Related papers: Criticality in spreading processes without time-sc…
In this paper we study a simple model of a purely excitatory neural network that, by construction, operates at a critical point. This model allows us to consider various markers of criticality and illustrate how they should perform in a…
A rigorous understanding of brain dynamics and function requires a conceptual bridge between multiple levels of organization, including neural spiking and network-level population activity. Mounting evidence suggests that neural networks of…
Dynamical processes taking place on networks have received much attention in recent years, especially on various models of random graphs (including small world and scale free networks). They model a variety of phenomena, including the…
At the point of a second order phase transition also termed as a critical point, systems display long range order and their macroscopic behaviors are independent of the microscopic details making up the system. Due to these properties, it…
An essential requirement for the representation of functional patterns in complex neural networks, such as the mammalian cerebral cortex, is the existence of stable network activations within a limited critical range. In this range, the…
Analytical studies of network epidemiology almost exclusively focus on the extreme situations where the time scales of network dynamics are well separated (longer or shorter) from that of epidemic propagation. In realistic scenarios,…
The time variation of contacts in a networked system may fundamentally alter the properties of spreading processes and affect the condition for large-scale propagation, as encoded in the epidemic threshold. Despite the great interest in the…
Branching processes are widely used to model phenomena from networks to neuronal avalanching. In a large class of continuous-time branching processes, we study the temporal scaling of the moments of the instant population size, the survival…
Continuous phase transitions are studied in a two dimensional nonequilibrium model with an infinite number of absorbing configurations. Spreading from a localized source is characterized by nonuniversal critical exponents, which vary…
Dynamical processes exhibiting absorbing states are essential in the modeling of a large variety of situations from material science to epidemiology and social sciences. Such processes exhibit the possibility of avalanching behavior upon…
The propagations of diseases, behaviors and information in real systems are rarely independent of each other, but they are coevolving with strong interactions. To uncover the dynamical mechanisms, the evolving spatiotemporal patterns and…
Evidence of critical dynamics has been recently found in both experiments and models of large scale brain dynamics. The understanding of the nature and features of such critical regime is hampered by the relatively small size of the…
In temporal networks, both the topology of the underlying network and the timings of interaction events can be crucial in determining how some dynamic process mediated by the network unfolds. We have explored the limiting case of the speed…
Two crucial elements facilitate the understanding and control of communicable disease spread within a social setting. These components are, the underlying contact structure among individuals that determines the pattern of disease…
Spreading processes have been largely studied in the literature, both analytically and by means of large-scale numerical simulations. These processes mainly include the propagation of diseases, rumors and information on top of a given…
As a promising computational paradigm, occurrence of critical states in artificial and biological neural networks has attracted wide-spread attention. An often-made explicit or implicit assumption is that one single critical state is…
We describe the critical window for percolation in the universality class of sparse growing random graphs. In our models, vertices arrive sequentially and connect independently to each earlier vertex $v$ with probability proportional to a…
Self-organized criticality has been proposed to be a universal mechanism for the emergence of scale-free dynamics in many complex systems, and possibly in the brain. While such scale-free patterns were identified experimentally in many…
Abrupt shifts in ecosystems, brains, markets, and climate are often diagnosed as signs of approaching a tipping point, i.e. a critical bifurcation where stability is lost. Here we reveal a broader and more deceptive mechanism:…
The "critical brain hypothesis" posits that neural circuitry may be tuned close to a "critical point" or "phase transition" -- a boundary between different operating regimes of the circuit. The renormalization group and theory of critical…