相关论文: Two-dimensional individual clustering model

We prove large-data local stability theorems for several spin models in two dimensions.

The scaling properties of the cluster size distribution of a system of diffusing clusters is studied in terms of a simple kinetic mean field model. It is shown that a one parameter family of mathematically valid scaling solutions exists.…

The two-time distribution gives the limiting joint distribution of the heights at two different times of a local 1D random growth model in the curved geometry. This distribution has been computed in a specific model but is expected to be…

We construct a continuum model for biological aggregations in which individuals experience long-range social attraction and short range dispersal. For the case of one spatial dimension, we study the steady states analytically and…

Networks provide a mathematically rich framework to represent social contacts sufficient for the transmission of disease. Social networks are often highly clustered and fail to be locally tree-like. In this paper, we study the effects of…

This paper develops a quasispecies model where cells can adopt a two-cell survival strategy. Within this strategy, pairs of cells join together, at which point one of the cells sacrifices its own replicative ability for the sake of the…

Bi-clustering is a useful approach in analyzing biological data when observations come from heterogeneous groups and have a large number of features. We outline a general Bayesian approach in tackling bi-clustering problems in moderate to…

Cell-cell adhesion is an inherently nonlocal phenomenon. Numerous partial differential equation models with nonlocal term have been recently presented to describe this phenomenon, yet the mathematical properties of nonlocal adhesion model…

Sexual reproduction in Nature requires two sexes, which raises the question why the reproductive scheme did not evolve to have three or more sexes. Here we construct a constrained optimization model based on the communication theory to…

The two-parent reproduction model of Derrida and Peliti is simulated on a rugged fitness landscape. Fixed fitness values for each possible genotype are assigned randomly, with all fit individuals having the same probability of reproduction.…

We report on a study of a finite system of classical confined particles in two-dimensions in the presence of a uniform magnetic field and interacting via a two-body repulsive potential. We develop a simple analytical method of analysis to…

Persistence is considered in diffusion--limited cluster--cluster aggregation, in one dimension and when the diffusion coefficient of a cluster depends on its size $s$ as $D(s) \sim s^\gamma$. The empty and filled site persistences are…

We prove that for q>=1, there exists r(q)<1 such that for p>r(q), the number of points in large boxes which belongs to the infinite cluster has a normal central limit behaviour under the random cluster measure phi_{p,q} on Z^d, d>=2.…

We examine the two-dimensional extension of the model of Kessler and Sander of competition between two species identical except for dispersion rates. In this class of models, the spatial inhomogeneity of reproduction rates gives rise to an…

We consider the problem of analyzing the heterogeneity of clustering distributions for multiple groups of observed data, each of which is indexed by a covariate value, and inferring global clusters arising from observations aggregated over…

The $q=2$ random cluster model is studied in the context of two mean field models: The Bethe lattice and the complete graph. For these systems, the critical exponents that are defined in terms of finite clusters have some anomalous values…

We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…

We investigate the formation of clusters of galaxies in an expanding universe using a new code that regrids at a region of high density. In particular we investigate two models for the initial conditions, both with the standard CDM power…

Pattern formation in microbial colonies of competing strains under purely space-limited population growth has recently attracted considerable research interest. We show that the reproduction time statistics of individuals has a significant…

In this paper we present some basic uniqueness results for evolutive equations under density constraints. First, we develop a rigorous proof of a well-known result (among specialists) in the case where the spontaneous velocity field…