Frequency-spatial transformation: a proposal for parsimonious intra-cortical communication

This work examines a neural network model of a cortical module, where neurons are organized on a 2-dimensional sheet and are connected with higher probability to their spatial neighbors. Motivated by recent findings 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 dynamics of the neurons, the frequency of the spreading signal decreases as it propagates through the network. Depending on the input signal frequency, different neural assemblies will hence fire at their specific resonance frequency. We show analytically that the resulting frequency-spatial transformation is well-formed; an injective, fixed, mapping is obtained. Extensive numerical simulations demonstrate that a homogeneous, well-formed transformation may also be obtained in neural networks with cortical-like "Mexican-hat" connectivity. We hypothesize that a frequency-spatial transformation may serve as a basis for parsimonious cortical communication.