Physics of psychophysics: Large dynamic range in critical square lattices of spiking neurons

Abstract

Psychophysics try 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 $\rho \propto h^m$ 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 stacked two layers of square lattices, and a fraction of connectivity between the first and second layer, we obtain at the output layer $\rho_ 2 \propto h^{m_2}$, with $m_2 = 0.08 \approx m^2$, which corresponds to a huge dynamic range. This enhancement of the dynamic range only occurs when the layers are close to their critical point.