Related papers: New method to study stochastic growth equations: a…
Stochastic dynamical systems arise naturally across nearly all areas of science and engineering. Typically, a dynamical system model is based on some prior knowledge about the underlying dynamics of interest in which probabilistic features…
A family of exponential martingales of a stochastic Laplacian growth problem is proposed. Stochastic Laplacian growth describes a regularized interface dynamics in a two-fluid system, where the viscous fluid is incompressible at a large…
We develop statistical mechanics for stochastic growth processes as applied to Laplacian growth by using its remarkable connection with a random matrix theory. The Laplacian growth equation is obtained from the variation principle and…
The statistics of the average height fluctuation of the one-dimensional Kardar-Parisi-Zhang(KPZ)-type surface is investigated. Guided by the idea of local stationarity, we derive the scaling form of the characteristic function in the…
In this paper, inspired from our previous algorithm, which was based on the theory of Tsallis statistical mechanics, we develop a new evolving stochastic learning algorithm for neural networks. The new algorithm combines deterministic and…
We study discrete KPZ growth models deposited on square lattice substrates, whose (average) lateral size enlarges as $L= L_0 + \omega t^{\gamma}$. Our numerical simulations reveal that the competition between the substrate expansion and the…
The emergence of complex behaviors in cellular automata is an area that has been widely developed in recent years with the intention to generate and analyze automata that produce space-moving patterns or gliders that interact in a periodic…
At the scale of the individual cell, protein production is a stochastic process with multiple time scales, combining quick and slow random steps with discontinuous and smooth variation. Hybrid stochastic processes, in particular…
Height fluctuations of growing surfaces can be characterized by the probability distribution of height in a spatial point at a finite time. Recently there has been spectacular progress in the studies of this quantity for the…
This paper presents a statistically sound method for measuring the accuracy with which a probabilistic model reflects the growth of a network, and a method for optimising parameters in such a model. The technique is data-driven, and can be…
Self-organizing complex systems can be modeled using cellular automaton models. However, the parametrization of these models is crucial and significantly determines the resulting structural pattern. In this research, we introduce and…
We study coarse pattern formation in a cellular automaton modelling a spatially-extended stochastic neural network. The model, originally proposed by Gong and Robinson [36], is known to support stationary and travelling bumps of localised…
We present a comprehensive numerical investigation of non-universal parameters and corrections related to interface fluctuations of models belonging to the Kardar-Parisi-Zhang (KPZ) universality class, in d=1+1, for both flat and curved…
Cellular automata (CA) are discrete-time dynamical systems with local update rules on a lattice. Despite their elementary definition, CA support a wide spectrum of macroscopic phenomena central to statistical physics: equilibrium and…
We consider Markov Decision Problems defined over continuous state and action spaces, where an autonomous agent seeks to learn a map from its states to actions so as to maximize its long-term discounted accumulation of rewards. We address…
This paper introduces a simple formalism for dealing with deterministic, non- deterministic and stochastic cellular automata in an unified and composable manner. This formalism allows for local probabilistic correlations, a feature which is…
Elementary cellular automata (ECA) present iconic examples of complex systems. Though described only by one-dimensional strings of binary cells evolving according to nearest-neighbour update rules, certain ECA rules manifest complex…
The numerical integration of stochastic growth equations on non-Euclidean networks presents unique challenges due to the nonlinearities that occur in many relevant models and of the structural constraints of the networks. In this work, we…
We conjecture the universal probability distribution at large time for the one-point height in the 1D Kardar-Parisi-Zhang (KPZ) stochastic growth universality class, with initial conditions interpolating from any one of the three main…
The stochastic growth-fragmentation model describes the temporal evolution of a structured cell population through a discrete-time and continuous-state Markov chain. The simulations of this stochastic process and its invariant measure are…