The minimum amount of information and the asymptotic minimum amount of entropy of a random partition which separates the points of a Poisson point process are found. Related information theoretic bounds are applied to yield an upper bound to the throughput of a random access broadcast channel. It is shown that more information is needed to separate points by partitions consisting of intervals t...

The phase transition of two-dimensional Ising model on random point patterns is investigated using Monte Carlo simulation and the critical temperature is calculated using the Bethe approximation. We find a linear relation between the critical temperature and the structural characteristics of the random point pattern, as described by Aboav's parameter. Numerical results and analytical calculatio...

It will be shown and induced that the d-dimensional indices in the Banach spaces version conditions ∑ n(E‖Xn‖/|n|) < ∞ are sufficient to yield limmin1≤ j≤d(nj)→∞(1/ |nα|)∑k≤n ∏d j=1(1− (kj − 1)/nj)Xk = 0 a.s. for arrays of James-type orthogonal random elements. Particularly, it will be shown also that there are the best possible sufficient conditions for multi-indexed independent real-valued ra...

One-dimensional light amplification in individual p-sexiphenyl nanofibers is investigated. The influence of fiber morphology on light propagation properties is studied via optical and atomic force microscopy. Isolated nanofibers are shown to yield low-threshold random laser emission in the deep blue. Model calculations of coherent light propagation in one-dimensional random media qualitatively ...

We study approximations of optimization problems with probabilistic constraints in which the original distribution of the underlying random vector is replaced with an empirical distribution obtained from a random sample. We show that such a sample approximation problem with risk level larger than the required risk level will yield a lower bound to the true optimal value with probability approac...

In this study test-day records of milk (kg), fat (g), and protein (g) yields, somatic cell score (SCS, cells/ML) collected by Animal Breeding Center of Iran during 2007 and 2009 were used to estimate genetic parameters using random regression model. Models with different order of Legendre polynomials were compared using Bayesian information criterion (BIC).For milk, fat yield and SCS genetic an...