Alsmost finished introduction.

Few more papers.

cite.bib

@@ -55,6 +55,17 @@
   year={2017},
 }# Cited
 
+@article{bolding2018recurrent,
+  title={Recurrent cortical circuits implement concentration-invariant odor coding},
+  author={Bolding, Kevin A and Franks, Kevin M},
+  journal={Science},
+  volume={361},
+  number={6407},
+  pages={eaat6904},
+  year={2018},
+  publisher={American Association for the Advancement of Science}
+}# Cited
+
 @article{breckow1985mechanics,
   title={Mechanics of the transduction of sound in the tympanal organ of adults and larvae of locusts},
   author={Breckow, Joachim and Sippel, Martin},
@@ -388,6 +399,17 @@
   year={1978},
   publisher={Springer}
 }
+@article{ketkar2023multifaceted,
+  title={Multifaceted luminance gain control beyond photoreceptors in Drosophila},
+  author={Ketkar, Madhura D and Shao, Shuai and Gjorgjieva, Julijana and Silies, Marion},
+  journal={Current Biology},
+  volume={33},
+  number={13},
+  pages={2632--2645},
+  year={2023},
+  publisher={Elsevier}
+}# Cited
+
 @article{kohler2017morphological,
   title={{Morphological and colour morph clines along an altitudinal gradient in the meadow grasshopper Pseudochorthippus parallelus}},
   author={K{\"o}hler, G{\"u}nter and Samietz, J{\"o}rg and Schielzeth, Holger},
@@ -453,6 +475,15 @@
   year={2014},
 }# Cited
 
+@article{mann2025resonant,
+  title={Resonant song recognition and the evolution of acoustic communication in crickets},
+  author={Mann, Winston and Erregger, Bettina and Hennig, Ralf Matthias and Clemens, Jan},
+  journal={iScience},
+  volume={28},
+  number={2},
+  year={2025},
+  publisher={Elsevier}
+}
 @article{meyer1996well,
   title={How well are frequency sensitivities of grasshopper ears tuned to species-specific song spectra?},
   author={Meyer, Jens and Elsner, Norbert},

main.tex

@@ -107,25 +107,42 @@
 \newcommand{\muf}{\mu_{f_i}} % Average feature value
 
 \section{Introduction}
+% % Drosophila/visual/article:
+% \bcite{ketkar2023multifaceted}
 
-% Why functional models of sensory systems?
+% % Drosophila/auditory/article:
-Our scientific understanding of sensory processing systems is based on the
+% \bcite{ozeri2018fast}
-distributed accumulation of specific anatomical, physiological, and ethological
+
-evidence. This leaves us with the challenge of integrating the available
+% % Primate/auditory/review:
-knowledge fragments into a coherent whole in order to address more and more
+% \bcite{barbour2011intensity}
-far-reaching questions, from the interaction between individual processing
+
-steps to comparisons between similar systems across different species. One way
+% % Cricket/auditory/article:
-to deal with this challenge is to build a unified framework that captures the
+% \bcite{benda2008spike}
-essential functional aspects of a sensory system. However, building such a
+
-framework is a challenging task in itself. It requires a wealth of existing
+% % Locust/auditory/article:
-knowledge of the system and the stimuli it operates on, a clearly defined
+% \bcite{clemens2010intensity}
-scope, and careful abstraction of the underlying structures and mechanisms.
+
+% % Rodent/olfactory/article:
+% \bcite{bolding2018recurrent}
+
+% Introduction to intensity invariance:
+Intensity invariance is a fundamental property of sensory systems across
+modalities and species, from fruit flies~(\bcite{ozeri2018fast};
+\bcite{ketkar2023multifaceted}) over crickets~(\bcite{benda2008spike}) and
+grasshoppers~(\bcite{clemens2010intensity}) to
+rodents~(\bcite{bolding2018recurrent}) and
+primates~(\bcite{barbour2011intensity}). It allows for the robust recognition
+of behaviorally relevant stimuli despite variations in stimulus intensity.
+However, the computational mechanisms underlying intensity invariance are often
+difficult to disentangle. Here, we use a physiologically inspired functional
+model of the grasshopper song recognition pathway to investigate the emergence
+of intensity invariance throughout the auditory processing stream.
 
 % 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
+The auditory system of grasshoppers~(\textit{Acrididae}) has been studied
-auditory system of grasshoppers~(\textit{Acrididae}). Grasshoppers rely on
+extensively over the years. Grasshoppers rely on their sense of hearing for
-their sense of hearing for intraspecific communication --- including mate
+intraspecific communication --- including mate
 attraction~(\bcite{helversen1972gesang}) and
 evaluation~(\bcite{stange2012grasshopper}), sender
 localization~(\bcite{helversen1988interaural}), courtship
@@ -143,11 +160,6 @@ 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}).
-% Could go lower to concluding part:
-% 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.
 
