friday.
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In the following, we outline the structure of the proposed model of the
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grasshopper auditory pathway, from the initial reception of sound waves up to
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the generation of a high-dimensional, time-varying feature representation that
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is suitable for species-specific song recognition. We provide a side-by-side
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account of the known physiological processing steps and their functional
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approximation by basic mathematical operations. We then elaborate on the key
|
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mechanisms that drive the emergence of intensity-invariant song representations
|
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within the auditory pathway.
|
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both:~\bcite{ronacher2015computational}). The exisiting framework relies on
|
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pulse trains as input signals, which were designed to capture the essential
|
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structural properties of natural song envelopes~(\bcite{clemens2013feature}).
|
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We extended this framework by a physiologically plausible preprocessing stage
|
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--- including spectral filtering, envelope extraction, logarithmic compression,
|
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and intensity adaptation --- which allows the model to operate on unmodified
|
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recordings of natural grasshopper songs. The result is a comprehensible account
|
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of the known
|
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|
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% RIPPED FROM RESULTS, MAYBE INTEGRATE SOMEWHERE HERE:
|
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% The robustness of song recognition is tied to the degree of intensity
|
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% invariance of the finalized feature representation. Ideally, the values of each
|
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% feature should depend only on the relative amplitude dynamics of the song
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% pattern but not on the overall intensity of the song. In the grasshopper, the
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% emergence of intensity-invariant representations along the song recognition
|
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% pathway likely is a distributed process that involves different neuronal
|
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% populations, which raises the question of what the essential computational
|
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% mechanisms are that drive this process. Within the model pathway, we identified
|
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% two key mechanisms that render the song representation more invariant to
|
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% intensity variations. The two mechanisms each comprise a nonlinear signal
|
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% transformation followed by a linear signal transformation but differ in the
|
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% specific operations involved, as outlined in the following sections.
|
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|
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% SCRAPPED UNTIL FURTHER NOTICE:
|
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% Multi-species, multi-individual communally inhabited environments\\
|
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% - Temporal overlap: Simultaneous singing across individuals/species common\\
|
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% - Frequency overlap: Little speciation into frequency bands (likely unused)\\
|
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% - "Biotic noise": Hetero-/conspecifics ("Another one's songs are my noise")\\
|
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% - "Abiotic noise": Wind, water, vegetation, anthropogenic\\
|
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% - Effects of habitat structure on sound propagation (landscape - soundscape)\\
|
||||
% $\rightarrow$ Sensory constraints imposed by the (acoustic) environment
|
||||
% Its evolutionary significance makes the grasshopper auditory system ---
|
||||
% specifically, the pathway responsible for species-specific song recognition
|
||||
% --- an intriguing candidate for attempting to construct a functional model
|
||||
% framework.
|
||||
|
||||
% Cluster of auditory challenges (interlocking constraints $\rightarrow$ tight coupling):\\
|
||||
% From continuous acoustic input, generate neuronal representations that...\\
|
||||
% 1)...allow for the separation of relevant (song) events from ambient noise floor\\
|
||||
% 2)...compensate for behaviorally non-informative song variability (invariances)\\
|
||||
% 3)...carry sufficient information to characterize different song patterns,
|
||||
% recognize the ones produced by conspecifics, and make appropriate behavioral
|
||||
% decisions based on context (sender identity, song type, mate/rival quality)
|
||||
% Another, more substantial modification is that
|
||||
% the feature detector outputs are temporally averaged in a way that does not
|
||||
% condense them into single feature values but retains their time-varying
|
||||
% structure. This is in line with the fact that songs are no discrete units but
|
||||
% part of a continuous acoustic stream that the auditory system has to process in
|
||||
% real time. Moreover, a time-varying feature representation only stabilizes
|
||||
% after a certain delay following the onset of a song, which emphasizes the
|
||||
% temporal dynamics of evidence accumulation towards a final categorical
|
||||
% decision. The most notable difference between our model pathway and the
|
||||
% existing framework, however, lays in the addition of a physiologically inspired
|
||||
% preprocessing stage, whose starting point corresponds to the initial reception
|
||||
% of airborne sound waves. This allows the model to operate on unmodified
|
||||
% recordings of natural grasshopper songs instead of condensed pulse train
|
||||
% approximations, which widens its scope towards more realistic, ecologically
|
||||
% relevant scenarios.
|
||||
|
||||
% How can the auditory system of grasshoppers meet these challenges?\\
|
||||
% - What are the minimum functional processing steps required?\\
|
||||
% - Which known neuronal mechanisms can implement these steps?\\
|
||||
% - Which and how many stages along the auditory pathway contribute?\\
|
||||
% $\rightarrow$ What are the limitations of the system as a whole?
