Related papers: Discussion of "Functional Models for Time-Varying …

Several new geometric quantile-based measures for multivariate dispersion, skewness, kurtosis, and spherical asymmetry are defined. These measures differ from existing measures, which use volumes and are easy to calculate. Some theoretical…

The effects of any quantum measurement can be described by a collection of measurement operators {M_m} acting on the quantum state of the measured system. However, the Hilbert space formalism tends to obscure the relationship between the…

Determining the measurement uncertainty region is a difficult problem for generic sets of observables. For this reason the literature on exact measurement uncertainty regions is focused on symmetric sets of observables, where the symmetries…

Uncertainty relations are usually stated as bounds on selected combinations of variances, but the full covariance matrix contains substantially richer information about the geometry of quantum state space and about the operational…

We consider pairs of quantum observables (POVMs) and analyze the relation between the notions of non-disturbance, joint measurability and commutativity. We specify conditions under which these properties coincide or differ---depending for…

The aim of the present article is to give an introduction to the concept of quasi-unitary equivalence and to define several (pseudo-)metrics on the space of self-adjoint operators acting possibly in different Hilbert spaces. As some of the…

We study the local dimensions and local multifractal properties of measures on doubling metric spaces. Our aim is twofold. On one hand, we show that there are plenty of multifractal type measures in all metric spaces which satisfy only mild…

The metric Mahler measure was first studied by Dubickas and Smyth in 2001 as a means of phrasing Lehmer's conjecture in topological language. More recent work of the author examined a parametrized family of generalized metric Mahler…

Wibral et al. propose a measure of interaction delays rooted in an information-theoretic framework and contrast their measure with the bivariate momentary information transfer (MIT), introduced in Pompe, B., & Runge, J. (2011). Momentary…

We present a new method for describing quantum measurements in relativistic systems that applies (i) to any QFT and for any field-detector coupling, (ii) to the measurement of any observable, and (iii) to arbitrary size, shape and motion of…

The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures. This paper includes eight sections. Section 1 is a longer introduction, which gives a…

This paper contains a study of multivariate second order stochastic mappings indexed by an abstract set $\Lambda$ in close connection to their operator covariance functions. The characterizations of the normal Hilbert module or of Hilbert…

Uncertainty principle is one of the cornerstones of quantum theory. In the literature, there are two types of uncertainty relations, the operator form concerning the variances of physical observables and the entropy form related to entropic…

We develop a comprehensive framework for spatio-temporal prediction of time-varying vector fields using operator-valued reproducing kernel Hilbert spaces (OV RKHS). By integrating Sobolev regularity with Koopman operator theory, we…

Any metric theory of gravity whose interaction with quantum particles is described by a covariant wave equation is equivalent to a vector theory that satisfies Maxwell-type equations identically. This result does not depend on any…

The Hilbert space effect algebra is a fundamental mathematical structure which is used to describe unsharp quantum measurements in Ludwig's formulation of quantum mechanics. Each effect represents a quantum (fuzzy) event. The relation of…

We study spectral parametric correlations in quantum chaotic systems and introduce the number covariance as a measure of such correlations. We derive analytic results for the classical random matrix ensembles using the binary correlation…

This article primarily aims to unify the various formalisms of multivariate coefficients of variation, leveraging advanced concepts of generalized means, whether weighted or not, applied to the eigenvalues of covariance matrices. We…

Consider a BV function on a Riemannian manifold. What is its differential? And what about the Hessian of a convex function? These questions have clear answers in terms of (co)vector/matrix valued measures if the manifold is the Euclidean…

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…