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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…
The study of dynamical large deviations allows for a characterization of stationary states of lattice gas models out of equilibrium conditioned on averages of dynamical observables. The application of this framework to the two-dimensional…
Cellular Automata (CAs) are computational models that can capture the essential features of systems in which global behavior emerges from the collective effect of simple components, which interact locally. During the last decades, CAs have…
We consider fluctuations of the time-averaged current in the one-dimensional weakly-asymmetric exclusion process on a ring. The optimal density profile which sustains a given fluctuation exhibits an instability for low enough currents,…
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…
Many-variable differential equations with random coefficients provide powerful models for the dynamics of many interacting species in ecology. These models are known to exhibit a dynamical phase transition from a phase where population…
The dynamical behavior of non-uniform cellular automata is compared with the one of classical cellular automata. Several differences and similarities are pointed out by a series of examples. Decidability of basic properties like…
The control of chaotic systems implies inducing an unpredictable system to follow a desired trajectory using the smallest "force". In low-dimensional continuous systems, one method is that of reconstructing the tangent space, so that the…
We consider discrete dynamical systems and lattice models in statistical mechanics from the point of view of their symmetry groups. We describe a C program for symmetry analysis of discrete systems. Among other features, the program…
Recent research on deep graph learning has shifted from static to dynamic graphs, motivated by the evolving behaviors observed in complex real-world systems. However, the temporal extension in dynamic graphs poses significant data…
We study two common types of time-noncontinuous updates for one dimensional stochastic cellular automata with arbitrary nearest neighbor interactions and arbitrary open boundary conditions. We first construct the stationary states using the…
We consider two-opinion voter models on dense dynamic random graphs. Our goal is to understand and describe the occurrence of consensus versus polarisation over long periods of time. The former means that all vertices have the same opinion,…
We investigate a social system of agents faced with a binary choice. We assume there is a correct, or beneficial, outcome of this choice. Furthermore, we assume agents are influenced by others in making their decision, and that the agents…
A general mathematical method is presented for the systematic construction of coupled map lattices (CMLs) out of deterministic cellular automata (CAs). The entire CA rule space is addressed by means of a universal map for CAs that we have…
In an adaptive population which models financial markets and distributed control, we consider how the dynamics depends on the diversity of the agents' initial preferences of strategies. When the diversity decreases, more agents tend to…
In this paper computer simulation results of higher order density correlation for cellular automaton models of traffic flow are presented. The examinations show the jamming transition as a function of both the density and the magnitude of…
Dynamical systems can be analyzed as computational devices capable of performing information processing. In coupled oscillators, enlarged capabilities are expected when the set of units is formed by subsets with collective behaviour within…
The path-preference traffic flow cellular automaton is suggested to model the dynamics of transcription. The main difference from the simple traffic flow model is that it contains another preferential paths at some sites. In this paper, we…
Most neural models of causality assume static causal graphs, failing to capture the dynamic and sparse nature of physical interactions where causal relationships emerge and dissolve over time. We introduce the Causal Process Framework and…
This paper introduces a novel approach for modelling time-varying connectivity in neuroimaging data, focusing on the slow fluctuations in synaptic efficacy that mediate neuronal dynamics. Building on the framework of Dynamic Causal…