Related papers: Two-dimensional individual clustering model
We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…
In an attempt to explain the uniqueness of the coding mechanism of living cells as contrasted with multi-species structure of ecosystems we examine two models of individuals with some replicative properties. In the first model the system…
The classical double bubble theorem characterizes the minimizing partitions of $\mathbb{R}^n$ into three chambers, two of which have prescribed finite volume. In this paper we prove a variant of the double bubble theorem in which two of the…
Traditionally, population models distinguish individuals on the basis of their current state. Given a distribution, a discrete time model then specifies (precisely in deterministic models, probabilistically in stochastic models) the…
This work examines the global dynamics of classical solutions of a two-stage (juvenile-adult) reaction-diffusion population model in time-periodic and spatially heterogeneous environments. It is shown that the sign of the principal…
After generalizing the concept of clusters to incorporate clusters that are linked to other clusters through some relatively narrow bridges, an approach for detecting patches of separation between these clusters is developed based on an…
Clustering aims to divide a set of points into groups. The current paradigm assumes that the grouping is well-defined (unique) given the probability model from which the data is drawn. Yet, recent experiments have uncovered several…
In a geographically distributed population, assortative clustering plays an important role in evolution by modifying local environments. To examine its effects in a linear habitat, we consider a one-dimensional grid of cells, where each…
In the article we establish the global well-posedness in W^{1,(6,2)}(R \times R+) of the integro-differential equation containing the cube of the one dimensional Laplacian and the transport term. Our proof relies on a fixed point technique.…
We analyze the Schelling model of segregation in which a society of n individuals live in a ring. Each individual is one of two races and is only satisfied with his location so long as at least half his 2w nearest neighbors are of the same…
An exact, number-conserving solution to the generalized, orbit-dependent pairing problem is derived by introducing an infinite-dimensional algebra. A method for obtaining eigenvalues and eigenvectors of the corresponding Hamiltonian is also…
In this paper we study a broad class of non-local advection-diffusion models describing the behaviour of an arbitrary number of interacting species, each moving in response to the non-local presence of others. Our model allows for different…
We consider three-dimensional clusters of identical bubbles packed around a central bubble and calculate their energy and optimal shape. We obtain the surface area and bubble pressures to improve on existing growth laws for…
Dynamical behavior of the clusters during relaxation is studied in two-dimensional Potts model using cluster algorithm. Average cluster size and cluster formation velocity are calculated on two different lattice sizes for different number…
Tissue growth can be modeled in two dimension by only using circular granular cells, which can grow and produce child. Linear spring-dashpot model is used to bind the cells with a cut-off interaction range of 1.1 times sum of radii of…
These notes address two problems. First, we investigate the question of ``how many'' are (in Baire sense) vector fields in $L^1_t L^q_x$, $q \in [1, \infty)$, for which existence and/or uniqueness of local, distributional solutions to the…
The concept of qudit (a d-level system) cluster state is proposed by generalizing the qubit cluster state (Phys. Rev. Lett. \textbf{86}, 910 (2001)) according to the finite dimensional representations of quantum plane algebra. We…
In this paper the initial value problem and global properties of solutions are studied for the scalar second order ODE: $ (|u'|^{l}u')' + c|u'|^{\alpha}u' + d|u|^\beta u=0$, where $\alpha,\beta,l,c, d$ are positive constants. In particular,…
We study a process termed "agglomerative percolation" (AP) in two dimensions. Instead of adding sites or bonds at random, in AP randomly chosen clusters are linked to all their neighbors. As a result the growth process involves a diverging…
Most generative models for clustering implicitly assume that the number of data points in each cluster grows linearly with the total number of data points. Finite mixture models, Dirichlet process mixture models, and Pitman--Yor process…