Related papers: Two-dimensional individual clustering model
We show that the $i$-dimensional plaqutte random-cluster model with coefficients in $\mathbb{Z}_q$ is dual to a $(d-i)$-dimensional plaquette random cluster model. In addition, we explore boundary conditions, infinite volume limits, and…
This study concentrates on clustering problems and aims to find compact clusters that are informative regarding the outcome variable. The main goal is partitioning data points so that observations in each cluster are similar and the outcome…
Outlier detection and cluster number estimation is an important issue for clustering real data. This paper focuses on spectral clustering, a time-tested clustering method, and reveals its important properties related to outliers. The…
Part I of the thesis gives a complete analysis of gaps in a one-dimensional creation-annihilation model. Part II contains a proof of the existence of infinitely many holes in the two-dimensional DLA cluster.
A two species reaction-diffusion model, in which particles diffuse on a one-dimensional lattice and annihilate when meeting each other, has been investigated. Mean field equations for general choice of reaction rates have been solved…
We numerically investigate the vibrational spectra of single-component clusters in two-dimensions. Stable configurations of clusters at local energy minima are obtained, and for each the hessian matrix is evaluated and diagonalized to…
The ubiquitous occurrence of cluster patterns in nature still lacks a comprehensive understanding. It is known that the dynamics of many such natural systems is captured by ensembles of Stuart-Landau oscillators. Here, we investigate…
Using a simulated annealing, we examine a bipartitioning of small worlds obtained by adding a fraction of randomly chosen links to a one-dimensional chain or a square lattice. Models defined on small worlds typically exhibit a mean-field…
Bayesian mixture models are widely used for clustering of high-dimensional data with appropriate uncertainty quantification. However, as the dimension of the observations increases, posterior inference often tends to favor too many or too…
Subspace clustering is the classical problem of clustering a collection of data samples that approximately lie around several low-dimensional subspaces. The current state-of-the-art approaches for this problem are based on the…
We present exact results for a lattice model of cluster growth in 1D. The growth mechanism involves interface hopping and pairwise annihilation supplemented by spontaneous creation of the stable-phase, +1, regions by overturning the…
We study a percolation model on the square lattice, where clusters "freeze" (stop growing) as soon as their volume (i.e. the number of sites they contain) gets larger than N, the parameter of the model. A model where clusters freeze when…
Stochastic modeling of disease dynamics has had a long tradition. Among the first epidemic models including a spatial structure in the form of local interactions is the contact process. In this article we investigate two extensions of the…
Exactly solvable two-dimensional polygon models, counted by perimeter and area, are described by $q$-algebraic functional equations. We provide techniques to extract the scaling behaviour of these models up to arbitrary order and apply them…
Usual formulations of the clustering coefficient can be shown to be insufficient in the task of describing the local topology of very simple networks. Motivated by this, we review some alternatives in order to present an extension, the…
We prove that the two-dimensional Schelling segregation model yields monochromatic regions of size exponential in the area of individuals' neighborhoods, provided that the tolerance parameter is a constant strictly less than 1/2 but…
The formation history of rich clusters is investigated using a hybrid N-body simulation in which high spatial and mass resolution can be achieved self-consistently within a small region of a very large volume. The evolution of three massive…
We consider a spatial multi-type branching model in which individuals migrate in geographic space according to random walks and reproduce according to a state-dependent branching mechanism which can be sub-, super- or critical depending on…
This paper studies the bounded confidence model on growing fully-mixed populations. In this model, in addition to the usual opinion clusters, significant secondary clusters of smaller size appear systematically, while those secondary…
The work is devoted to establishing the global well-posedness in $W^{(1,2),2}(R\times R^{+})$ of the integro-differential problem involving the two nonlocal terms describing the diffusion and the production in the biological system in the…