相关论文: On Mean Divergence Measures
We study a family of inequalities on pairs of measure spaces involving functions defined on product domains. Our main result establishes a Jensen-type inequality under a general product-measure framework, extending classical inequalities…
This paper is dedicated to the analysis and detailed study of a procedure to generate both the weighted arithmetic and harmonic means of $n$ positive real numbers. Together with this interpretation, we prove some relevant properties that…
We consider sequences of compositions of quadratic polynomials $f_{c_n} (z) = z^2 + c_n$. For such sequences one can naturally generalize the definitions of the Julia set and basin of infinity from the autonomous case. In this setting the…
We discuss the classical problem of measuring the regularity of distribution of sets of $N$ points in $\mathbb{T}^d$. A recent line of investigation is to study the cost ($=$ mass $\times$ distance) necessary to move Dirac measures placed…
We propose a measure of macroscopic coherence based on the degree of disturbance caused by a coarse-grained measurement. Based on our measure, we point out that recently proposed criteria of macroscopic coherence may lead to inconsistent…
We study here the error of numerical integration on metric measure spaces adapted to a decomposition of the space into disjoint subsets. We consider both the error for a single given function, and the worst case error for all functions in a…
We study the sublinear multivariate mean estimation problem in $d$-dimensional Euclidean space. Specifically, we aim to find the mean $\mu$ of a ground point set $A$, which minimizes the sum of squared Euclidean distances of the points in…
In this paper we provide the asymptotic theory of the general of $\phi$-divergences measures, which include the most common divergence measures : Renyi and Tsallis families and the Kullback-Leibler measure. We are interested in divergence…
The aim of this paper is to present some new Fejer-type results for convex functions. Improvements of Young's inequality (the arithmetic-geometric mean inequality) and other applications to special means are pointed as well.
The distortion of six different intrinsic metrics and quasi-metrics under conformal and quasiregular mappings is studied in a few simple domains $G\subsetneq\mathbb{R}^n$. The already known inequalities between the hyperbolic metric and…
Quantifying how distinguishable two stochastic processes are lies at the heart of many fields, such as machine learning and quantitative finance. While several measures have been proposed for this task, none have universal applicability and…
We prove surface and volume mean value formulas for classical solutions to uniformly parabolic equations in divergence form. We then use them to prove the parabolic strong maximum principle and the parabolic Harnack inequality. We emphasize…
We demonstrate the simple and deep equivalence between quantum coherence and nonclassicality and the definite way in which they determine metrological resolution. Moreover, we define a coherence observable consistent with a classical…
We establish finite-sample error bounds in expectation for transformed Fr\'echet means in Hadamard spaces under minimal assumptions. Transformed Fr\'echet means provide a unifying framework encompassing classical and robust notions of…
Meta-analysis aims to combine effect measures from several studies. For continuous outcomes, the most popular effect measures use simple or standardized differences in sample means. However, a number of applications focus on the absolute…
Several performance measures can be used for evaluating classification results: accuracy, F-measure, and many others. Can we say that some of them are better than others, or, ideally, choose one measure that is best in all situations? To…
Classical mean-value results of Wirsing type in analytic number theory are established under weaker than classical conditions.
Properties of weighted averages are studied for the general case that the individual measurements are subject to hidden correlations and have asymmetric statistical as well as systematic errors. Explicit expressions are derived for an…
Measurements on classical systems are usually idealized and assumed to have infinite precision. In practice, however, any measurement has a finite resolution. We investigate the theory of non-ideal measurements in classical mechanics using…
This is a review of the ideas behind the Fisher--Rao metric on classical probability distributions, and how they generalize to metrics on density matrices. As is well known, the unique Fisher--Rao metric then becomes a large family of…