Spatial Transformation A Proposal for Parsimonious Intra � cortical

This work examines a neural network model of a cortical mod ule where neurons are organized on a dimensional sheet and are connected with higher probability to their spatial neighbors Moti vated by recent ndings that cortical neurons have a resonant peak in their impedance magnitude function we present a frequency spatial transformation scheme that is schematically described as follows An external input signal applied to a small input subset of the neurons spreads along the network Due to a stochastic component in the neu rons dynamics the frequency of the spreading signal decreases as it propagates through the network Depending on the input signal fre quency di erent neural assemblies will hence re at their speci c res onance frequency We show analytically that the resulting frequency spatial transformation is well formed an injective xed mapping is obtained Extensive numerical simulations demonstrate that a homo geneous well formed transformation may also be obtained in neural networks with cortical like Mexican hat connectivity We hypothe size that a frequency spatial transformation may serve as a basis for parsimonious cortical communication Address Dept of Physiology Tel Aviv University Tel Aviv Israel E mail levi math tau ac il To whom correspondence should be addressed Address Depts of Computer Science and Physiology Tel Aviv University Tel Aviv Israel E mail ruppin math tau ac il Address Room D AT T Bell Laboratories Mountain Ave Murray Hill NJ USA E mail matias research att com Address Dept of Computer Science University of Maryland College Park MD USA E mail reggia cs umd edu