Pattern completion through phase coding in population neurodynamics

This article presents an alternative phase coding mechanism for Freeman's KIII model of population neurodynamics. Motivated by experimental evidence that supports the existence of a neural code based on synchronous oscillations, we propose an analogy between synchronization in neural populations and phase locking in KIII channels. An efficient method is proposed to extract phase differences across granule channels from their state-space trajectories. First, the scale invariance of the KIII model with respect to phase information is established. The phase code is then compared against the conventional amplitude code in terms of their bit-wise and across-fiber pattern recovery capabilities using decision-theoretic principles and a Hamming-distance classifier. Graph isomorphism in the Hebbian connections is exploited to perform an exhaustive evaluation of patterns on an 8-channel KIII model. Simulation results show that phase information outperforms amplitude information in the recovery of incomplete or corrupted stimuli.