Analog Computation at a Critical Point: A Novel Function for Neuronal Oscillations?

We show that a simple spin system biased at its critical point can encode spatial characteristics of external signals, such as the dimensions of "objects" in the visual field. in the temporal correlation functions of individual spins. Qualitative arguments suggest that regularly firing neurons should be described by a planar spin of unit length, and such XY models exhibit critical dynamics over a broad range of parameters. We show how to extract these spins from spike trains and then measure the interaction Hamiltonian using simulations of small dusters of cells. Static correlations among spike trains obtained from simulations of large arrays of cells are in agreement with the predictions from these Hamiltonians, and dynamic correlations display the predicted encoding of spatial information. We suggest that this novel representation of object dinwnsions in temporal correlations may be relevant to recent experiments on oscillatory neural firing in the visual cortex.