  Although there is increasing evidence of criticality in the brain, the
processes that guide neuronal networks to reach or maintain criticality remain
unclear. The present research examines the role of neuronal gain plasticity in
time-series of simulated neuronal networks composed of integrate-and-fire
stochastic spiking neurons, and the utility of fractal methods in assessing
network criticality. Simulated time-series were derived from a network model of
fully connected discrete-time stochastic excitable neurons. Monofractal and
multifractal analyses were applied to neuronal gain time-series. Fractal
scaling was greatest in networks with a mid-range of neuronal plasticity,
versus extremely high or low levels of plasticity. Peak fractal scaling
corresponded closely to additional indices of criticality, including average
branching ratio. Networks exhibited multifractal structure, or multiple scaling
relationships. Multifractal spectra around peak criticality exhibited elongated
right tails, suggesting that the fractal structure is relatively insensitive to
high-amplitude local fluctuations. Networks near critical states exhibited
mid-range multifractal spectra width and tail length, which is consistent with
literature suggesting that networks poised at quasi-critical states must be
stable enough to maintain organization but unstable enough to be adaptable.
Lastly, fractal analyses may offer additional information about critical state
dynamics of networks by indicating scales of influence as networks approach
critical states.
