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What is Statistics? Opinions vary. In fact, there is a continuous spectrum of attitudes toward statistics ranging from pure theoreticians, proving asymptotic efficiency and searching for most powerful tests, to wild practitioners, blindly…
Usual quantum mechanics predicts probabilities for the outcomes of measurements carried out at definite moments of time. However, realistic measurements do not take place in an instant, but are extended over a period of time. The assumption…
We explore the notion of spatial extent and structure, already alluded to in earlier literature, within the formulation of quantum mechanics on the noncommutative plane. Introducing the notion of average position and its measurement, we…
Many theoretical predictions derived from quantum mechanics have been confirmed experimentally during the last 80 years. However, interpretative aspects have long been subject to debate. Among them, the question of the existence of hidden…
This paper seeks to advance the theory of nonexpansive mappings by introducing and exploring a novel class of nonexpansive type mappings, which we aptly designate as perimetric nonexpansive mappings. We establish that the collection of…
I give a short review of the theory of twisted symmetries of differential equations, emphasizing geometrical aspects. Some open problems are also mentioned.
The goal of this contribution is to discuss various resonance expansions that have been proposed in the literature.
The purpose of this work is to discuss recent progress in deriving the fundamental laws of thermodynamics (0th, 1st and 2nd-law) from nonequilibrium quantum statistical mechanics. Basic thermodynamic notions are clarified and different…
This chapter seeks to outline a few basic problems in quantum statistical physics where recent experimental advances from the atomic physics community offer the hope of dramatic progress. The focus is on nonequilibrium situations where the…
This paper reviews recent advances in Bayesian nonparametric techniques for constructing and performing inference in infinite hidden Markov models. We focus on variants of Bayesian nonparametric hidden Markov models that enhance a…
Recently a sufficient and necessary condition for Pauli's spin- statistics connection in nonrelativistic quantum mechanics has been established [quant-ph/0208151]. The two-dimensional part of this result is extended to n-particle systems…
Using the system-bath model Hamiltonian this thesis covers the equilibrium and out of equilibrium properties of quantum open systems. Topics included are the calculation of thermodynamical quantities of open systems, derivation of quantum…
Much is known about asymptotic expansions for asymptotically normal distributions if these distributions are either absolutely continuous or pure lattice distributions. In this paper we begin an investigation of the discrete but non-lattice…
In this paper, we study the existence of the random fixed points under mild continuity assumptions. The main theorems consider the almost lower semicontinuous operators defined on Frechet spaces and also operators having properties weaker…
A new relativistic invariant version of nonlinear Maxwell equations is offerred. Some properties of these equations are considered.
Exact calculations of some universal quantities of two-dimensional statistical models in the vicinity of their fixed points are illustrated.
Inscribability of polytopes is a classic subject but also a lively research area nowadays. We illustrate this with a selection of well-known results and recent developments on six particular topics related to inscribable polytopes. Along…
In this paper we apply techniques from nonstandard analysis to study expansive dynamical systems. Among other results, we provide a necessary and sufficient condition for an expansive homeomorphism on a compact metric space to admit…
We review progress on questions related to front propagation into unstable states and point out open problems in the area. We strive to highlight different theoretical perspectives and challenges while also addressing more practical…
We present a review of recent work on the statistical mechanics of non equilibrium processes based on the analysis of large deviations properties of microscopic systems. Stochastic lattice gases are non trivial models of such phenomena and…