We consider a particle system on Z with finite state space and interactions of infinite range. Assuming that the rate of change is continuous and decays sufficiently fast, we introduce a perfect simulation algorithm for the stationary process. The basic tool we use is a representation of the infinite range change rates as a mixture of finite range change rates. The perfect simulation scheme pro...

In this paper, we consider some boundary value problems (BVP) for fractional order partial differential equations ‎(FPDE)‎ with non-local boundary conditions. The solutions of these problems are presented as series solutions analytically via modified Mittag-Leffler functions. These functions have been modified by authors such that their derivatives are invariant with respect to fractional deriv...

Several equivalent definitions are possible; for instance, M ~ = ( 1 ) k+l, where k is the sum of digits in the binary representation ofj. With respect to a shift along the symbolic chain, the Thue-Morse sequence supports a unique translation-invariant ergodic probability measure, t3) Although organized by a simple deterministic rule, the Thue-Morse sequence is not periodic. The Fourier spectru...

Since its introduction by Bak,Tang and Wiesenfeld, the abelian sandpile dynamics has been studied extensively in finite volume. There are many problems posed by the existence of a sandpile dynamics in an infinite volume S: its invariant distribution should be the thermodynamic limit (does the latter exist?) of the invariant measure for the finite volume dynamics; the extension of the sand grain...

In 1967 Furstenberg proved that every infinite closed subset of T = R/Z simultaneously invariant under multiplication by 2 and by 3 is equal to T (cf. [8]), which motivated the still unresolved question whether this scarcity of invariant sets is paralleled by a corresponding scarcity of invariant probability measures: is Lebesgue measure the only nonatomic probability measure on T which is inva...

This paper presents a new similarity measure to be used for general tasks including supervised learning, which is represented by the K-nearest neighbor classifier (KNN). The proposed similarity measure is invariant to large differences in some dimensions in the feature space. The proposed metric is proved mathematically to be a metric. To test its viability for different applications, the KNN u...

We prove Cameron-Martin type quasi-invariance results for the heat kernel measure of infinite-dimensional Kolmogorov and related diffusions. first study quantitative functional inequalities appropriate finite-dimensional approximations these diffusions, we hold with dimension-independent coefficients. Applying an approach developed by Baudoin, Driver, Gordina, Melcher previously, uniform bounds...

We introduce a new renormalization procedure on double rotations, which is reminiscent of the classical Rauzy induction. Using this we prove that set parameters induce infinite type rotations has Hausdorff dimension strictly smaller than 3 <mml:annot...