相关论文: Discussion of "Functional Models for Time-Varying …

This paper introduces a comprehensive framework for complex-valued probability measures and explores their novel applications in information theory and statistical analysis. We define a complex probability measure as a phase-modulated…

Pairs of metrics in a two-dimensional linear vector space are considered, one of which is a Minkowski type metric. Their simultaneous diagonalizability is studied and canonical presentations for them are suggested.

Units equivariance (or units covariance) is the exact symmetry that follows from the requirement that relationships among measured quantities of physics relevance must obey self-consistent dimensional scalings. Here, we express this…

Barbour's interpretation of Mach's principle led him to postulate that gravity should be formulated as a dynamical theory of spatial conformal geometry, or in his terminology, "shapes." Recently, it was shown that the dynamics of General…

Measurement uncertainty relations are quantitative bounds on the errors in an approximate joint measurement of two observables. They can be seen as a generalization of the error/disturbance tradeoff first discussed heuristically by…

Distance covariance is a popular measure of dependence between random variables. It has some robustness properties, but not all. We prove that the influence function of the usual distance covariance is bounded, but that its breakdown value…

This is the second of two works concerning the Sobolev calculus on metric measure spaces and its applications. In this work, we focus on several approaches to vector calculus in the non-smooth setting of complete and separable metric spaces…

This work applies a quantitative metric well-known to the data assimilation community to a new context in order to capture the relative representativeness of non-simultaneous or non-co-located observations and quantify how these…

Skew information is a pivotal concept in quantum information, quantum measurement, and quantum metrology. Further studies have lead to the uncertainty relations grounded in metric-adjusted skew information. In this work, we present an…

The need for appropriate ways to measure the distance or similarity between data is ubiquitous in machine learning, pattern recognition and data mining, but handcrafting such good metrics for specific problems is generally difficult. This…

Since Pearson's correlation was introduced at the end of the 19th century many dependence measures have appeared in the literature. Recently we have suggested four simple axioms for dependence measures of random variables that take values…

The space discreteness hypothesis asserts that the nature of space at short distances is radically different from that at large distances. Based on the Bronstein inequality, here, we use a totally disconnected topological space…

Distance correlation is a recent extension of Pearson's correlation, that characterises general statistical independence between Euclidean-space-valued random variables, not only linear relations. This review delves into how and when…

The classical and continuum limit of a quantum gravitational setting could lead, at mesoscopic regimes, to a very different notion of geometry w.r.t. the pseudo-Riemannian one of special and general relativity. A possible way to…

Covariance functions and variograms play a fundamental role in exploratory analysis and statistical modelling of spatial and spatio-temporal datasets. In this paper, we construct a new class of spatial covariance functions using the Fourier…

This paper proposes a multivariate nonlinear function-on-function regression model, which allows both the response and the covariates can be multi-dimensional functions. The model is built upon the multivariate functional reproducing kernel…

We define a measure of redundant information based on projections in the space of probability distributions. Redundant information between random variables is information that is shared between those variables. But in contrast to mutual…

The relation between continuous functions and random vectors is revealed in the paper that the main meaning is described as, for any given continuous function, there must be a sequence of probability spaces and a sequence of random vectors…

The general formalism of quantum mechanics for the description of statistical experiments is briefly reviewed, introducing in particular position and momentum observables as POVM characterized by their covariance properties with respect to…

It is shown that quantum mechanics is noncontextual if quantum properties are represented by subspaces of the quantum Hilbert space (as proposed by von Neumann) rather than by hidden variables. In particular, a measurement using an…