Alex Reyes

Center for Neural Science, New York University, USA

Title: Mathematical structures and operations for representing sound frequency and intensity


In the central nervous system, neurons are often organized topographically so that sensory features are represented contiguously in the brain.  This anatomical architecture has led to the notion of a place code where the location of the active neurons represents a feature of the sensory input.   Though conceptually simple, the implementation of a place code is problematic partly because the fundamental processing unit (e.g. single neurons, columns, clusters, canonical microcircuits) of the nervous system is ill-defined. The motifs have important theoretical implications as each impose limits on the computations that networks may perform.

            The tonotopic organization of the auditory system, where the preferred frequencies of neurons vary systematically along one axis, provides a substrate for representing sound frequency via a place coding scheme. Indeed, cochlear implants enable the deaf to discriminate pitch simply by delivering focal electrical stimulation to different locations in the cochlea. The aim of this study is to examine the mathematical basis (i.e. topology and algebraic operations) for representing both frequency and intensity in cortex.  Preliminary analyses suggest that the optimal functional architecture consists of overlapping clusters of neurons with flexible borders rather than the classically defined cortical columns. Sound frequency and intensity are represented, respectively, by the location and width of the clusters.  The architecture supports an algebraic structure that has an `additive' operation for excitation and a 'multiplicative' operation for inhibition. These operations provide a means for adjusting cluster dimensions. The results explain qualitatively experimental results such as the limits of frequency and intensity discrimination and loudness summation. Simulations with spiking neurons are currently being performed to examine the network analog of these mathematical operations.



Professor Alex Reyes runs the Lab for Cortical Network Dynamics at the Center for Neural Science, New York University. The goal of his research is to understand the network mechanisms that underlie sensory representation in cortex. During a sensory stimulus, the responses of neurons depend on the patterns of connections between excitatory and inhibitory cells and on their intrinsic and synaptic properties. The right balance between excitation and inhibition is critical for encoding features of sensory space and imbalance can lead to neuropathologies. The aim of his work is to uncover general principles and focus upon the emergent properties of networks rather than on the fine details of cortical circuits. His research combines experiments in cultures and in vivo with theory and computer simulations.