相关论文: Intermittency and Aging for the Symbiotic Branchin…
Approximating the time to extinction of infection is an important problem in infection modelling. A variety of different approaches have been proposed in the literature. We study the performance of a number of such methods, and characterize…
This paper develops a point-mutation model describing the evolutionary dynamics of a population of adult stem cells. Such a model may prove useful for quantitative studies of tissue aging and the emergence of cancer. We consider two modes…
We study the ageing properties of the semi-infinite kinetic spherical model at the critical point and in the ordered low-temperature phase, both for Dirichlet and Neumann boundary conditions. The surface fluctuation-dissipation ratio and…
We corroborate the idea of a close connection between replica symmetry breaking and aging in the linear response function for a large class of finite-dimensional systems with short-range interactions. In these system, characterized by a…
The goal of this article is to contribute towards the conceptual and quantitative understanding of the evolutionary benefits for (microbial) populations to maintain a seed bank (consisting of dormant individuals) when facing fluctuating…
The first-passage-time problem for a Brownian motion with alternating infinitesimal moments through a constant boundary is considered under the assumption that the time intervals between consecutive changes of these moments are described by…
We introduce a novel approach of epidemic modeling by combining age-structured models with damped wave equations. This transforms the parabolic-type reaction-diffusion model into a hyperbolic system that shares many properties with a wave…
We introduce and discuss a kinetic framework describing the time evolution of the statistical distributions of a population divided into the compartments of susceptible, infectious, recovered, and resistant in the presence of a microbial…
A stochastic genetic model for biological aging is introduced bridging the gap between the bit-string Penna model and the Pletcher-Neuhauser approach. The phenomenon of exponentially increasing mortality function at intermediate ages and…
Current modeling of infectious diseases allows for the study of complex and realistic scenarios that go from the population to the individual level of description. However, most epidemic models assume that the spreading process takes place…
In this paper, we study a spatial model for dormancy in random environment via a two-type branching random walk in continuous-time, where individuals can switch between dormant and active states through spontaneous switching independent of…
The versatility of renewal theory is owed to its abstract formulation. Renewals can be interpreted as steps of a random walk, switching events in two-state models, domain crossings of a random motion, etc. We here discuss a renewal process…
The parabolic Anderson model is the Cauchy problem for the heat equation on the integer lattice with a random potential $\xi$. We consider the case when $\{\xi(z):z\in\mathbb{Z}^d\}$ is a collection of independent identically distributed…
This is a survey on the intermittent behavior of the parabolic {Anderson} model, which is the Cauchy problem for the heat equation with random potential on the lattice $\Z^d$. We first introduce the model and give heuristic explanations of…
Our Recent advancements in stochastic processes have illuminated a paradox associated with the Einstein model of Brownian motion. The model predicts an infinite propagation speed, conflicting with the second law of thermodynamics. The…
This paper concerns modeling of the evolution of intermittency region between two weakly miscible phases due to temporal and spatial variations of its characteristic length scale. First, the need of a more general description allowing for…
We present a new model for the diffusion of innovation. Here, the population is segmented into distinct groups. Adoption by a particular group of some cultural product may be inhibited both by large numbers of its own members already having…
In 1962, Dyson introduced dynamics in random matrix models, in particular into GUE (also for beta=1 and 4), by letting the entries evolve according to independent Ornstein-Uhlenbeck processes. Dyson shows the spectral points of the matrix…
Turbulence is known to show intermittency. That is, statistical properties vary with the length scale in a way not accounted for by statistical similarity where dimensionless ratios of moments are constant. Intermittency occurs even in the…
We consider a model of Branching Brownian Motion in which the usual spatially-homogeneous and catalytic branching at a single point are simultaneously present. We establish the almost sure growth rates of population in certain…