Related papers: Orbits of Bernoulli Measures in Cellular Automata
A deterministic reformulation of quantum mechanics can bypass the usual philosophical interpretations of probability and stochasticity that are found in the literature. This can be obtained with the ontological formulation of quantum…
We investigate the conditions under which the mean-field formulation of a probabilistic, totalistic cellular automaton approximates the logistic equation. We show that this goal can be only fulfilled for an infinite-range neighborhood. We…
We propose distribution-free runs-based control charts for detecting location shifts. Using the fact that given the number of total successes, the outcomes of a sequence of Bernoulli trials are random permutations, we are able to control…
This paper proposes a dynamical notion of discrete geodesics, understood as straightest trajectories in discretized curved spacetime. The notion is generic, as it is formulated in terms of a general deviation function, but readily…
We study dynamical systems acting on the path space of a stationary (non-simple) Bratteli diagram. For such systems we explicitly describe all ergodic probability measures invariant with respect to the tail equivalence relation (or the…
Cyclic cellular automata (CCA) are models of excitable media. Started from random initial conditions, they produce several different kinds of spatial structure, depending on their control parameters. We introduce new tools from information…
This article introduces new tools to study self-organisation in a family of simple cellular automata which contain some particle-like objects with good collision properties (coalescence) in their time evolution. We draw an initial…
We define the notion of stochastic stability, already present in the literature in the context of smooth dynamical systems, for invariant measures of cellular automata perturbed by a random noise, and the notion of strongly stochastically…
The density classification task is to determine which of the symbols appearing in an array has the majority. A cellular automaton solving this task is required to converge to a uniform configuration with the majority symbol at each site. It…
A very simple event frequency approximation algorithm that is sensitive to event timeliness is suggested. The algorithm iteratively updates categorical click-distribution, producing (path of) a random walk on a standard $n$-dimensional…
Number-conserving cellular automata are discrete dynamical systems that simulate interacting particles like e.g. grains of sand. In an earlier paper, I had already derived a uniform construction for all transition rules of one-dimensional…
Cellular automata are arrays of finite state machines that can exist in a finite number of states. These machines update their states simultaneously based on specific local rules that govern their interactions. This framework provides a…
Local unitary invariants allow one to test whether multipartite states are equivalent up to local basis changes. Equivalently, they specify the geometry of the "orbit space" obtained by factoring out local unitary action from the state…
The random beta-transformation K is isomorphic to a full shift. This relation gives an invariant measure for K that yields the Bernoulli convolution by projection. We study the local dimension of the invariant measure for K for special…
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 present a method to construct a symplecticity preserving renormalization group map of a chain of weakly nonlinear symplectic maps and obtain a general reduced symplectic map describing its long-time behaviour. It is found that the…
We introduce the boolean convolution for probability measures on the unit circle. Roughly speaking, it describes the distribution of the product of two boolean independent unitary random variables. We find an analogue of the characteristic…
For a dynamical system, we study the set of points $\cal W$ whose orbit approximates any chosen point at certain specified rates. Our basic setting is that of left shift acting on topological Markov chains endowed with a local weak Gibbs…
The internal structure of a measuring device, which depends on what its components are and how they are organized, determines how it categorizes its inputs. This paper presents a geometric approach to studying the internal structure of…
This study aims at finding a method for constructing molecular dynamics like models using the formalism of cellular automata for fast simulation of fluid dynamic systems (including compressible phenomena). In as much as the results…