Related papers: Orbits of Bernoulli Measures in Cellular Automata
We have recently introduced the two new computing models of self-similar cellular automata and self-similar Petri nets. Self-similar automata result from a progressive, infinite tessellation of space and time. Self-similar Petri nets…
While for synchronous deterministic cellular automata there is an accepted definition of reversibility, the situation is less clear for asynchronous cellular automata. We first discuss a few possibilities and then investigate what we call…
The hermitian analog of Aleksandrov's area measures of convex bodies is investigated. A characterization of those area measures which arise as the first variation of unitarily invariant valuations is established. General smooth area…
We investigate the evolution of quantum information under Pauli measurement circuits. We focus on the case of one- and two-dimensional systems, which are relevant to the recently introduced Floquet topological codes. We define local…
A digit function is presented which provides the $i$th-digit in base $p$ of any real number $x$. By means of this function, formulated within $\mathcal{B}$-calculus, the local, nonlocal and global dynamical behaviors of cellular automata…
Cellular automata are a fundamental computational model with applications in mathematics, computer science, and physics. In this work, we explore the study of cellular automata to cases where the universe is a group, introducing the concept…
We explore the class of exchangeable Bernoulli distributions building on their geometrical structure. Exchangeable Bernoulli probability mass functions are points in a convex polytope and we have found analytical expressions for their…
Determining the measurement uncertainty region is a difficult problem for generic sets of observables. For this reason the literature on exact measurement uncertainty regions is focused on symmetric sets of observables, where the symmetries…
In Basili and Pratelli (2024), a novel and coherent concept of interval probability measures has been introduced, providing a method for representing imprecise probabilities and uncertainty. Within the framework of set algebra, we…
We investigate subshifts with a general algebraic structure and cellular automata on them, with an emphasis on (order-theoretic) lattices. Our main results concern the characterization of Boolean algebraic subshifts, conditions for…
We prove that certain Gibbs measures on subshifts of finite type are nonsingular and ergodic for certain countable equivalence relations, including the orbit relation of the adic transformation (the same as equality after a permutation of…
Certain fermionic quantum field theories are equivalent to probabilistic cellular automata, with fermionic occupation numbers associated to bits. We construct an automaton that represents a discrete model of spinor gravity in four…
It is shown that irreversible classical cellular automata can be performed by quantum algorithm using additional ancilla registers. The algorithm for cellular automata states analysis has been proposed. This algorithm is based on the…
Position uncertainty (delocalization) measures for a particle on the sphere are proposed and illustrated on several examples of states. The new measures are constructed using suitably the standard multiplication angle operator variances.…
Revisiting the notion of m-almost equicontinuous cellular automata introduced by R. Gilman, we show that the sequence of image measures of a shift ergodic measure m by iterations of a m-almost equicontinuous automata F, converges in Cesaro…
We establish a connection between percolation on the Cayley graphs of a group and the dynamical diversity of cellular automata on that group. Specifically, we demonstrate that Gilman's dichotomy between equicontinuity and sensitivity with…
We define unimodular measures on the space of rooted simplicial complexes and associate to each measure a chain complex and a trace function. As a consequence, we can define $\ell^2$-Betti numbers of unimodular random rooted simplicial…
We study linear response for families of skew-product dynamical systems with contracting fibres. Our approach is based on a sectional transfer operator acting on families of probability measures along the fibres. The operator allows to…
It is believed that some numerical technique must be employed for the determination of the system parameters of a visual binary or a star with a planet because the relevant equations are not only highly nonlinear but also transcendental…
We study cellular automata with randomly selected rules. Our setting are two-neighbor rules with a large number $n$ of states. The main quantity we analyze is the asymptotic probability, as $n \to \infty$, that the random rule has a…