|
||||
%% BACKUP OF PREVIOUS ITERATION:
|
||||
% % Why functional models of sensory systems?
|
||||
% Our scientific understanding of sensory processing systems is based on the
|
||||
% distributed accumulation of specific anatomical, physiological, and ethological
|
||||
% evidence. This leaves us with the challenge of integrating the available
|
||||
% knowledge fragments into a coherent whole in order to address more and more
|
||||
% far-reaching questions, from the interaction between individual processing
|
||||
% steps to comparisons between similar systems across different species. One way
|
||||
% to deal with this challenge is to build a unified framework that captures the
|
||||
% essential functional aspects of a sensory system. However, building such a
|
||||
% framework is a challenging task in itself. It requires a wealth of existing
|
||||
% knowledge of the system and the stimuli it operates on, a clearly defined
|
||||
% scope, and careful abstraction of the underlying structures and mechanisms.
|
||||
|
||||
% How can a human observer conceive a grasshopper's auditory percepts?\\
|
||||
% - How to investigate the workings of the auditory pathway as a whole?\\
|
||||
% - How to systematically test effects and interactions of processing parameters?\\
|
||||
% - How to integrate the available knowledge on anatomy, physiology, ethology?\\
|
||||
% $\rightarrow$ Abstract, simplify, formalize $\rightarrow$ Functional model framework
|
||||
% % Why the grasshopper auditory system?
|
||||
% % Why focus on song recognition among other auditory functions?
|
||||
% One sensory system that has been extensively studied over the years is the
|
||||
% auditory system of grasshoppers~(\textit{Acrididae}). Grasshoppers rely on
|
||||
% their sense of hearing for intraspecific communication --- including mate
|
||||
% attraction~(\bcite{helversen1972gesang}) and
|
||||
% evaluation~(\bcite{stange2012grasshopper}), sender
|
||||
% localization~(\bcite{helversen1988interaural}), courtship
|
||||
% display~(\bcite{elsner1968neuromuskularen}), and rival
|
||||
% deterrence~(\bcite{greenfield1993acoustic}) --- and have evolved a variety of
|
||||
% acoustic signals for different behavioral
|
||||
% contexts~(\bcite{otte1970comparative}). The most conspicuous acoustic signals
|
||||
% of grasshoppers are their species-specific calling songs, which broadcast the
|
||||
% presence of the singing individual to potential mates within range. These songs
|
||||
% are usually more characteristic of a species than morphological
|
||||
% traits~(\bcite{tishechkin2016acoustic}; \bcite{tarasova2021eurasius}), which
|
||||
% can vary greatly within species~(\bcite{rowell1972variable};
|
||||
% \bcite{kohler2017morphological}). The reliance on songs to mediate reproduction
|
||||
% represents a strong evolutionary driving force that resulted in a massive
|
||||
% species diversification~(\bcite{vedenina2011speciation};
|
||||
% \bcite{sevastianov2023evolution}), with over 6800 recognized species in the
|
||||
% \textit{Acrididae} family~(\bcite{cigliano2024orthoptera}).
|
||||
|
||||
% % What are the signals that the auditory system is supposed to recognize?
|
||||
% Grasshopper songs are amplitude-modulated broad-band acoustic signals. They
|
||||
% consist of a series of noisy syllables and relatively quiet pauses, which form
|
||||
% a characteristic repetitive pattern~(\bcite{helversen1977stridulatory};
|
||||
% \bcite{stumpner1994song}). Song recognition depends on certain structural
|
||||
% parameters of this pattern --- such as the duration of syllables and
|
||||
% pauses~(\bcite{helversen1972gesang}), the slope of pulse
|
||||
% onsets~(\bcite{helversen1993absolute}), and the accentuation of syllable onsets
|
||||
% relative to the preceeding pause~(\bcite{balakrishnan2001song};
|
||||
% \bcite{helversen2004acoustic}) --- which are sufficiently conveyed by the
|
||||
% amplitude modulation of the song alone~(\bcite{helversen1997recognition}).
|
||||
|
||||
% % Why is intensity invariance important for song recognition?
|
||||
% Grasshopper songs, like all acoustic signals, are subject to sound attenuation,
|
||||
% which depends on the distance from the sound source, the frequency content of
|
||||
% the signal, and the vegetation of the habitat~(\bcite{michelsen1978sound}).