 % What are the signals that the auditory system is supposed to recognize?
 Grasshopper songs are amplitude-modulated broad-band acoustic signals. They
@@ -163,144 +175,163 @@ 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 sender, the frequency content of the
+which depends on the distance from the sound source, the frequency content of
-signal, and the vegetation of the habitat~(\bcite{michelsen1978sound}). The
+the signal, and the vegetation of the habitat~(\bcite{michelsen1978sound}).
-amplitude dynamics of the song pattern degrade fairly quickly, which limits the
+Sound attenuation has two major consequences for song recognition. First, the
-effective communication range of grasshoppers to~\mbox{1\,-\,2\,m} in their
+amplitude dynamics of the song pattern degrade with increasing distance to the
-typical grassland habitats~(\bcite{lang2000acoustic}). Moreover, the intensity
+sender, which limits the effective communication range of grasshoppers
-of a song at the receiver's position varies with the location of the sender,
+to~\mbox{1\,-\,2\,m} in their typical grassland
-which should ideally not affect the recognition of the song.
+habitats~(\bcite{lang2000acoustic}). Second, the intensity of a song at the
-
+receiver's position varies with the position of the sender, which should
-This neccessitates that the auditory system achieves a certain degree of
+ideally not affect song recognition. The auditory system thus needs to achieve
-intensity invariance --- a time scale-selective sensitivity to faster amplitude
+a certain degree of intensity invariance --- a time scale-selective sensitivity
-dynamics and simultaneous insensitivity to slower, more sustained amplitude
+to faster amplitude dynamics and simultaneous insensitivity to more sustained
-dynamics. Intensity invariance in different auditory systems is often
+amplitude dynamics. Intensity invariance is commonly associated with neural
-associated with neuronal adaptation~(\bcite{benda2008spike};
+adaptation~(\bcite{benda2008spike}; \bcite{barbour2011intensity};
-\bcite{barbour2011intensity}; \bcite{ozeri2018fast}; more
+\bcite{ozeri2018fast}; more general:~\bcite{benda2021neural}). Different neuron
-general:~\bcite{benda2021neural}). In the grasshopper auditory system, a number
+types in the grasshopper auditory system exhibit spike-frequency adaptation in
-of neuron types along the processing chain exhibit spike-frequency adaptation
+response to sustained stimulation~(\bcite{romer1976informationsverarbeitung};
-in response to sustained stimulus
-intensities~(\bcite{romer1976informationsverarbeitung};
 \bcite{gollisch2004input}; \bcite{hildebrandt2009origin};
-\bcite{clemens2010intensity}; \bcite{fisch2012channel}) and thus likely
+\bcite{clemens2010intensity}; \bcite{fisch2012channel}). Accordingly, intensity
-contribute to the emergence of intensity-invariant song representations. This
+invariance is not the result of a single processing step but rather a gradual
-means that intensity invariance is not the result of a single processing step
+process, in which different neuronal populations contribute to varying
-but rather a gradual process, in which different neuronal populations
+degrees~(\bcite{clemens2010intensity}) and by different
-contribute to varying degrees~(\bcite{clemens2010intensity}) and by different
+mechanisms~(\bcite{hildebrandt2009origin}).
-mechanisms~(\bcite{hildebrandt2009origin}). Approximating this process within a
-functional model framework thus requires a considerable amount of
-simplification. In this work, we demonstrate that even a small number of basic
-physiologically inspired signal transformations --- specifically, pairs of
-nonlinear and linear operations --- is sufficient to achieve a meaningful
-degree of intensity invariance.
 
