Good day. Finished invariance introduction paragraph. Added more sources.

main.tex

@@ -93,10 +93,11 @@ formalization of the underlying structures and mechanisms.
 One sensory system about which extensive information has been gathered over the
 years is the auditory system of grasshoppers~(\textit{Acrididae}). Grasshoppers
 rely on their sense of hearing primarily for intraspecific communication, which
-includes mate attraction and evaluation~(\bcite{helversen1972gesang},
-\bcite{helversen1993absolute}, \bcite{helversen1997recognition}), sender
-localization~(\bcite{helversen1988interaural}), courtship display~(SOURCE),
-rival deterrence~(\bcite{greenfield1993acoustic}), and loss-of-signal predator
+includes mate attraction~(\bcite{helversen1972gesang}) and
+evaluation~(\bcite{stange2012grasshopper}), sender
+localization~(\bcite{helversen1988interaural}), courtship
+display~(\bcite{elsner1968neuromuskularen}), rival
+deterrence~(\bcite{greenfield1993acoustic}), and loss-of-signal predator
 alarm~(SOURCE). In accordance with this rich behavioral repertoire,
 grasshoppers have evolved a variety of sound production mechanisms to generate
 acoustic communication signals for different contexts and ranges using their
@@ -131,34 +132,62 @@ forewings~(\bcite{helversen1977stridulatory}, \bcite{stumpner1994song},
 a brief pulse of sound. Multiple pulses make up a syllable; and the alternation
 of syllables and relatively quiet pauses forms a characteristic, through noisy,
 waveform pattern. Song recognition depends on certain temporal and structural
-properties of this pattern, such as the slope of pulse
-onsets~(\bcite{helversen1993absolute}), the accentuation of syllable
-onsets~(\bcite{balakrishnan2001song}, \bcite{helversen2004acoustic}), and the
-ratio of syllable duration to pause duration~(\bcite{helversen1972gesang}).
-This signal design
+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}). The amplitude modulation, or envelope, of the
+song is sufficient for recognition~(\bcite{helversen1997recognition}). However,
+the essential recognition cues can vary considerably with external physical
+factors, which requires the auditory system to be invariant to such variations
+in order to reliably recognize songs under different conditions. For instance,
+the temporal structure of grasshopper songs warps with
+temperature~(\bcite{skovmand1983song}). The auditory system can compensate for
+this variability by reading out relative temporal relationships rather than
+absolute time intervals~(\bcite{creutzig2009timescale},
+\bcite{creutzig2010timescale}), as those remain relatively constant across
+different temperatures~(\bcite{helversen1972gesang}). Another, perhaps even
+more fundamental external source of song variability lays in the attenuation of
+sound intensity with increasing distance to the sender. Sound attenuation
+depends on both the frequency content of the signal and the vegetation of the
+habitat~(\bcite{michelsen1978sound}). For the receiving auditory system, this
+has two major implications. First, the amplitude dynamics of the song pattern
+are steadily degraded over distance, which limits the effective communication
+range of grasshoppers to~\mbox{1\,-\,2\,m} in their typical grassland
+habitats~(\bcite{lang2000acoustic}). Second, the overall intensity level of
+songs at the receiver's position varies depending on the location of the
+sender, which should ideally not affect the recognition of the song pattern.
+This neccessitates that the auditory system achieves a certain degree of
+intensity invariance --- a time scale-selective sensitivity to faster amplitude
+dynamics and simultaneous insensitivity to slower, more sustained amplitude
+dynamics. Intensity invariance in different auditory systems is often
+associated with neuronal adaptation~(\bcite{benda2008spike},
+\bcite{barbour2011intensity}, \bcite{ozeri2018fast}), which represents an
+important principle of dynamic sensory systems in
+general~(\bcite{benda2021neural}). In the grasshopper auditory system, a number
+of neuron types along the processing chain exhibit spike-frequency adaptation
+in response to sustained stimulus
+intensities~(\bcite{romer1976informationsverarbeitung},
+\bcite{gollisch2002energy}, \bcite{hildebrandt2009origin},
+\bcite{clemens2010intensity}) and thus likely contribute to the emergence of
+intensity-invariant song representations. This means that 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}). 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. Due to the critical role of intensity-invariant
+representations for reliable song recognition, these transformations are at the
+core of the proposed model framework.
 
 
-The
-amplitude modulation, or envelope, of the song is sufficient for successful
-recognition~(\bcite{helversen1997recognition}). Because grasshoppers are
-poikilothermic, the temporal structure of their songs warps with
-temperature~(\bcite{skovmand1983song}), which poses a major challenge for the
-auditory system. 
-
-
-
-
-Songs = Amplitude-modulated (AM) broad-band acoustic signals\\
-- Generated by stridulatory movement of hindlegs against forewings\\
-- Shorter time scales: Characteristic temporal waveform pattern\\
-- Longer time scales: High degree of periodicity (pattern repetition)\\
-- Sound propagation: Signal intensity varies strongly with distance to sender\\
-- Ectothermy: Temporal structure warps with temperature\\
-$\rightarrow$ Sensory constraints imposed by properties of the acoustic signal itself
 
 Multi-species, multi-individual communally inhabited environments\\
 - Temporal overlap: Simultaneous singing across individuals/species common\\
-- Frequency overlap: No/hardly any niche speciation into frequency bands\\
+- 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)\\