|
||||
% This has two major consequences for the receiving auditory system. First, the
|
||||
% amplitude dynamics of the song pattern degrade with increasing distance to the
|
||||
% sender, which limits the effective communication range of grasshoppers
|
||||
% to~\mbox{1\,-\,2\,m} in their typical grassland
|
||||
% habitats~(\bcite{lang2000acoustic}). Second, the intensity of a song at the
|
||||
% receiver's position varies with the position of the sender, which should
|
||||
% ideally not affect song recognition. The auditory system thus needs to achieve
|
||||
% a certain degree of intensity invariance --- a time scale-selective sensitivity
|
||||
% to faster amplitude dynamics and simultaneous insensitivity to more sustained
|
||||
% amplitude dynamics. Intensity invariance is commonly associated with neuronal
|
||||
% adaptation~(\bcite{benda2008spike}; \bcite{barbour2011intensity};
|
||||
% \bcite{ozeri2018fast}; more general:~\bcite{benda2021neural}). Different neuron
|
||||
% types in the grasshopper auditory system exhibit spike-frequency adaptation in
|
||||
% response to sustained stimulation~(\bcite{romer1976informationsverarbeitung};
|
||||
% \bcite{gollisch2004input}; \bcite{hildebrandt2009origin};
|
||||
% \bcite{clemens2010intensity}; \bcite{fisch2012channel}). Accordingly, intensity
|
||||
% invariance is not the result of a single processing step but rather a gradual
|
||||
% process, in which different neuronal populations contribute to varying
|
||||
% degrees~(\bcite{clemens2010intensity}) and by different
|
||||
% mechanisms~(\bcite{hildebrandt2009origin}).
|
||||
|
||||
% % How can song recognition be modelled functionally (feat. Jan Clemens & Co.)?
|
||||
% % How did we expand on the previous framework?
|
||||
% In the current study, we use a physiologically inspired functional model of the
|
||||
% grasshopper song recognition pathway to investigate the emergence of intensity
|
||||
% invariance along the auditory processing stream. The model pathway expands on a
|
||||
% previous functional model framework for song recognition --- including feature
|
||||
% extraction, evidence accumulation, and categorical decision making --- in both
|
||||
% crickets~(\bcite{clemens2013computational}; \bcite{hennig2014time}) and
|
||||
% grasshoppers~(\bcite{clemens2013feature}; review on
|
||||
% both:~\bcite{ronacher2015computational}). The exisiting framework relies on
|
||||
% pulse trains as input signals, which were designed to capture the essential
|
||||
% structural properties of natural song envelopes~(\bcite{clemens2013feature}).
|
||||
% The extracted song features are compressed into a single preference value for
|
||||
% each presented input signal, which serves as predictor for the behavioral
|
||||
% response of the animal. We extended this framework by a physiologically
|
||||
% plausible preprocessing stage --- including envelope extraction, logarithmic
|
||||
% compression, and intensity adaptation --- that allows the model to operate on
|
||||
% recordings of natural grasshopper songs. Furthermore, we modified the feature
|
||||
% extraction stage in a way that retains the time-varying structure of individual
|
||||
% song features.
|
||||
|
||||
\section{Methods}
|
||||
% This maybe does not quite fit here, but it is the most general part of the
|
||||
@@ -449,9 +480,13 @@ $i$-th ascending neuron:
|
||||
\label{eq:conv}
|
||||
\end{equation}
|
||||
We use Gabor kernels as basis functions for creating different template
|
||||
patterns. An arbitrary one-dimensional, real Gabor kernel is generated by
|
||||
multiplication of a Gaussian envelope with standard deviation or kernel width
|
||||
$\kwi$ and a sinusoidal carrier with frequency $\kfi$ and phase $\kpi$:
|
||||
patterns. Gabor functions presumably capture the essential structural
|
||||
properties of the filter functions found in various auditory
|
||||
neurons~(\bcite{rokem2006spike}; \bcite{clemens2011efficient};
|
||||
\bcite{clemens2012nonlinear}). An arbitrary one-dimensional, real Gabor kernel
|
||||
is generated by multiplication of a Gaussian envelope with standard deviation
|
||||
or kernel width $\kwi$ and a sinusoidal carrier with frequency $\kfi$ and phase
|
||||
$\kpi$:
|
||||
\begin{equation}
|
||||
k_i(t,\,\kwi,\,\kfi,\,\kpi)\,=\,e^{-\frac{t^{2}}{2{\kwi}^{2}}}\,\cdot\,\sin(\kfi\,t\,+\,\kpi), \qquad \kfi\,=\,2\pi f_{\text{sin}_i}
|
||||
\label{eq:gabor}
|
||||
@@ -1596,6 +1631,70 @@ natural song variation.
