Related papers: Branching Process in a Stochastic Extremal Model
We study the susceptibility, i.e., the mean cluster size, in random graphs with given vertex degrees. We show, under weak assumptions, that the susceptibility converges to the expected cluster size in the corresponding branching process. In…
Spontaneous symmetry breaking (SSB) occurs when modes of asymmetric profile appear in a symmetric, double-well potential, due to the nonlinearity of the potential exceeding a critical value. In this study, we examine SSB in a periodic…
Natural microbial populations often have complex spatial structures. This can impact their evolution, in particular the ability of mutants to take over. While mutant fixation probabilities are known to be unaffected by sufficiently…
The literature considers multi-type Markov branching processes (BPs), where the offspring distribution depends only on the living (current) population. We analyse the total-current population-dependent BPs where the offspring distribution…
The scaled Brownian motion (SBM) is regarded as one of the paradigmatic random processes, featuring the anomalous diffusion property characterized by the diffusion exponent. It is a Gaussian, self-similar process with independent…
The stable-regenerative multiple-stable model has been shown recently to have distinct candidate extremal index and extremal index. To understand further this rare phenomenon, two more results are established here for the double-stable…
We consider restricted Boltzmann machine (RBMs) trained over an unstructured dataset made of blurred copies of definite but unavailable ``archetypes'' and we show that there exists a critical sample size beyond which the RBM can learn…
We consider a critical continuous-time branching process (a Yule process) in which the individuals independently execute symmetric $\alpha-$stable random motions on the real line starting at their birth points. Because the branching process…
We report a simple method to accurately determine the threshold and the exponent $\nu$ of the Bak-Sneppen model and also investigate the BS universality class. For the random-neighbor version of the BS model, we find the threshold…
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 explore the critical behaviors in the dynamics of information transfer of a biologically-inspired system by an individual-based model. "Quorum response", a type of social interaction which has been recognized taxonomically in animal…
We describe a general-purpose method for finding high-quality solutions to hard optimization problems, inspired by self-organized critical models of co-evolution such as the Bak-Sneppen model. The method, called Extremal Optimization,…
We propose a general scenario to analyze social and economic changes in modern environments. We illustrate the ideas with a model that incorporating the main trends is simple enough to extract analytical results and, at the same time,…
We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…
We propose a spreading model in multilayer networks and study the nature of nonequilibrium phase transition in the model. The model integrates the susceptible-infected-susceptible (or susceptible-infected-recovered) spreading dynamics with…
We are interested in the impact of natural selection in a prey-predator community. We introduce an individual-based model of the community that takes into account both prey and predator phenotypes. Our aim is to understand the phenotypic…
We consider two, apparently similar, models of biological evolution which have been claimed to exhibit self-organized critical behaviour. A careful reanalysis of these models, including several new analytic results for one of them, suggests…
A dynamical model of an ecological community is analyzed within a "mean-field approximation" in which one of the species interacts with the combination of all of the other species in the community. Within this approximation the model may be…
In this thesis we present few theoretical studies of the models of self-organized criticality. Following a brief introduction of self-organized criticality, we discuss three main problems. The first problem is about growing patterns formed…
Schr\"odinger bridges (SBs) provide an elegant framework for modeling the temporal evolution of populations in physical, chemical, or biological systems. Such natural processes are commonly subject to changes in population size over time…