 % How can song recognition be modelled functionally (feat. Jan Clemens & Co.)?
 % How did we expand on the previous framework?
-% (Still can't stand some of this paragraph's structure and wording...)
+In the current study, we leverage functional modelling to trace the emergence
-Invariance to non-informative song variations is crucial for reliable song
+of intensity invariance through individual processing steps of the grasshopper
-recognition; however, it is not sufficient to this end. In order to recognize a
+song recognition pathway. The model pathway we propose here expands on a
-conspecific song as such, the auditory system needs to extract sufficiently
+previous functional model framework for song recognition --- including feature
-informative features of the song pattern and then integrate the gathered
+extraction, evidence accumulation, and categorical decision making --- in both
-information into a final categorical percept. Previous authors have proposed a
-functional model framework that describes this process --- feature extraction,
-evidence accumulation, and categorical decision making --- in both
 crickets~(\bcite{clemens2013computational}; \bcite{hennig2014time}) and
 grasshoppers~(\bcite{clemens2013feature}; review on
-both:~\bcite{ronacher2015computational}). Their framework provides a
+both:~\bcite{ronacher2015computational}). The exisiting framework relies on
-comprehensible and biologically plausible account of the computational
+pulse trains as input signals, which were designed to capture the essential
-mechanisms required for species-specific song recognition, which has served as
+structural properties of natural song envelopes~(\bcite{clemens2013feature}).
-the inspiration for the development of the model pathway we propose here. The
+We extended this framework by a physiologically plausible preprocessing stage
-existing framework relies on pulse trains as input signals, which were designed
+--- including spectral filtering, envelope extraction, logarithmic compression,
-to capture the essential structural properties of natural song
+and intensity adaptation --- which allows the model to operate on unmodified
-envelopes~(\bcite{clemens2013feature}). In the first step, a bank of parallel
+recordings of natural grasshopper songs. The result is a comprehensible account
-linear-nonlinear feature detectors is applied to the input signal. Each feature
+of the known
-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. For instance, we were able to investigate the contribution
-of different processing stages to the emergence of intensity-invariant song
-representations based on actual field recordings of songs at different
-distances from the sender.
-% Forgive me, it's friday.
-In the following, we outline the structure of the proposed model of the
-grasshopper auditory pathway, from the initial reception of sound waves up to
-the generation of a high-dimensional, time-varying feature representation that
-is suitable for species-specific song recognition. We provide a side-by-side
-account of the known physiological processing steps and their functional
-approximation by basic mathematical operations. We then elaborate on the key
-mechanisms that drive the emergence of intensity-invariant song representations
-within the auditory pathway.
 
-% RIPPED FROM RESULTS, MAYBE INTEGRATE SOMEWHERE HERE:
-% 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 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
-% 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.
 
-% SCRAPPED UNTIL FURTHER NOTICE:
+% Its evolutionary significance makes the grasshopper auditory system ---
-% Multi-species, multi-individual communally inhabited environments\\
+% specifically, the pathway responsible for species-specific song recognition
-% - Temporal overlap: Simultaneous singing across individuals/species common\\
+% --- an intriguing candidate for attempting to construct a functional model
-% - Frequency overlap: Little speciation into frequency bands (likely unused)\\
+% framework.
-% - "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):\\
+% Another, more substantial modification is that
-% From continuous acoustic input, generate neuronal representations that...\\
+% the feature detector outputs are temporally averaged in a way that does not
-% 1)...allow for the separation of relevant (song) events from ambient noise floor\\
+% condense them into single feature values but retains their time-varying
-% 2)...compensate for behaviorally non-informative song variability (invariances)\\
+% structure. This is in line with the fact that songs are no discrete units but
-% 3)...carry sufficient information to characterize different song patterns,
+% part of a continuous acoustic stream that the auditory system has to process in
-% recognize the ones produced by conspecifics, and make appropriate behavioral
+% real time. Moreover, a time-varying feature representation only stabilizes
-% decisions based on context (sender identity, song type, mate/rival quality)
+% 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?\\
+%% BACKUP OF PREVIOUS ITERATION:
-% - What are the minimum functional processing steps required?\\
+% % Why functional models of sensory systems?
-% - Which known neuronal mechanisms can implement these steps?\\
+% Our scientific understanding of sensory processing systems is based on the
-% - Which and how many stages along the auditory pathway contribute?\\
+% distributed accumulation of specific anatomical, physiological, and ethological
-% $\rightarrow$ What are the limitations of the system as a whole?
+% 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?\\
+% % Why the grasshopper auditory system?
-% - How to investigate the workings of the auditory pathway as a whole?\\
+% % Why focus on song recognition among other auditory functions?
-% - How to systematically test effects and interactions of processing parameters?\\
+% One sensory system that has been extensively studied over the years is the
-% - How to integrate the available knowledge on anatomy, physiology, ethology?\\
+% auditory system of grasshoppers~(\textit{Acrididae}). Grasshoppers rely on
-% $\rightarrow$ Abstract, simplify, formalize $\rightarrow$ Functional model framework
+% 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
+patterns. Gabor functions presumably capture the essential structural
-multiplication of a Gaussian envelope with standard deviation or kernel width
+properties of the filter functions found in various auditory
-$\kwi$ and a sinusoidal carrier with frequency $\kfi$ and phase $\kpi$:
+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