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In most of the recent immunological literature the differences across antigen receptor populations are examined via non-parametric statistical measures of species overlap and diversity borrowed from ecological studies. While this approach…
The Pearson family of ergodic diffusions with a quadratic diffusion coefficient and a linear force are characterized by explicit dynamics of their integer moments and by explicit relaxation spectral properties towards their steady state.…
Using an efficient one and two qubit gate simulator, operating on graphical processing units, we investigate ergodic properties of a quantum Ising spin 1/2 model on a two dimensional lattice, which is periodically driven by a…
Brownian yet non-Gaussian diffusion has recently been observed in numerous biological and active matter system. The cause of the non-Gaussian distribution have been elaborately studied in the idea of a superstatistical dynamics or a…
We introduce a class of discrete random walk model driven by global memory effects. At any time the right-left transitions depend on the whole previous history of the walker, being defined by an urn-like memory mechanism. The characteristic…
We consider adaptive maximum-likelihood-type estimators and adaptive Bayes-type ones for discretely observed ergodic diffusion processes with observation noise whose variance is constant. The quasi-likelihood functions for the diffusion and…
The Rosenzweig-Porter model is a one-parameter family of random matrices with three different phases: ergodic, extended non-ergodic and localized. We characterize numerically each of these phases and the transitions between them. We focus…
A novel over-dispersed discrete distribution, namely the PoiTG distribution is derived by the convolution of a Poisson variate and an independently distributed transmuted geometric random variable. This distribution generalizes the…
In considering evolution of transcribed regions, regulatory modules, and other genomic loci of interest, we are often faced with a situation in which the number of allelic states greatly exceeds the population size. In this limit, the…
In this paper, an alternative mixed Poisson distribution is proposed by amalgamating Poisson distribution and a modification of the Quasi Lindley distribution. Some fundamental structural properties of the new distribution, namely the shape…
We consider a nonlinear drift-diffusion system for multiple charged species in a porous medium in 2D and 3D with periodic microstructure. The system consists of a transport equation for the concentration of the species and Poisson's…
We present a novel mathematical model of heterogeneous cell proliferation where the total population consists of a subpopulation of slow-proliferating cells and a subpopulation of fast-proliferating cells. The model incorporates two…
We consider parametric tests for multidimensional ergodic diffusions based on high frequency data. We propose two-step testing method for diffusion parameters and drift parameters. To construct test statistics of the tests, we utilize the…
Several results of large deviations are obtained for distributions that are associated with the Poisson--Dirichlet distribution and the Ewens sampling formula when the parameter $\theta$ approaches infinity. The motivation for these results…
The paper deals with a three-dimensional family of diffusion processes on an infinite-dimensional simplex. These processes were constructed by Borodin and Olshanski (arXiv:0706.1034; arXiv:0902.3395), and they include, as limit objects, the…
With the multiallelic parent-independent mutation-drift model, the equilibrium proportions of alleles are known to be Dirichlet distributed. A special case is the biallelic model, in which the proportions are beta distributed. A sample…
Motivated by genome-wide association studies, we consider a standard linear model with one additional random effect in situations where many predictors have been collected on the same subjects and each predictor is analyzed separately.…
A random-walk Metropolis sampler is geometrically ergodic if its equilibrium density is super-exponentially light and satisfies a curvature condition [Stochastic Process. Appl. 85 (2000) 341-361]. Many applications, including Bayesian…
Motivated by the problem of Many-Body Localization and the recent numerical results for the level and eigenfunction statistics on the random regular graphs, a generalization of the Rosenzweig-Porter random matrix model is suggested that…
We consider a class of stochastic kinetic equations, depending on two time scale separation parameters $\epsilon$ and $\delta$: the evolution equation contains singular terms with respect to $\epsilon$, and is driven by a fast ergodic…