The behaviour of a Pólya-like urn which generates Ewens' sampling formula in population genetics is investigated. Connections are made with work of Watterson and Kingman and to the Poisson-Dirichlet distribution. The order in which novel types occur in the urn is shown to parallel the age distribution of the infinitely many alleles diffusion model and consequences of this property are explored....

Measure-valued Pólya urn processes (MVPP) are Markov chains with an additive structure that serve as extension of the generalized k-color model towards a continuum possible colors. We prove that, for any MVPP (μn)n≥0 on Polish space X, normalized sequence (μn/μn(X))n≥0 agrees marginal predictive distributions some random process (Xn)n≥1. Moreover, μn=μn−1+RXn, n≥1, where x↦Rx is transition kern...

A very simple specific case of a Polya urn scheme is as follows. At each trial one draws a ball from an urn with balls of two different colours. Then, one looks at the ball, and returns the ball to the urn together with another ball of the same colour. Then one makes another draw. Et cetera. At the first draw there is one ball of each colour. The rechargeable Polya urn scheme is essentially the...

The present study focuses on the impact of eddy viscosity turbulence models benchmark INSEAN E779A marine propeller hydroacoustic performance under non-cavitating and open water conditions. In numerical calculations, Realisable k-epsilon (k-?), k-? Shear Stress Transport (k-? SST) Spalart-Allmaras models, which are widely used in hydrodynamic fields, selected. Hydroacoustic model is predicted w...

Response-adaptive design involves the sequential selection of design points chosen depending on the outcomes at previously selected design points. The response-adaptive design has been extensively studied in the literature; see Rosenberger (1996), Flournoy and Rosenberger (1995) and Hu and Ivanova (2004) for details. An important family of adaptive designs can be developed from the generalized ...

To every generalized urn model there exists a finite (Mealy) automaton with identical propositional calculus. The converse is true as well.

To understand the relative importance of natural selection and random genetic drift in finite but growing populations, the asymptotic behavior of a class of generalized Polya urns is studied using the method of ordinary differential equation (ODE). Of particular interest is the replicator process: two balls (individuals) are chosen from an urn (the population) at random with replacement and bal...