|
||||
|
||||
\section{Conclusions \& outlook}
|
||||
|
||||
% RIPPED FROM INTRODUCTION:
|
||||
% Multi-species, multi-individual communally inhabited environments\\
|
||||
% - Temporal overlap: Simultaneous singing across individuals/species common\\
|
||||
% - Frequency overlap: Little speciation into frequency bands (likely unused)\\
|
||||
% - "Biotic noise": Hetero-/conspecifics ("Another one's songs are my noise")\\
|
||||
% - "Abiotic noise": Wind, water, vegetation, anthropogenic\\
|
||||
% - Effects of habitat structure on sound propagation (landscape - soundscape)\\
|
||||
% $\rightarrow$ Sensory constraints imposed by the (acoustic) environment
|
||||
|
||||
% Cluster of auditory challenges (interlocking constraints $\rightarrow$ tight coupling):\\
|
||||
% From continuous acoustic input, generate neuronal representations that...\\
|
||||
% 1)...allow for the separation of relevant (song) events from ambient noise floor\\
|
||||
% 2)...compensate for behaviorally non-informative song variability (invariances)\\
|
||||
% 3)...carry sufficient information to characterize different song patterns,
|
||||
% recognize the ones produced by conspecifics, and make appropriate behavioral
|
||||
% decisions based on context (sender identity, song type, mate/rival quality)
|
||||
|
||||
% How can the auditory system of grasshoppers meet these challenges?\\
|
||||
% - What are the minimum functional processing steps required?\\
|
||||
% - Which known neuronal mechanisms can implement these steps?\\
|
||||
% - Which and how many stages along the auditory pathway contribute?\\
|
||||
% $\rightarrow$ What are the limitations of the system as a whole?
|
||||
|
||||
% How can a human observer conceive a grasshopper's auditory percepts?\\
|
||||
% - How to investigate the workings of the auditory pathway as a whole?\\
|
||||
% - How to systematically test effects and interactions of processing parameters?\\
|
||||
% - How to integrate the available knowledge on anatomy, physiology, ethology?\\
|
||||
% $\rightarrow$ Abstract, simplify, formalize $\rightarrow$ Functional model framework
|
||||
|
||||
\textbf{Differences between the model pathway and the previous framework:}
|
||||
In the first step, a bank of parallel linear-nonlinear feature detectors is
|
||||
applied to the input signal. Each feature detector consists of a convolutional
|
||||
filter and a subsequent sigmoidal nonlinearity. The outputs of these feature
|
||||
detectors are temporally averaged to obtain a single feature value per
|
||||
detector, which is then assigned a specific weight. The linear combination of
|
||||
weighted feature values results in a single preference value, that serves as
|
||||
predictor for the behavioral response of the animal to the presented input
|
||||
signal. Our model pathway adopts the general structure of the existing
|
||||
framework but modifies it in several key aspects. The convolutional filters,
|
||||
which have previously been fitted to behavioral data for each individual
|
||||
species~(\bcite{clemens2013computational}), are replaced by a larger, generic
|
||||
set of unfitted Gabor basis functions in order to cover a wide range of
|
||||
possible song features across different species. Gabor functions approximate
|
||||
the general structure of the filters used in the existing framework as well as
|
||||
the filter functions found in various auditory neurons~(\bcite{rokem2006spike};
|
||||
\bcite{clemens2011efficient}; \bcite{clemens2012nonlinear}). The fitted
|
||||
sigmoidal nonlinearities in the existing framework consistently exhibited very
|
||||
steep slopes and are therefore replaced by shifted Heaviside step-functions,
|
||||
which results in a binarization of the feature detector outputs. Another, more
|
||||
substantial modification is that the feature detector outputs are temporally
|
||||
averaged in a way that does not condense them into single feature values but
|
||||
retains their time-varying structure. This is in line with the fact that songs
|
||||
are no discrete units but part of a continuous acoustic stream that the
|
||||
auditory system has to process in real time. Moreover, a time-varying feature
|
||||
representation only stabilizes after a certain delay following the onset of a
|
||||
song, which emphasizes the temporal dynamics of evidence accumulation towards a
|
||||
final categorical decision. The most notable difference between our model
|
||||
pathway and the existing framework, however, lays in the addition of a
|
||||
physiologically inspired preprocessing stage, whose starting point corresponds
|
||||
to the initial reception of airborne sound waves. This allows the model to
|
||||
operate on unmodified recordings of natural grasshopper songs instead of
|
||||
condensed pulse train approximations, which widens its scope towards more
|
||||
realistic, ecologically relevant scenarios.
|
||||
|
||||
\textbf{The role of repetitive songs for the feature representation:}
|
||||
Most grasshopper songs are produced by stridulation, which refers to the
|
||||
pulling of the serrated stridulatory file on the hindlegs across a resonating
|
||||
|
||||
Reference in New Issue
Block a user