Mathematical Sciences: Mathematical Models of Neural Processing in the Auditory Brainstem

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The investigators will use mathematical analysis and computation to investigate neural processing in the auditory brainstem and midbrain. The project has four main topics: (1) Mathematical development of a model for azimuthal localization in the lateral superior olive based on intensity differences; (2) Development and analysis of computational models for azimuthal localization by the medial superior olive and avian analogues based on phase differences; (3) Models for the neural processing of echoes in the lateral lemniscus of the bat and mathematical questions of signal reconstruction; (4) General principles of neural processing. The purpose of this project is to understand the basic organizational principles of parts of the brain that analyze sounds. These parts are made up of small signaling devices called neurons, which are organized and connected so that they perform specific functions (for example, to determine the location of a sound based on the fact that the sound will be louder at the ear more closely directed toward the sound source). Progress in understanding these principles of organization may make possible the design of artificial hearing devices that could be used in industrial robots or could be used to improve the hearing of humans with serious hearing deficiencies.