Related papers: Preferential growth: Solution and application to m…
Finding the most powerful node in a dynamic random network, the largest set in a partition-valued stochastic process, or the largest family in an evolving population at a given time, can be a very difficult problem. This is particularly the…
We study the basic preferential attachment process, which generates a sequence of random trees, each obtained from the previous one by introducing a new vertex and joining it to one existing vertex, chosen with probability proportional to…
We investigate the Plackett-Luce (PL) model based listwise learning-to-rank (LTR) on data with partitioned preference, where a set of items are sliced into ordered and disjoint partitions, but the ranking of items within a partition is…
Heavy particles in turbulent flows have been shown to accumulate in regions of high strain rate or low vorticity, a process otherwise known as preferential concentration. This can be observed in geophysical flows, and is inferred to occur…
Monolayer cluster growth in far-from-equilibrium systems is investigated by applying simulation and analytic techniques to minimal hard core particle (exclusion) models. The first model (I), for post-deposition coarsening dynamics, contains…
This work presents a technique for particle size generation and placement in arbitrary closed domains. Its main application is the simulation of granular media described by disks. Particle size generation is based on the statistical…
We consider the time evolution of the supercritical Galton-Watson model of branching particles with extra parameter (mass). In the moment of the division the mass of the particle (which is growing linearly after the birth) is divided in…
A new model that describes adsorption and clustering of particles on a surface is introduced. A {\it clustering} transition is found which separates between a phase of weakly correlated particle distributions and a phase of strongly…
Assuming a uniform $q$-variant of the prime $k$-tuple conjecture, we compute moments of the number of primes in arithmetic progressions to a large modulus $q$ as the residue classes vary. Consequently, depending on the size of $\varphi(q)$,…
We study the cluster size distribution of particles for a two-species exclusion process which involves totally asymmetric transport process of two oppositely directed species with stochastic directional switching of the species on a 1D…
We prove almost sure convergence of the maximum degree in an evolving graph model combining a growing number of local choices with sublinear preferential attachment. At each step in the growth of the graph, a new vertex is introduced. Then…
We outline a theoretical framework for estimating the evolution of the particle size distribution in colloid and nanoparticle synthesis, when the primary growth mode is by externally controlled addition of singlet building blocks. The…
The availability of large scale streaming network data has reinforced the ubiquity of power-law distributions in observations and enabled precision measurements of the distribution parameters. The increased accuracy of these measurements…
Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies…
A family of models of growing hypergraphs with preferential rules of new linking is introduced and studied. The model hypergraphs evolve via the hyperedge-based growth as well as the node-based one, thus generalizing the…
We study a stochastic model for tumor cell growth with both multiplicative and additive colored noise as well as a non-zero cross-correlations in between. Whereas the death rate within the logistic model is altered by a deterministic term…
Cluster analysis aims at partitioning data into groups or clusters. In applications, it is common to deal with problems where the number of clusters is unknown. Bayesian mixture models employed in such applications usually specify a…
A preferential attachment model for a growing network incorporating deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step $t=1,2,\ldots$, with probability $\pi_1>0$ a new vertex with one…
Initialisation of the EM algorithm in model-based clustering is often crucial. Various starting points in the parameter space often lead to different local maxima of the likelihood function and, so to different clustering partitions. Among…
A recent model for the stock market calculates future price distributions of a stock as a wave function of a quantum particle confined in an infinite potential well. In such a model the question arose as to how to estimate the classical…