Power spectrum and critical exponents in the 2D stochastic Wilson–Cowan model

Abstract

The power spectrum of brain activity is composed by peaks at characteristic frequencies superimposed to a background that decays as a power law of the frequency, $$f^{-\beta }$$ f - β , with an exponent $$\beta $$ β close to 1 (pink noise). This exponent is predicted to be connected with the exponent $$\gamma $$ γ related to the scaling of the average size with the duration of avalanches of activity. “Mean field” models of neural dynamics predict exponents $$\beta $$ β and $$\gamma $$ γ equal or near 2 at criticality (brown noise), including the simple branching model and the fully-connected stochastic Wilson–Cowan model. We here show that a 2D version of the stochastic Wilson–Cowan model, where neuron connections decay exponentially with the distance, is characterized by exponents $$\beta $$ β and $$\gamma $$ γ markedly different from those of mean field, respectively around 1 and 1.3. The exponents $$\alpha $$ α and $$\tau $$ τ of avalanche size and duration distributions, equal to 1.5 and 2 in mean field, decrease respectively to $$1.29\pm 0.01$$ 1.29 ± 0.01 and $$1.37\pm 0.01$$ 1.37 ± 0.01 . This seems to suggest the possibility of a different universality class for the model in finite dimension.

Criticality of neuronal avalanches in human sleep and their relationship with sleep macro- and micro-architecture

“…Alternatively, a recent work has shown that, in a 2D Wilson-Cowan neural network, the value of the exponent k is related to the network connectivity, with for a 2D connectivity, and when the mean-field approximation holds. 77 This may suggest that, in our case, the mean-field approximation is justified for relatively small avalanches involving few electrodes, but not for large-scale EEG avalanches. However, to verify whether this is due to the structure of the underlying, collective neural activity, simultaneous multi-scale recordings would be needed.…”

Excitation/Inhibition balance relates to cognitive function and gene expression in temporal lobe epilepsy: a high density EEG assessment with aperiodic exponent

“…We cannot rule out that the exponent of the PSD captures other signal properties beyond E/I balance (e.g. criticality 109 ). The largest part of the literature investigating the PSD features in epilepsy has seldom disentangled the periodic from the aperiodic component.…”

Criticality explains structure-function relationships in the human brain

“…It has been proposed that the brain experiences both continuous phase transitions with scale-free avalanches, and discontinuous transitions, which are beneficial for self-sustained replay activity and memory functioning [20][21][22]. The roles of topology and learning have also been investigated [11,[23][24][25][26][27], with some notable insights on the role of modularity [28,29].…”