The biophysics and biochemistry of a cochlea-like organ in the ear of Neotropical bush-crickets (Insecta: Tettigonidae)

There has been an increasing interest in the study of complex auditory processes in the mammalian cochlea (e.g. frequency resolution, frequency discrimination and active amplification). These processes depend on the propagation of frequency information in the form of travelling waves (of the type exemplified in a tsunami) along the tonotopically arranged auditory sensilla. The physiological and biophysical bases of traveling waves in the mammalian cochlea remain elusive, yet vital to understanding tonotopy (the mapping of sound frequency across space) and active amplification. In vertebrates, both location and osseous protective material make the inner ear difficult to access without altering its integrity. While conventional methods for hearing research in vertebrates have improved notably in recent years, these still require surgical procedures to gain physical access to the inner ear, compromising the natural conditions of the hearing system. Indeed, measurement of auditory activity in-vivo has only been done through small surgical openings or other isolated places. Remarkably, complex auditory processes are not unique to vertebrates, and similar mechanisms for sound filtering, amplification, and frequency analysis have also been found in the ears of insects. Hearing organs in insects are unusually small, highly sensitive, and easily accessible by means of non-destructive methods. Among insects, bushcrickets (Insecta: Orthoptera) have a unique hearing system which consists of minute tympanal ears located in the forelegs, and inner ears with tonotopically organised auditory sensilla within a fluid-filled cavity. Unlike in vertebrates, the bush-cricket inner ear is not coiled, but stretched. Critically, the assessment of auditory processes in this small-scale ear is proposed to be possible in a non- vi invasive manner. The purpose of this thesis was to further the knowledge of acoustic perception in bush-crickets by providing new data on the travelling wave phenomenon, the suitability of bush-crickets for non-invasive experimentation, and the elemental composition of the liquid contained in the bush-cricket inner ear. It was demonstrated that transparency is the cuticle property that allows the observation and measurement of travelling waves and tonotopy in bush-crickets through the use of light measurement techniques, specifically laser Doppler vibrometry. This approach provides a non-invasive alternative for measuring the natural motion of the sensillia-bearing surface embedded in the intact inner ear’s fluid. Subsequently, this experimental technique was used to generate novel data on inner ear mechanics from a number of bush-cricket species. Finally, in the form of a chemical analysis, I established that the inner ear’s liquid differs from the hemolymph based on the variation of their ion concentration values. From a biomechanical perspective, the presence of a liquid-filled cavity along with a species-specific ion concentration, likely contributes to an optimal functioning of the hearing organ just as it occurs in vertebrates. These results highlight the importance of considering analogous models of vertebrate hearing systems for advanced studies of auditory function. Such models can be used to effectively observe, collect, and measure auditory data otherwise impossible to attain noninvasively in vertebrates, and specifically mammalian species

Compositional nonlinear audio signal processing with Volterra series

We develop a compositional theory of nonlinear audio signal processing based on a categorification of the Volterra series. We augment the classical definition of the Volterra series to be functorial with respect to a base category whose objects are temperate distributions and whose morphisms are certain linear transformations. This leads to formulae describing how the outcomes of nonlinear transformations are affected if their input signals are first linearly processed. We then consider how nonlinear audio systems change, and introduce as a model thereof the notion of morphism of Volterra series. We show how morphisms can be parameterized and used to generate indexed families of Volterra series, which are well-suited to model nonstationary or time-varying nonlinear phenomena. We describe how Volterra series and their morphisms organize into a functor category, Volt, whose objects are Volterra series and whose morphisms are natural transformations. We exhibit the operations of sum, product, and series composition of Volterra series as monoidal products on Volt and identify, for each in turn, its corresponding universal property. We show, in particular, that the series composition of Volterra series is associative. We then bridge between our framework and a subject at the heart of audio signal processing: time-frequency analysis. Specifically, we show that an equivalence between a certain class of second-order Volterra series and the bilinear time-frequency distributions (TFDs) can be extended to one between certain higher-order Volterra series and the so-called polynomial TFDs. We end with prospects for future work, including the incorporation of nonlinear system identification techniques and the extension of our theory to the settings of compositional graph and topological audio signal processing.Comment: Master's thesi

Treatise on Hearing: The Temporal Auditory Imaging Theory Inspired by Optics and Communication

A new theory of mammalian hearing is presented, which accounts for the auditory image in the midbrain (inferior colliculus) of objects in the acoustical environment of the listener. It is shown that the ear is a temporal imaging system that comprises three transformations of the envelope functions: cochlear group-delay dispersion, cochlear time lensing, and neural group-delay dispersion. These elements are analogous to the optical transformations in vision of diffraction between the object and the eye, spatial lensing by the lens, and second diffraction between the lens and the retina. Unlike the eye, it is established that the human auditory system is naturally defocused, so that coherent stimuli do not react to the defocus, whereas completely incoherent stimuli are impacted by it and may be blurred by design. It is argued that the auditory system can use this differential focusing to enhance or degrade the images of real-world acoustical objects that are partially coherent. The theory is founded on coherence and temporal imaging theories that were adopted from optics. In addition to the imaging transformations, the corresponding inverse-domain modulation transfer functions are derived and interpreted with consideration to the nonuniform neural sampling operation of the auditory nerve. These ideas are used to rigorously initiate the concepts of sharpness and blur in auditory imaging, auditory aberrations, and auditory depth of field. In parallel, ideas from communication theory are used to show that the organ of Corti functions as a multichannel phase-locked loop (PLL) that constitutes the point of entry for auditory phase locking and hence conserves the signal coherence. It provides an anchor for a dual coherent and noncoherent auditory detection in the auditory brain that culminates in auditory accommodation. Implications on hearing impairments are discussed as well.Comment: 603 pages, 131 figures, 13 tables, 1570 reference