Related papers: Time-dependent branching processes: a model of osc…
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…
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…
Power-law-shaped avalanche-size distributions are widely used to probe for critical behavior in many different systems, particularly in neural networks. The definition of avalanche is ambiguous. Usually, theoretical avalanches are defined…
A collective chaotic phase with power law scaling of activity events is observed in a disordered mean field network of purely excitatory leaky integrate-and-fire neurons with short-term synaptic plasticity. The dynamical phase diagram…
The activity of a sparse network of leaky integrate-and-fire neurons is carefully revisited with reference to a regime of a bona-fide asynchronous dynamics. The study is preceded by a finite-size scaling analysis, carried out to identify a…
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…
When brain signals are recorded in an electroencephalogram or some similar large-scale record of brain activity, oscillatory patterns are typically observed that are thought to reflect the aggregate electrical activity of the underlying…
We derive rigorous results describing the asymptotic dynamics of a discrete time model of spiking neurons introduced in \cite{BMS}. Using symbolic dynamic techniques we show how the dynamics of membrane potential has a one to one…
We investigate the possibility that narrowband oscillations may emerge from completely asynchronous, independent neural firing. We find that a population of asynchronous neurons may produce narrowband oscillations if each neuron fires…
We discuss basic features of emergent complexity in dynamical systems far from equilibrium by focusing on the network structure of their state space. We start by measuring the distributions of avalanche and transient times in Random Boolean…
We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…
Recent observation for scale invariant neural avalanches in the brain have been discussed in details in the scientific literature. We point out, that these results do not necessarily imply that the properties of the underlying neural…
We characterise the dynamics of neuronal activity, in terms of field theory, using neural units placed on a 2D-lattice modelling the cortical surface. The electrical activity of neuronal units was analysed with the aim of deriving a neural…
A self-organising model is proposed to explain the criticality in cortical networks deduced from recent observations of neuronal avalanches. Prevailing understanding of self-organised criticality (SOC) dictates that conservation of energy…
The asymptotic behavior, as $n\rightarrow \infty $ of the conditional distribution of the number of particles in a decomposable critical branching process $\mathbf{Z}% (m)=(Z_{1}(m),...,Z_{N}(m)),$ with $N$ types of particles at moment…
In the analysis of highly-oscillatory evolution problems, it is commonly assumed that a single frequency is present and that it is either constant or, at least, bounded from below by a strictly positive constant uniformly in time. Allowing…
Biological neural networks are notoriously hard to model due to their stochastic behavior and high dimensionality. We tackle this problem by constructing a dynamical model of both the expectations and covariances of the fractions of active…
In many complex systems a continuous input of energy over time can be suddenly relaxed in the form of avalanches. Conventional avalanche models disregard the possibility of internal dynamical effects in the inter-avalanche periods, and thus…
We extend existing connections between random walks, branching processes, and spatial branching processes, and their respective scaling limits, to include processes in dependent random environments. More specifically, we prove new scaling…
The brain is in a state of perpetual reverberant neural activity, even in the absence of specific tasks or stimuli. Shedding light on the origin and functional significance of such a dynamical state is essential to understanding how the…