Related papers: Critical values in Bak-Sneppen type models
We introduce a kinetic framework for modeling the time evolution of the statistical distributions of the population densities in the three compartments of susceptible, infectious, and recovered individuals, under epidemic spreading driven…
We present two classes of nonequilibrium models with critical behavior. Each model is characterized by an integer $q>1$, and is defined on configurations of $q$-valued spins on regular lattices. The definitions of the models are very…
Nonequilibrium kinetic Ising models evolving under the competing effect of spin flips at zero temperature and Kawasaki-type spin-exchange kinetics at infinite temperature T are investigated here in one dimension from the point of view of…
Given a discrete spatial structure $X$, we define continuous-time branching processes that model a population breeding and dying on $X$. These processes are usually called branching random walks. They are characterized by breeding rates…
We study the discrete Bak-Sneppen model introduced by Barbay and Kenyon (2001) "On the discrete Bak-Sneppen model of self-organized criticality". We extend their results as well as the non-triviality result of Meester and Znamenskiy (2002)…
We obtain a Bernstein-type inequality for sums of Banach-valued random variables satisfying a weak dependence assumption of general type and under certain smoothness assumptions of the underlying Banach norm. We use this inequality in order…
We study the limit distribution of the largest fitness for two models of weakly correlated and identically distributed random fitnesses. The correlated fitness is given by a linear combination of a fixed number of independent random…
Extremal dynamics represents a path to self-organized criticality in which the order parameter is tuned to a value of zero. The order parameter is associated with a phase transition to an absorbing state. Given a process that exhibits a…
Discrete-element simulations are used to monitor several micro-scale characteristics within a granular material, demonstrating their convergence during loading toward the critical state, their stationarity at the critical state, and the…
Statistical system models provide the basis for the examination of various sorts of distributions. Classification distributions are a very common and versatile form of statistics in e.g. real economic, social, and IT systems. The…
The $NK$ model, introduced by Kauffman, Levin, and Weinberger, is a random field used to describe the fitness landscape of certain species with $N$ genetic loci, each interacting with $K$ others. The model has wide applications in…
We study a one-dimensional model which undergoes a transition between an active and an absorbing phase. Monte Carlo simulations supported by some additional arguments prompted as to predict the exact location of the critical point and…
We introduce a class of Kac-like kinetic equations on the real line, with general random collisional rules, which include as particular cases models for wealth redistribution in an agent-based market or models for granular gases with a…
In the Hegselmann-Krause model, an agent updates its opinion by averaging with others whose opinions differ by at most a given confidence threshold. With agents' initial opinions uniformly distributed on the unit interval, we provide a…
This paper proposes a unified version of survival models that accounts for both zero-adjustment and cure proportions in various latent competing causes, useful in data where survival times may be zero or cure proportions are present. These…
Bootstrap percolation is a wide class of monotone cellular automata with random initial state. In this work we develop tools for studying in full generality one of the three `universality' classes of bootstrap percolation models in two…
The effect of blocking between different species occurring in one dimension is investigated here numerically in the case of particles following branching and annihilating random walk with two offsprings. It is shown that two-dimensional…
Basic human values represent a set of values such as security, independence, success, kindness, and pleasure, which we deem important to our lives. Each of us holds different values with different degrees of significance. Existing studies…
We study the universal critical behaviour near weakly first-order phase transitions for a three-dimensional model of two coupled scalar fields -- the cubic anisotropy model. Renormalization-group techniques are employed within the formalism…
The feature space (including both input and output variables) characterises a data mining problem. In predictive (supervised) problems, the quality and availability of features determines the predictability of the dependent variable, and…