Criticality in spreading processes without time-scale separation and the critical brain hypothesis

Abstract

Spreading processes on networks are ubiquitous in both human-made and natural systems. Understanding their behavior is of broad interest; from the control of epidemics to understanding brain dynamics. While in some cases there exists a clear separation of time scales between the propagation of a single spreading cascade and the initiation of the next -- such that spreading can be modelled as directed percolation or a branching process -- there are also processes for which this is not the case, such as zoonotic diseases or spiking cascades in neural networks. For a large class of relevant network topologies, we show here that in such a scenario the nature of the overall spreading fundamentally changes. This change manifests itself in a transition between different universality classes of critical spreading, which determines the onset and the properties of an avalanche turning epidemic or neural activity turning epileptic, for example. We present analytical results in the mean-field limit giving the critical line along which scale-free spreading behaviour can be observed. The two limits of this critical line correspond to the universality classes of directed and undirected percolation, respectively. Outside these two limits, this duality manifests itself in the appearance of critical exponents from the universality classes of both directed and undirected percolation. We find that the transition between these exponents is governed by a competition between merging and propagation of activity, and identify an appropriate scaling relationship for the transition point. Finally, we show that commonly used measures, such as the branching ratio and dynamic susceptibility, fail to establish criticality in the absence of time-scale separation calling for a reanalysis of criticality in the brain.

25 pages, 17 figures, 3 tables. Update with substantial re-write to introduction and discussion, minor tweaks throughout

References in corpus (15)

• Emergent complex neural dynamics
• Theory of Rumour Spreading in Complex Social Networks
• Dynamical synapses causing self-organized criticality in neural networks
• Criticality in the brain: A synthesis of neurobiology, models and cognition
• Landau-Ginzburg theory of cortex dynamics: Scale-free avalanches emerge at the edge of synchronization
• Self-organized adaptation of a simple neural circuit enables complex robot behaviour
• Impact of Single Links in Competitive Percolation -- How complex networks grow under competition
• Griffiths phases on complex networks
• On the critical behavior of the Susceptible-Infected-Recovered (SIR) model on a square lattice
• Quasi-Critical Brain Dynamics on a Non-Equilibrium Widom Line
• Hysteresis, neural avalanches and critical behaviour near a first-order transition of a spiking neural network
• A simple, distance-dependent formulation of the Watts-Strogatz model for directed and undirected small-world networks
• Finite-size scaling of the stochastic susceptible-infected-recovered model
• Tailored ensembles of neural networks optimize sensitivity to stimulus statistics
• Directed random graphs with given degree distributions

Cited by in corpus (13)

• Tackling the subsampling problem to infer collective properties from limited data
• Correlation functions as a tool to study collective behaviour phenomena in biological systems
• Synchronization transitions on connectome graphs with external force
• Spatial-temporal analysis of neural desynchronization in sleep-like states reveals critical dynamics
• Emergence of order from chaos through a continuous phase transition in a turbulent reactive flow system
• Scale-free behavior of weight distributions of connectomes
• Information propagation in Gaussian processes on multilayer networks
• Memory in neural activity: long-range order without criticality
• Global excitability and network structure in the human brain
• Barrier-Controlled Non-Equilibrium Criticality in Reactive Particle Systems
• Revisiting and modeling power-law distributions in empirical outage data of power systems
• Finite-size correlation behavior near a critical point: a simple metric for monitoring the state of a neural network
• Critical and quasicritical behavior in a three-species dynamical model of semi-directed percolation