Related papers: Bochner's technique for statistical structures
We investigate the influence of diffraction on the statistics of energy levels in quantum systems with a chaotic classical limit. By applying the geometrical theory of diffraction we show that diffraction on singularities of the potential…
By the example of a Fourier transform, the possibilities of Hilbert space geometry applications for statistical model construction are analyzed. In accordance with Bohr's complementarity principle, mutually-complementary coordinate and…
I introduce a new geometrical approach to thermo--statistical mechanics. Here I highlight the main physical ideas, and how do they translate into geometrical language. I contrast the present approach with previous…
Within the continuous endeavour of improving the efficiency and resilience of air transport, the trend of using concepts and metrics from statistical physics has recently gained momentum. This scientific discipline, which integrates…
This work develops, from a functional analytic perspective, the construction of random variables in Lebesgue spaces L^p. It extends classical notions of measurability, integrability, and expectation to L^p valued functions, using Pettis's…
The field of computational statistics refers to statistical methods or tools that are computationally intensive. Due to the recent advances in computing power some of these methods have become prominent and central to modern data analysis.…
The statistical convergence is handled for sequences with the natural density, in general. In a recent paper, the statistical convergence for nets in Riesz spaces has been studied and investigated by developing topology-free techniques in…
We study different notions of connected constructive metric spaces. They differ the types of connected components and how different components relate to each other. These notions are equivalent in classical point set topology but they give…
These lecture notes want to illustrate the close connection between statistical mechanics and field theory not only on the formal level, i.e. that many concepts of one area can easily be taken over to the other one, but also on the level of…
Following Le Jan and Watanabe we define a connection associated with a non-degenrrate diffusion operators. This connection is characterized here and shown to be the Levi-Civita connection for gradient systems. This both explains why such…
This paper is a study of almost contact statistical manifolds. Especially this study is focused on almost cosymplectic statistical manifolds. We obtained basic properties of such manifolds. It is proved a characterization theorem and a…
We study multivariate polynomials over `structured' grids. We begin by proposing an interpretation as to what it means for a finite subset of a field to be structured; we do so by means of a numerical parameter, the nullity. We then extend…
In this paper we introduce a general framework for the study of limits of relational structures in general and graphs in particular, which is based on a combination of model theory and (functional) analysis. We show how the various…
We combine Homotopy Type Theory with axiomatic cohesion, expressing the latter internally with a version of "adjoint logic" in which the discretization and codiscretization modalities are characterized using a judgmental formalism of "crisp…
A new category of algebro-geometric objects is defined. This construction is a vast generalization of existing F1-theories, as it contains the the theory of monoid schemes on the one hand and classical algebraic theory, e.g. Grothendieck…
In this article, we pursue two main objectives. The first is to show that the fundamental results of Green-Lazarsfeld (1987, 1991) on generic vanishing theorems, and works of Budur-Wang (2015, 2020) on cohomology jumping loci, can be…
This paper investigates some issues arising in categorical models of reversible logic and computation. Our claim is that the structural (coherence) isomorphisms of these categorical models, although generally overlooked, have decidedly…
The aim of these notes is to provide a reasonably short and "hands-on" introduction to the differential calculus on associative algebras over a field of characteristic zero. Following a suggestion of Ginzburg's we call the resulting theory…
Several authors, including the American Statistician (ASA), have noted the challenges facing statisticians when attacking large, complex, unstructured problems, as opposed to well-defined textbook problems. Clearly, the standard paradigm of…
A suite of relational notions of shape are presented at the level of configuration space geometry, with corresponding new theories of shape mechanics and shape statistics. These further generalize two quite well known examples: --1)…