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Cascading large-amplitude bursts in neural activity, termed avalanches, are thought to provide insight into the complex spatially distributed interactions in neural systems. In human neuroimaging, for example, avalanches occurring during…
We investigate the breakdown of disordered networks under the action of an increasing external---mechanical or electrical---force. We perform a mean-field analysis and estimate scaling exponents for the approach to the instability. By…
We investigate the complex spatio-temporal dynamics in avalanche driven surface growth by means of scaling theory. We study local activity statistics, avalanche kinetics, and temporal correlations in the global interface velocity, obtaining…
We investigate how the properties of inhomogeneous patterns of activity, appearing in many natural and social phenomena, depend on the temporal resolution used to define individual bursts of activity. To this end, we consider time series of…
Recent experimental observations have supported the hypothesis that the cerebral cortex operates in a dynamical regime near criticality, where the neuronal network exhibits a mixture of ordered and disordered patterns. However, A…
We explore in the mean-field approximation the robustness with respect to dissipation of self-organized criticality in sandpile models. To this end, we generalize a recently introduced self-organized branching process, and show that the…
We describe a chain of unidirectionally coupled adaptive excitable elements slowly driven by a stochastic process from one end and open at the other end, as a minimal toy model of unresolved irreducible uncertainty in a system performing…
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:…
Self-organized critical states are found in many natural systems, from earthquakes to forest fires, they have also been observed in neural systems, particularly, in neuronal cultures. However, the presence of critical states in the awake…
We study a neural network model of interacting stochastic discrete two--state cellular automata on a regular lattice. The system is externally tuned to a critical point which varies with the degree of stochasticity (or the effective…
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…
We revisit the scaling properties of a model for non-equilibrium wetting [Phys. Rev. Lett. 79, 2710 (1997)], correcting previous estimates of the critical exponents and providing a complete scaling scheme. Moreover, we investigate a special…
Thermal or finite-size scaling analyses of importance sampling Monte Carlo time series in the vicinity of phase transition points often combine different estimates for the same quantity, such as a critical exponent, with the intent to…
Many complex systems respond to a continuous input of energy by an accumulation of stress over time, interrupted by sudden energy releases called avalanches. Recently, it has been pointed out that several basic features of avalanche…
The brain keeps its overall dynamics in a corridor of intermediate activity and it has been a long standing question what possible mechanism could achieve this task. Mechanisms from the field of statistical physics have long been suggesting…
Complex systems, when poised near a critical point of a phase transition between order and disorder, exhibit a dynamics comprising a scale-free mixture of order and disorder which is universal, i.e. system-independent (1-5). It allows…
We model spontaneous cortical activity with a network of coupled spiking units, in which multiple spatio-temporal patterns are stored as dynamical attractors. We introduce an order parameter, which measures the overlap (similarity) between…
The Wilson-Cowan model constitutes a paradigmatic approach to understanding the collective dynamics of networks of excitatory and inhibitory units. It has been profusely used in the literature to analyze the possible phases of neural…
While information processing in complex systems can be described in abstract, general terms, there are cases in which the relation between these computations and the physical substrate of the underlying system is itself of interest.…
We study the scaling behaviors in the wind velocity time series collected at the atmospheric surface layer and compare them with two commonly used cascade models, the truncated stable distribution and the log-normal model. Results show that…