Related papers: Intermediate model between Majority voter PCA and …
As one of the newest members in the field of artificial immune systems (AIS), the Dendritic Cell Algorithm (DCA) is based on behavioural models of natural dendritic cells (DCs). Unlike other AIS, the DCA does not rely on training data,…
From the perspective of the large deviations theory of occupational measures, the paper considers Probabilistic Cellular Automata (PCA) as Markov chains on infinite dimensional space. It turns out that for a wide range of PCA, the…
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…
This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…
Thermal noise in a cellular automaton refers to a random perturbation to its function which eventually leads this automaton to an equilibrium state controlled by a temperature parameter. We study the 1-dimensional majority-3 cellular…
We study a probabilistic cellular automaton to describe two population biology problems: the threshold of species coexistence in a predator-prey system and the spreading of an epidemic in a population. By carrying out time-dependent…
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…
We present numerical results obtained from the modelling of a stochastic, highly connected and mobile community. The spread of attributes like health, disease among the community members is simulated using cellular automata on a planar 2…
Quantum cellular automata consist in arrays of identical finite-dimensional quantum systems, evolving in discrete-time steps by iterating a unitary operator G. Moreover the global evolution G is required to be causal (it propagates…
This article introduces the notion of clouds in asynchronous cellular automata (ACAs). We show that the cloud behaviour of ACAs has similarity with natural clouds across the sky, election model of parliamentary democratic system, and…
We focus on a family of one-dimensional probabilistic cellular automata with memory two: the dynamics is such that the value of a given cell at time $t+1$ is drawn according to a distribution which is a function of the states of its two…
The phase transition kinetics in three phase systems was investigated using the numerically efficient cell dynamics method. A phasefield model with a simple analytical free energy and single order parameter was used to study the kinetics…
We study the problem of reconstructing the probability measure of the Curie-Weiss model from a sample of the voting behaviour of a subset of the population. While originally used to study phase transitions in statistical mechanics, the…
A model of multicellular systems with several types of cells is developed from the phase field model. The model is presented as a set of partial differential equations of the field variables, each of which expresses the shape of one cell.…
People are often divided into conformists and contrarians, the former tending to align to the majority opinion in their neighborhood and the latter tending to disagree with that majority. In practice, however, the contrarian tendency is…
The proposed stochastic model for pedestrian dynamics is based on existing approaches using cellular automata, combined with substantial extensions, to compensate the deficiencies resulting of the discrete grid structure. This agent motion…
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 use analytical methods to investigate cellular automata for traffic flow. Two different mean-field approaches are presented, which we call site-oriented and car-oriented, respectively. The car-oriented mean-field theory yields the exact…
Principal components analysis (PCA) is a classical method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. For a simple model of factor analysis type, it is proved that…
Principal component analysis (PCA) is a most frequently used statistical tool in almost all branches of data science. However, like many other statistical tools, there is sometimes the risk of misuse or even abuse. In this paper, we…