Related papers: Scaling behaviour in probabilistic neuronal cellul…

We demonstrate, both analytically and numerically, that learning dynamics of neural networks is generically attracted towards a self-organized critical state. The effect can be modeled with quartic interactions between non-trainable…

The transport and chemical reactions of solutes are modelled as a cellular automaton in which molecules of different species perform a random walk on a regular lattice and react according to a local probabilistic rule. The model describes…

The activity in the brain cortex remarkably shows a simultaneous presence of robust collective oscillations and neuronal avalanches, where intermittent bursts of pseudo-synchronous spiking are interspersed with long periods of quiescence.…

Empirical evidence of scaling behaviors in neuronal avalanches suggests that neuronal populations in the brain operate near criticality. Departure from scaling in neuronal avalanches has been used as a measure of distance to criticality and…

The result of 2-dimensional Gaussian lattice fit to a speckle intensity pattern based on a linear model that includes nearest-neighbor interactions is presented. We also include a Monte Carlo simulation of the same spatial speckle pattern…

In real-world applications, observations are often constrained to a small fraction of a system. Such spatial subsampling can be caused by the inaccessibility or the sheer size of the system, and cannot be overcome by longer sampling.…

There is mounting empirical evidence that many communities of living organisms display key features which closely resemble those of physical systems at criticality. We here introduce a minimal model framework for the dynamics of a community…

Cellular automata and other discrete dynamical systems have long been studied as models of emergent complexity. Recently, neural cellular automata have been proposed as models to investigate the emerge of a more general artificial…

We extend recent results on the exact hydrodynamics of a system of diffusive active particles displaying a motility-induced phase separation to account for typical fluctuations of the dynamical fields. By calculating correlation functions…

Signaling networks are designed to sense an environmental stimulus and adapt to it. We propose and study a minimal model of signaling network that can sense and respond to external stimuli of varying strength in an adaptive manner. The…

We study the role of scale-free structure and noise in collective dynamics of neuronal networks. For this purpose, we simulate and study analytically a cortical circuit model with stochastic neurons. We compare collective neuronal activity…

In a recent work, mean-field analysis and computer simulations were employed to analyze critical self-organization in networks of excitable cellular automata where randomly chosen synapses in the network were depressed after each spike (the…

In neuroscience, synaptic plasticity refers to the set of mechanisms driving the dynamics of neuronal connections, called synapses and represented by a scalar value, the synaptic weight. A Spike-Timing Dependent Plasticity (STDP) rule is a…

We study the fluctuations of the two-time dependent global roughness of finite size elastic lines in a quenched random environment. We propose a scaling form for the roughness distribution function that accounts for the two-time,…

Massively parallel recordings of spiking activity in cortical networks show that covariances vary widely across pairs of neurons. Their low average is well understood, but an explanation for the wide distribution in relation to the static…

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…

Armed conflict data display scaling and universal dynamics in both social and physical properties like fatalities and geographic extent. We propose a randomly branching, armed-conflict model that relates multiple properties to one another…

Activity or spin patterns on random scale-free network are studied by mean field analysis and computer simulations. These activity patterns evolve in time according to local majority-rule dynamics which is implemented using (i) parallel or…

We propose and investigate a one-parameter probabilistic mixture of one-dimensional elementary cellular automata under the guise of a model for the dynamics of a single-species unstructured population with nonoverlapping generations in…

In this work, we propose a nonlinear stochastic model of a network of stochastic spiking neurons. We heuristically derive the mean-field limit of this system. We then design a Monte Carlo method for the simulation of the microscopic system,…