Related papers: Phase Transitions of Cellular Automata
Although traffic simulations with cellular-automata models give meaningful results compared with empirical data, highway traffic requires a more detailed description of the elementary dynamics. Based on recent empirical results we present a…
Many biological and medical questions can be modeled using time-to-event data in finite-state Markov chains, with the phase-type distribution describing intervals between events. We solve the inverse problem: given a phase-type…
We study a non-ergodic one-dimensional probabilistic cellular automata, where each component can assume the states $\+$ and $\-.$ We obtained the limit distribution for a set of measures on $\{\+,\-\}^\Z.$ Also, we show that for certain…
The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a…
We propose a new Monte Carlo method for efficiently sampling trajectories with fixed initial and final conditions in a system with discrete degrees of freedom. The method can be applied to any stochastic process with local interactions,…
We extend Cellular Automata to time-varying discrete geometries. In other words we formalize, and prove theorems about, the intuitive idea of a discrete manifold which evolves in time, subject to two natural constraints: the evolution does…
We introduce a new class of cellular automata to model reaction-diffusion systems in a quantitatively correct way. The construction of the CA from the reaction-diffusion equation relies on a moving average procedure to implement diffusion,…
Number-conserving (or {\em conservative}) cellular automata have been used in several contexts, in particular traffic models, where it is natural to think about them as systems of interacting particles. In this article we consider several…
The traditional concept of phase transitions has, in recent years, been widened in a number of interesting ways. The concept of a topological phase transition separating phases with a different ground state topology, rather than phases of…
In this paper I present a first attempt for a possible description of fluids dynamics by mean of a cellular automata technique. With the use of simple and elementary rules, based on random behaviour either, the model permits to obtain the…
Cellular automata are both computational and dynamical systems. We give a complete classification of the dynamic behaviour of elementary cellular automata (ECA) in terms of fundamental dynamic system notions such as sensitivity and…
A classical local cellular automaton can describe an interacting quantum field theory for fermions. We construct a simple classical automaton for a particular version of the Thirring model with imaginary coupling. This interacting fermionic…
The synchronization of two stochastically coupled one-dimensional cellular automata (CA) is analyzed. It is shown that the transition to synchronization is characterized by a dramatic increase of the statistical complexity of the patterns…
We analyze a stochastic 5-neighbor cellular automaton with several conserved quantities, including the particle density. By examining the eigenvalue problem of the associated transition matrix, we derive an explicit formula for the…
We present a new method for simulating Markovian jump processes with time-dependent transitions rates, which avoids the transformation of random numbers by inverting time integrals over the rates. It relies on constructing a sequence of…
Cellular automata (CA) exemplify systems where simple local interaction rules can lead to intricate and complex emergent phenomena at large scales. The various types of dynamical behavior of CA are usually categorized empirically into…
A commonly used model for fault-tolerant computation is that of cellular automata. The essential difficulty of fault-tolerant computation is present in the special case of simply remembering a bit in the presence of faults, and that is the…
Lattice models exhibit significant potential in investigating phase transitions, yet they encounter numerous computational challenges. To address these issues, this study introduces a Monte Carlo-based approach that transforms lattice…
In a physical system, changing parameters such as temperature can induce a phase transition: an abrupt change from one state of matter to another. Analogous phenomena have recently been observed in large language models. Typically, the task…
We propose a 2-dimensional cellular automaton model to simulate pedestrian traffic. It is a vmax=1 model with exclusion statistics and parallel dynamics. Long-range interactions between the pedestrians are mediated by a so called floor…