Related papers: Scaling behaviour in probabilistic neuronal cellul…
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 have studied one-dimensional cellular automata with updating rules depending stochastically on the difference of the heights of neighbouring cells. The probability for toppling depends on a parameter lambda which goes to one with…
Scale-invariant neuronal avalanches have been observed in cell cultures and slices as well as anesthetized and awake brains, suggesting that the brain operates near criticality, i.e. within a narrow margin between avalanche propagation and…
Scale-free behavior as well as oscillations are frequently observed in the activity of many natural systems. One important example is the cortical tissues of mammalian brain where both phenomena are simultaneously observed. Rhythmic…
We address the problem of identifying functional interactions among stochastic neurons with variable-length memory from their spiking activity. The neuronal network is modeled by a stochastic system of interacting point processes with…
Spontaneous brain activity in the absence of external stimuli is not random but contains complex dynamical structures such as neuronal avalanches with power-law duration and size distributions. These experimental observations have been…
In a series of two papers, we investigate the large deviations and asymptotic behavior of stochastic models of brain neural networks with random interaction coefficients. In this first paper, we take into account the spatial structure of…
The presence of both critical behavior and oscillating patterns in brain dynamics is a very interesting issue. In this paper, we consider a model for a neuron population, where each neuron is modeled by an over-damped rotator. We find that…
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.…
The $1/f$-like decay observed in the power spectrum of electro-physiological signals, along with scale-free statistics of the so-called neuronal avalanches, constitute evidences of criticality in neuronal systems. Recent in vitro studies…
In this paper we study a simple model of a purely excitatory neural network that, by construction, operates at a critical point. This model allows us to consider various markers of criticality and illustrate how they should perform in a…
In this paper we address the question of statistical model selection for a class of stochastic models of biological neural nets. Models in this class are systems of interacting chains with memory of variable length. Each chain describes the…
We deal with the problem of bridging the gap between two scales in neuronal modeling. At the first (microscopic) scale, neurons are considered individually and their behavior described by stochastic differential equations that govern the…
The idea that information-processing systems operate near criticality to enhance computational performance is supported by scaling signatures in brain activity. However, external signals raise the question of whether this behavior is…
Inspired by extremely simplified view of the earthquakes we propose the stochastic domino cellular automaton model exhibiting avalanches. From elementary combinatorial arguments we derive a set of nonlinear equations describing the…
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…
We study a simple model for a neuron function in a collective brain system. The neural network is composed of uncorrelated random scale-free network for eliminating the degree correlation of dynamical processes. The interaction of neurons…
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…
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…
A simple one-dimensional cellular automaton model with threshold dynamics is introduced. The cumulative distribution of the size of the relaxations is analytically computed and behaves as a power law with an exponent equal to -1. This…