相关论文: The Earth Mover's Correlation
Metric spaces are a fundamental component of mathematics and have a paramount importance as a framework for measuring distance. They can be found in many different branches of mathematics, such as analysis and topology. This paper offers an…
It is generally believed that coupling the graviton (a classical Fierz-Pauli massless spin-2 field) to its own energy-momentum tensor successfully recreates the dynamics of the Einstein field equations order by order; however the validity…
The spatial dependence of magnetic fields in simple configurations is an usual topic in introductory electromagnetism lessons, both in high school and in university courses. In typical experiments, magnetic fields are obtained taking…
This paper surveys some recent developments in measures of association related to a new coefficient of correlation introduced by the author. A straightforward extension of this coefficient to standard Borel spaces (which includes all Polish…
The quantum metric tensor was introduced for defining the distance in the parameter space of a system. However, it is also useful for other purposes, like predicting quantum phase transitions. Due to the physical information this tensor…
We provide a geometric interpretation to Bayesian inference that allows us to introduce a natural measure of the level of agreement between priors, likelihoods, and posteriors. The starting point for the construction of our geometry is the…
Scalar-tensor theories of gravity are known to allow significant deviations from general relativity through various astrophysical phenomena. In this paper, we formulate a scalar-connection gravity by setting up scalars and connection…
The stability of the orbital motion of two long cylindrical magnets interacting exclusively with magnetic forces is described. To carry out analytical studies a model of magnetically interacting symmetric tops [1] is used. The model was…
We demonstrate that local application of a weak external field increases distinguishability between states with and without initial correlations. We consider the case where a two-level system linearly and adiabatically interacts with an…
From a combinatorial point of view, we consider the Earth Mover's Distance (EMD) associated with a metric measure space. The specific case considered is deceptively simple: Let the finite set [n] = {1,...,n} be regarded as a metric space by…
In most text books of mechanics, Newton's laws or Hamilton's equations of motion are first written down and then solved based on initial conditions to determine the constants of the motions and to describe the trajectories of the particles.…
We use results by Kirilin to show that in general relativity the nonleading terms in the energy-momentum tensor of a particle depends on the parameterization of the gravitational field. While the classical metric that is calculated from…
In this paper, we consider the following query problem: given two weighted point sets $A$ and $B$ in the Euclidean space $\mathbb{R}^d$, we want to quickly determine that whether their earth mover's distance (EMD) is larger or smaller than…
Position measurements are examined under the assumption that object position x_t and probe position X_t just after the measurement are expressed by a linear combination of positions x_0 and X_0 just before the measurement. The Heisenberg…
The bimetric variational principle is a subtle reinterpretation of general relativity that assumes the spacetime connection to be generated by an independent metric. Unlike the so called Palatini formalism that promotes the connection into…
This article presents several alternatives to Pearson's correlation coefficient and many examples. In the samples where the rank in a discrete variable counts more than the variable values, the mixtures that we propose of Pearson's and…
Conformally related metrics and Lagrangians are considered in the context of scalar-tensor gravity cosmology. After the discussion of the problem, we pose a lemma in which we show that the field equations of two conformally related…
The description of an observer's measurement in general relativity and the standard model of particle physics is closely related to the spacetime metric. In order to understand and interpret measurements, which test the metric structure of…
Classical dependence measures such as Pearson correlation, Spearman's $\rho$, and Kendall's $\tau$ can detect only monotonic or linear dependence. To overcome these limitations, Szekely et al.(2007) proposed distance covariance as a…
A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a…