Physics Of Psychophysics: Large Dynamic Range In Critical Square Lattices Of Spiking Neurons

Psychophysics tries to relate physical input magnitudes to psychological or neural correlates. Microscopic models to account for macroscopic psychophysical laws, in the sense of statistical physics, are an almost unexplored area. Here we examine a sensory epithelium composed of two connected square lattices of stochastic integrate-and-fire cells. With one square lattice, we obtain a Stevens's law rho alpha h(m) with Stevens's exponent m = 0.254 and a sigmoidal saturation, where rho is the neuronal network activity and h is the input intensity (external field). We relate Stevens's power-law exponent with the field critical exponent as m = 1/delta(h) = beta/sigma. We also show that this system pertains to the directed percolation (DP) universality class (or, perhaps, the compact-DP class). With two stacked layers of square lattices and a fraction of connectivity between the first and second layer, we obtain at the output layer rho(2) alpha h(m2), with m(2) = 0.08 approximate to m(2), which corresponds to a huge dynamic range. This enhancement of the dynamic range only occurs when the layers are close to their critical point.