This paper connects the analysis of the length of the longest weakly increasing subsequence of inhomogeneous random words to a Riemnn-Hilbert problem and an associated system of integrable partial differential equations. In particular, we show that the Poissonization of the distribution function of this length can be identified as the Jimbo-Miwa-Ueno tau function. © 2001 Elsevier Science B.V. A...

We study time{inhomogeneous stochastic dynamical systems with vanishing noise. Conditions implying strong ergodicity are proposed; the asymptotic probability distribution is characterized and we estimate the speed of relaxation. Applying these results to simulated annealing enables us to introduce systems that converge faster than a classical annealing dynamics determined by a Gibbs factor.

Two cumulative damage models are considered, the inverse gamma process and a composed gamma process. They can be seen as ‘continuous’ analogues of Poisson and compound Poisson processes, respectively. For these models the first passage time distribution functions are derived. Inhomogeneous versions of these processes lead to models closely related to the Weibull failure model. All models show i...

By using a time-dependent operator converting a distribution function (statistical operator) of a total system under consideration into the relevant form, new exact nonlinear generalized master equations (GMEs) are derived. The inhomogeneous nonlinear GME is a generalization of the linear Nakajima-Zwanzig GME and is suitable for obtaining both the linear and nonlinear equations describing the e...

High atomic number nanoparticles are of increasing interest in radiotherapy due to their significant positive impact on the local dose applied treatment site. In this work, three types metal were utilized investigate enhancement based GATE Monte Carlo simulation tool. Gold, gadolinium, and silver implanted at different concentrations a 1 cm radius sphere mimic cancerous tumor inside 10 × 30 cm3...