Optimization on the onset of a critical phase transition in the visual cortex

Activity in the brain propagates as waves of firing neurons,
namely avalanches. These waves size and duration distributions
have been experimentally shown to display a stable power law profile and
to have long-range correlations and $1/f^{\beta}$ power spectrum
\textit{in vivo} and \textit{in vitro}.
These are typical features of critical systems.
Criticality have the advantages of maximizing the response
dynamic range of neural networks,
optimizing memory and learning processes,
the computational power of the brain
and information processing flexibility.
We study a feedforward layered network model of the primary visual cortex that process input information via avalanches
that emerge spontaneously from a constant input presented to the retina.
We show for the first time that there is a minimum value for the time that the network takes to
process input information by varying the excitatory postsynaptic
potential parameter (EPSP) close to a critical point. Surprisingly, this point lies on the edge of a
Griffiths phase where avalanches are power-law distributed
and have a $1/f^{\beta}$ power spectrum with $0.3\leq\beta\leq1.5$, matching experiments.
The order-disorder continuous phase transition point may be analytically
approximated by a mean field calculation, and is
located close to the expected experimental value of EPSP in the cortex ($\approx1\textnormal{mV}$).
The system presents two second order phase transitions which are described by two independent order parameters
similarly to the Blume-Emery-Griffiths model.
We discuss how the model could be extended in order to describe recent experimental results
of a stable critical point in the visual system of turtles.