相关论文: Probabilistic cellular automata with conserved qua…

How do cellular automata behave in the limit of a very large number of cells? Is there a continuum limit with simple properties? We attack this problem by mapping certain classes of automata to quantum field theories for which powerful…

We consider the problem of approximate sampling from the finite volume Gibbs measure with a general pair interaction. We exhibit a parallel dynamics (Probabilistic Cellular Automaton) which efficiently implements the sampling. In this…

We introduce a pair of time-reversible models defined on the discrete space-time lattice with 3 states per site, specifically, a vacancy and a particle of two flavours (species). The local update rules reproduce the rule 54 reversible…

This paper introduces a new formalism for quantum cellular automata (QCAs), based on evolving tensor products of qubits using local unitary operators. It subsequently uses this formalism to analyze and validate several conjectures, stemming…

This paper presents a novel framework using neural cellular automata (NCA) to regenerate and predict geographic information. The model extends the idea of using NCA to generate/regenerate a specific image by training the model with various…

Cellular automata (CA) are a class of computational models that exhibit rich dynamics emerging from the local interaction of cells arranged in a regular lattice. In this work we focus on a generalised version of typical CA, called graph…

Probabilistic timed automata are classical timed automata extended with discrete probability distributions over edges. We introduce clock-dependent probabilistic timed automata, a variant of probabilistic timed automata in which transition…

We propose using Probabilistic Cellular Automata (PCA) to address inverse problems with the Bayesian approach. In particular, we use PCA to sample from an approximation of the posterior distribution. The peculiar feature of PCA is their…

The density classification task is a famous problem in the theory of cellular automata. It is unsolvable for deterministic automata, but recently solutions for stochastic cellular automata have been found. One of them is a set of stochastic…

Cellular automata (CA) provide a minimal formalism for investigating how simple local interactions generate rich spatiotemporal behavior in domains as diverse as traffic flow, ecology, tissue morphogenesis and crystal growth. However,…

A Cellular Automata (CA) rule is presented that can generate "loop patterns" in a 2D grid under fixed boundary conditions. A loop is a cyclically closed path represented by one-cells enclosed by zero-cells. A loop pattern can contain…

A framework for implementing reservoir computing (RC) and extreme learning machines (ELMs), two types of artificial neural networks, based on 1D elementary Cellular Automata (CA) is presented, in which two separate CA rules explicitly…

Non-uniform cellular automata (NUCA) are an extension of cellular automata (CA), which transform cells according to multiple different local rules. A NUCA is defined by a configuration of local rules called a local rule distribution. We…

Given a finite set of local constraints, we seek a cellular automaton (i.e., a local and uniform algorithm) that self-stabilises on the configurations that satisfy these constraints. More precisely, starting from a finite perturbation of a…

Invertible cellular automata are useful as models of physical systems with microscopically revesible dyanmics. There are several well-understood ways to construct them: partitioning rules, second-order rules, and alternating-grid rules. We…

Evidence and results suggesting that a Noether--like theorem for conservation laws in 1D RCA can be obtained. Unlike Noether's theorem, the connection here is to the maximal congruences rather than the automorphisms of the local dynamics.…

State-of-the-art review of cellular automata, cellular automata for partial differential equations, differential equations for cellular automata and pattern formation in biology and engineering.

We construct a cellular automaton (CA) model that describes the movement of a particle in a disordered system. The mathematical properties of the CA model were examined by varying the configuration of grid and determining the number of…

Starting from integrable cellular automata we present a novel form of Painlev\'e equations. These equations are discrete in both the independent variable and the dependent one. We show that they capture the essence of the behavior of the…

Recently popularized randomized methods for principal component analysis (PCA) efficiently and reliably produce nearly optimal accuracy --- even on parallel processors --- unlike the classical (deterministic) alternatives. We adapt one of…