Related papers: Observing scale-invariance in non-critical dynamic…

The hierarchical organization of the brain is a fundamental structural principle, while brain criticality is a leading hypothesis for its collective dynamics. However, the connection between structure and signatures of criticality remains…

Criticality has been proposed as a key principle underlying complex behavior in biological and artificial systems; however, how criticality translates from individual dynamics to collective behavior remains unclear. We study this question…

Extended numerical simulations of threshold models have been performed on a human brain network with N=836733 connected nodes available from the Open Connectome project. While in case of simple threshold models a sharp discontinuous phase…

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…

Many systems in Nature exhibit avalanche dynamics with scale-free features. A general scaling theory has been proposed for critical avalanche profiles in crackling noise, predicting the collapse onto a universal avalanche shape, as well as…

The human cortex is never at rest but in a state of sparse and noisy neural activity that can be detected at broadly diverse resolution scales. It has been conjectured that such a state is best described as a critical dynamical process --…

Recent experimental results on spike avalanches measured in the urethane-anesthetized rat cortex have revealed scaling relations that indicate a phase transition at a specific level of cortical firing rate variability. The scaling relations…

Criticality is hypothesized as a physical mechanism underlying efficient transitions between cortical states and remarkable information processing capacities in the brain. While considerable evidence generally supports this hypothesis,…

From 1/f noise to neuronal avalanches, evidence of scaling in brain activity has been increasingly linked to tuning to or near criticality. The concept of scaling is intimately related to the renormalization group (RG), in essence providing…

It has been postulated that the brain operates in a self-organized critical state that brings multiple benefits, such as optimal sensitivity to input. Thus far, self-organized criticality has typically been depicted as a one-dimensional…

The brain criticality hypothesis has largely only characterized brain dynamics in terms of their self-similarity, although experimental evidence suggests that the brain exhibits significant multifractality. To understand how multifractality…

One of the most impressive features of continuous phase transitions is the concept of universality, that allows to group the great variety of different critical phenomena into a small number of universality classes. All systems belonging to…

In contrast to the symmetries of translation in space, rotation in space, and translation in time, the known laws of physics are not universally invariant under transformation of scale. However, the action can be invariant under change of…

A random neighbor extremal stick-slip model is introduced. In the thermodynamic limit, the distribution of states has a simple analytical form and the mean avalanche size, as a function of the coupling parameter, is exactly calculable. The…

The "Self-organized criticality" (SOC), introduced in 1987 by Bak, Tang and Wiesenfeld, was an attempt to explain the 1/f noise, but it rapidly evolved towards a more ambitious scope: explaining scale invariant avalanches. In two decades,…

Scaling ideas and renormalization group approaches proved crucial for a deep understanding and classification of critical phenomena in thermal equilibrium. Over the past decades, these powerful conceptual and mathematical tools were…

We examine ways to write the Choptuik critical solution as the evolution of scale invariant variables. It is shown that a system of scale invariant variables proposed by one of the authors does not evolve periodically in the Choptuik…

It has recently been reported that statistical signatures of brain criticality, obtained from distributions of neuronal avalanches, can depend on the cortical state. We revisit these claims with a completely different and independent…

In this overview, we discuss the connections between the observations of critical dynamics in neuronal networks and the maximum entropy models that are often used as statistical models of neural activity, focusing in particular on the…

Many studies have found evidence that the brain operates at a critical point, a processus known as self-organized criticality. A recent paper found remarkable scalings suggestive of criticality in systems as different as neural cultures,…