Effects of randomness on the spin-1 2 and 1 antiferromagnetic Heisen-berg chains are studied using the quantum Monte Carlo method with the continuous-time loop algorithm. We precisely calculated the uniform susceptibility , string order parameter, spatial and temporal correlation length, and the dynamical exponent, and obtained a phase diagram. The generalization of the continuous-time loop alg...

By using stochastic calculus for two-parameter processes and chaos expansion into multiple Wiener-Itô integrals, we define a 2D-stochastic current over the Brownian sheet. This concept comes from geometric measure theory. We also study the regularity of the stochastic current with respect to the randomness variable in the Watanabe spaces and with respect to the spatial variable in the determini...

The theory of graph games with ω-regular winning conditions is the foundation for modeling and synthesizing reactive processes. In the case of stochastic reactive processes, the corresponding stochastic graph games have three players, two of them (System and Environment) behaving adversarially, and the third (Uncertainty) behaving probabilistically. We consider two problems for stochastic graph...

It is an open problem in the area of computable randomness whether Kolmogorov-Loveland randomness coincides with Martin-Löf randomness. Joe Miller and André Nies suggested some variations of Kolmogorov-Loveland randomness to approach this problem and to provide a partial solution. We show that their proposed notion of partial permutation randomness is still weaker than Martin-Löf randomness.

Nearest-neighbor analysis (NNA)—a method for assessing the degree to which a spatial point pattern departs from randomness in direction of being either clustered or regular—was imported into academic geography an article published 1954 by ecologists Clark and Evans. In its simplest form, concerned with distances first nearest neighbor, NNA hinged on behavior “nearest-neighbour statistic,” Rn, s...

Identification of the precise nature and attributes of the time series of climatological data is very important and is usually the first step for water resources planning and management. Such exercise is very important for hydro-climatic extremes. In many instances, a climatic time series is generally not statistically independent but is comprised of patterns of persistence, cycles, trends or s...

The process-based Spatial Logics are multi-modal logics developed for semantics on Process Algebras and designed to specify concurrent properties of dynamic systems. On the syntactic level, they combine modal operators similar to operators of Hennessy-Milner logic, dynamic logic, arrow logic, relevant logic, or linear logic. This combination generates expressive logics, sometimes undecidable, f...