Related papers: Cluster persistence in one-dimensional diffusion--…
The persistence probability is a statistical index that has been proposed to detect one or more communities embedded in a network. Even though its definition is straightforward, e.g, the probability that a random walker remains in a group…
Networks of person-person contacts form the substrate along which infectious diseases spread. Most network-based studies of the spread focus on the impact of variations in degree (the number of contacts an individual has). However, other…
Clusters are the dense inner regions of a wide-spread hierarchy of young stellar structures. They often reveal a continuation of this hierarchy inside of them, to smaller scales, when they are young, but orbital mixing eventually erases…
We consider a stochastic aggregation model on Z^d. Start with particles located at the vertices of the lattice, initially distributed according to the product Bernoulli measure with parameter \mu. In addition, there is an aggregate, which…
We study infection spread among biased random walks on $\mathbb{Z}^{d}$. The random walks move independently and an infected particle is placed at the origin at time zero. Infection spreads instantaneously when particles share the same site…
The dynamics of dispersal-structured populations, consisting of competing individuals that are characterized by different diffusion coefficients but are otherwise identical, is investigated. Competition is taken into account through…
Cluster analysis is an unsupervised learning strategy that can be employed to identify subgroups of observations in data sets of unknown structure. This strategy is particularly useful for analyzing high-dimensional data such as microarray…
In ballistic annihilation, infinitely many particles with randomly assigned velocities move across the real line and mutually annihilate upon contact. We introduce a variant with superimposed clusters of multiple stationary particles. Our…
We use experiments to study the evolution of bubble clusters in a swarm of freely rising, deformable bubbles. A new machine learning-aided algorithm allows us to identify and track bubbles in clusters and measure the cluster lifetimes. The…
We address the problem of validating the ouput of clustering algorithms. Given data $\mathcal{D}$ and a partition $\mathcal{C}$ of these data into $K$ clusters, when can we say that the clusters obtained are correct or meaningful for the…
We study the evolution of random graphs where edges are added one by one between pairs of weighted vertices so that resulting graphs are scale-free with the degree exponent $\gamma$. We use the branching process approach to obtain scaling…
We investigate a class of stochastic aggregation processes involving two types of clusters: active and passive. The mass distribution is obtained analytically for several aggregation rates. When the aggregation rate is constant, we find…
In critical percolation models, in a large cube there will typically be more than one cluster of comparable diameter. In 2D, the probability of $k>>1$ spanning clusters is of the order $e^{-\alpha k^{2}}$. In dimensions d>6, when $\eta = 0$…
Dissipation in granular media leads to interesting phenomena as there are cluster formation and crystallization in non-equilibrium dynamical states. The freely cooling system is examined concerning the energy decay and the cluster evolution…
The absolute magnitude of the brightest galaxy of clusters varies remarkably little and is nearly independent of all other physical properties of the cluster as, e.g., its spatial extension or its richness. The question arises whether the…
Series expansion methods are used to study directed bond percolation clusters on the square lattice whose lateral growth is restricted by a wall parallel to the growth direction. The percolation threshold $p_c$ is found to be the same as…
We study the Brownian motion of a classical particle in one-dimensional inhomogeneous environments where the transition probabilities follow quasiperiodic or aperiodic distributions. Exploiting an exact correspondence with the…
We analyze the behavior of an ensemble of inertial particles in a one-dimensional smooth Gaussian velocity field, in the limit of large inertia, but considering a finite correlation time for the random field. We derive in this limit a…
The average number $S_N(t)$ of distinct sites visited up to time t by N noninteracting random walkers all starting from the same origin in a disordered fractal is considered. This quantity $S_N(t)$ is the result of a double average: an…
The growth of a diffusion limited aggregation (DLA) cluster with mass $M$ and radius of gyration $R$ is described by a set of growth probabilities $\{ p_i\}$, where $p_i$ is the probability that the perimeter site $i$ will be the next to…