A Comparison Between Different Cycle Decompositions for Metropolis Dynamics

In the last decades the problem of metastability has been attacked on rigorous grounds via many different approaches and techniques which are briefly reviewed in this paper. It is then useful to understand connections between different point of views. In view of this we consider irreducible, aperiodic and reversible Markov chains with exponentially small transition probabilities in the framework of Metropolis dynamics. We compare two different cycle decompositions and prove their equivalence

Competitive nucleation in metastable systems

Metastability is observed when a physical system is close to a first order phase transition. In this paper the metastable behavior of a two state reversible probabilistic cellular automaton with self-interaction is discussed. Depending on the self-interaction, competing metastable states arise and a behavior very similar to that of the three state Blume-Capel spin model is found

Basic Ideas to Approach Metastability in Probabilistic Cellular Automata

Cellular Automata are discrete--time dynamical systems on a spatially extended discrete space which provide paradigmatic examples of nonlinear phenomena. Their stochastic generalizations, i.e., Probabilistic Cellular Automata, are discrete time Markov chains on lattice with finite single--cell states whose distinguishing feature is the \textit{parallel} character of the updating rule. We review some of the results obtained about the metastable behavior of Probabilistic Cellular Automata and we try to point out difficulties and peculiarities with respect to standard Statistical Mechanics Lattice models.Comment: arXiv admin note: text overlap with arXiv:1307.823

A comparison between different cycle decompositions for Metropolis dynamics

In the last decades the problem of metastability has been attacked on rigorous grounds via many different approaches and techniques which are briefly reviewed in this paper. It is then useful to understand connections between different point of views. In view of this we consider irreducible, aperiodic and reversible Markov chains with exponentially small transition probabilities in the framework of Metropolis dynamics. We compare two different cycle decompositions and prove their equivalence

Electrocardiography for Assessment of Hypertensive Heart Disease: A New Role for an Old Tool

Left ventricular (LV) hypertrophy (LVH), detected either by electrocardiography (ECG) or echocardiography (ECHO), has long been recognized as a powerful predictor of serious cardiovascular (CV) sequelae.A very large and highly consistent body of evidence indicates that LVH is not only an adaptation to increased hemodynamic load in hypertension, but is also independently associated with an enhanced risk for myocardial infarction, cardiac sudden death, congestive heart failure, and stroke in the general population, as well as in patients with systemic hypertension, coronary heart disease, chronic kidney disease, and atrial fibrillation. Intriguingly, the cumulative incidence of cardiovascular events increases progressively with increasing LV mass (LVM), without evidence of any threshold separating the postulated “compensatory” from “pathological” LVH. In other words, patients with LVM in the upper-normal range already have increased risk for CV events

Competitive nucleation in reversible Probabilistic Cellular Automata

The problem of competitive nucleation in the framework of Probabilistic Cellular Automata is studied from the dynamical point of view. The dependence of the metastability scenario on the self--interaction is discussed. An intermediate metastable phase, made of two flip--flopping chessboard configurations, shows up depending on the ratio between the magnetic field and the self--interaction. A behavior similar to the one of the stochastic Blume--Capel model with Glauber dynamics is found

Phase transitions in random mixtures of elementary cellular automata

We investigate one-dimensional probabilistic cellular automata, called Diploid Elementary Cellular Automata (DECA), obtained as random mixtures of two different elementary cellular automata rules. All the cells are updated synchronously and the probability for one cell to be 0 or 1 at time t depends only on the value of the same cell and that of its neighbors at time t−1. These very simple models show a very rich behavior strongly depending on the choice of the two elementary cellular automata that are randomly mixed together and on the parameter which governs probabilistically the mixture. In particular, we study the existence of phase transition for the whole set of possible DECA obtained by mixing the null rule which associates 0 to any possible local configuration, with any of the other 255 elementary rules. We approach the problem analytically via a mean field approximation and via the use of a rigorous approach based on the application of the Dobrushin criterion. The main feature of our approach is the possibility to describe the behavior of the whole set of considered DECA without exploiting the local properties of the individual models. The results that we find are consistent with numerical studies already published in the scientific literature and also with some rigorous results proven for some specific models