Related papers: Temporal profiles of avalanches on networks

We characterize the distributions of size and duration of avalanches propagating in complex networks. By an avalanche we mean the sequence of events initiated by the externally stimulated `excitation' of a network node, which may, with some…

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 collapse of interdependent networks, as well as similar avalanche phenomena, is driven by cascading failures. At the critical point, the cascade begins as a critical branching process, where each failing node (element) triggers, on…

Experiments in various neural systems found avalanches: bursts of activity with characteristics typical for critical dynamics. A possible explanation for their occurrence is an underlying network that self-organizes into a critical state.…

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…

As shown recently (arXiv:0801.3056), several types of neuronal complex networks involving non-linear integration-and-fire dynamics exhibit an abrupt activation along their transient regime. Interestingly, such an avalanche of activation has…

Neural avalanches are collective firings of neurons that exhibit emergent scale-free behavior. Understanding the nature and distribution of these avalanches is an important element in understanding how the brain functions. We study a model…

The vulnerability of an isolated network to cascades is fundamentally affected by its interactions with other networks. Motivated by failures cascading among electrical grids, we study the Bak-Tang-Wiesenfeld sandpile model on two…

Cortical networks exhibit synchronized activity which often occurs in spontaneous events in the form of spike avalanches. Since synchronization has been causally linked to central aspects of brain function such as selective signal…

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 introduce a novel tool for analyzing complex network dynamics, allowing for cascades of causally-related events, which we call causal webs (c-webs), to be separated from other non-causally-related events. This tool shows that…

Empirical estimation of critical points at which complex systems abruptly flip from one state to another is among the remaining challenges in network science. However, due to the stochastic nature of critical transitions it is widely…

Directed complex network of two-state model neurons linked by synapses which can be blocked or activated stochastically in time undergoes phase transition between the quiescent phase with zero activity and the active one with persistent…

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…

Burstiness, the tendency of interaction events to be heterogeneously distributed in time, is critical to information diffusion in physical and social systems. However, an analytical framework capturing the effect of burstiness on generic…

We use a discrete-time formulation to study the asymmetric avalanche process [Phys. Rev. Lett. vol. 87, 084301 (2001)] on a finite ring and obtain an exact expression for the average avalanche size of particles as a function of toppling…

The existence of power-law distributions is only a first requirement in the validation of the critical behavior of a system. Long-range spatio-temporal correlations are fundamental for the spontaneous neuronal activity to be the expression…

Recently, neuronal avalanches have been observed to display oscillations, a phenomenon regarded as the co-existence of a scale-free behaviour (the avalanches close to criticality) and scale-dependent dynamics (the oscillations). Ordinary…

Avalanches are often defined as signals higher than some detection level in bursty systems. The choice of the detection threshold affects the number of avalanches, but it can also affect their temporal correlations. We simulated the…

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…