Mathematical framework for place coding in the auditory system

In the auditory system, tonotopy is postulated to be substrate for a place code, where sound frequency encoded by location of neurons that fire during stimulus. Though conceptually simple, computations allow representation intensity and complex sounds are poorly understood. Here, mathematical framework developed in order define clearly conditions support code. To accommodate both information, neural network described as space with elements represent individual clusters neurons. A mapping then constructed from acoustic so encoded, respectively, size clusters. Algebraic operations -addition multiplication- derived elucidate rules representing, assembling, modulating multi-frequency networks. The resulting outcomes these consistent simulations well electrophysiological psychophysical data. analyses show how can purely without need rate or temporal coding schemes. algebraic used describe loudness summation suggest mechanism critical band. approach complements experimental computational approaches provides foundation interpreting data constructing models.