Related papers: Subsampled directed-percolation models explain sca…

Lightning, the most colossal discharge in nature, and flux avalanches in quantum superconductors--phenomena separated by twenty orders of magnitude in scale--display striking fractal similarity. We demonstrate that this is no mere analogy…

The observation of critical-like behavior in cortical networks represents a major step forward in elucidating how the brain manages information. Understanding the origin and functionality of critical-like dynamics, as well as their…

Activity in the brain propagates as waves of firing neurons, namely avalanches. These waves' size and duration distributions have been experimentally shown to display a stable power-law profile, long-range correlations and $1/f^{b}$ power…

The observation of apparent power-laws in neuronal systems has led to the suggestion that the brain is at, or close to, a critical state and may be a self-organised critical system. Within the framework of self-organised criticality a…

The branching process is the minimal model for propagation dynamics, avalanches and criticality, broadly used in neuroscience. A simple extension of it, adding inhibitory nodes, induces a much-richer phenomenology, including, an…

We investigate the connection between a formal property of the critical behavior of several systems in the presence of quenched disorder, known as "dimensional reduction", and the presence in the same systems at zero temperature of…

Avalanches in mean-field models can be mapped to memoryless branching processes defining a universality class. We present a reduced expression mapping a broad family of critical and subcriticial avalanches in mean-field models at the…

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…

Recently, a simple non-interacting-electron model, combining local quantum tunneling via quantum point contacts and global classical percolation, has been introduced in order to describe the observed ``metal-insulator transition'' in two…

Percolation refers to the emergence of a giant connected cluster in a disordered system when the number of connections between nodes exceeds a critical value. The percolation phase transitions were believed to be continuous until recently…

We consider the directed percolation process as a prototype of systems displaying a nonequilibrium phase transition into an absorbing state. The model is in a critical state when the activation probability is adjusted at some precise value…

It has long been argued that neural networks have to establish and maintain a certain intermediate level of activity in order to keep away from the regimes of chaos and silence. Strong evidence for criticality has been observed in terms of…

Avalanches in sandpiles are represented throughout a process of percolation in a Bethe lattice with a feedback mechanism. The results indicate that the frequency spectrum and probability distribution of avalanches resemble more to…

In all local low-dimensional models, scaling at critical points deviates from mean field behavior -- with one possible exception. This exceptional model with ``ordinary" behavior is an inherently non-equilibrium model studied some time ago…

Analytical expressions for scaling of brain wave spectra derived from the general nonlinear wave Hamiltonian form show excellent agreement with experimental "neuronal avalanche" data. The theory of the weakly evanescent nonlinear brain wave…

We study the critical behavior of a driven interface in a medium with random pinning forces by analyzing spatial and temporal correlations in a lattice model recently proposed by Sneppen [Phys. Rev. Lett. {\bf 69}, 3539 (1992)]. The static…

Analysis of degree-degree dependencies in complex networks, and their impact on processes on networks requires null models, i.e. models that generate uncorrelated scale-free networks. Most models to date however show structural negative…

Until now, most of our knowledge about the universality class of crystal plasticity has come from simulations using discrete dislocation dynamics. These are force-controlled, typically at zero temperature, and deal with the creation and…

The one-dimensional contact process with weak to intermediate quenched disorder in its transmission rates is investigated via quasi-stationary Monte Carlo simulation. We address the contested questions of both the nature of dynamical…

We present an interacting branching model of neural network dynamics, incorporating key biological features such as inhibition with several types of inhibitory interactions. We establish a hierarchy of analytical mean-field approximations…