Fractal analyses of networks of integrate-and-fire stochastic spiking neurons
Ariadne de Andrade Costa, Mary Jean Amon, Olaf Sporns, Luis Favela

TL;DR
This study uses fractal analysis on simulated neuronal networks to identify criticality, revealing that networks at critical states exhibit specific fractal properties and multifractal structures.
Contribution
It introduces the application of monofractal and multifractal methods to assess criticality in stochastic spiking neuron networks, linking fractal properties to network critical states.
Findings
Peak fractal scaling occurs at mid-range plasticity levels.
Networks near criticality show characteristic multifractal spectra.
Fractal analysis provides insights into network stability and adaptability.
Abstract
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…
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