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In Quantum Physics there are circumstances where the direct measurement of particular observables encounters diffculties; in some of these cases, however, its value can be evaluated, i.e. it can be inferred by measuring another observable…

Quantum Physics · Physics 2016-03-23 Giuseppe Nisticò , Angela Sestito

With growing success in experimental implementations it is critical to identify a "gold standard" for quantum information processing, a single measure of distance that can be used to compare and contrast different experiments. We enumerate…

Quantum Physics · Physics 2009-01-27 Alexei Gilchrist , Nathan K. Langford , Michael A. Nielsen

Comparisons of different treatments or production processes are the goals of a significant fraction of applied research. Unsurprisingly, two-sample problems play a main role in Statistics through natural questions such as `Is the the new…

Methodology · Statistics 2017-09-05 P. C. Álvarez-Esteban , E. del Barrio , J. A. Cuesta-Albertos , C. Matrán

The problem of identifying to which of a given set of classes objects belong is ubiquitous, occurring in many research domains and application areas, including medical diagnosis, financial decision making, online commerce, and national…

Machine Learning · Computer Science 2024-09-20 David J. Hand , Peter Christen , Sumayya Ziyad

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…

Machine Learning · Computer Science 2022-01-25 Martijn Gösgens , Anton Zhiyanov , Alexey Tikhonov , Liudmila Prokhorenkova

In the literature, there have been several methods and definitions for working out if two theories are "equivalent" (essentially the same) or not. In this article, we do something subtler. We provide means to measure distances (and explore…

Logic · Mathematics 2020-08-12 Michèle Friend , Mohamed Khaled , Koen Lefever , Gergely Székely

We propose a new and rather stringent criterion for testing the goodness of fit between a theory and experiment. It is motivated by the paradox that the criterion on \chi^2 for testing a theory is much weaker than the criterion for finding…

High Energy Physics - Phenomenology · Physics 2007-05-23 J. C. Collins , J. Pumplin

How should researchers analyze randomized experiments in which the main outcome is latent and measured in multiple ways but each measure contains some degree of error? We first identify a critical study-specific noncomparability problem in…

Econometrics · Economics 2026-01-13 Jiawei Fu , Donald P. Green

Precision predictions combined with precise measurements are a major tool in sharpening our understanding of the fundamental laws underlying microscopic as well as macroscopic systems. Here, I present a few remarkable examples covering the…

Nuclear Theory · Physics 2020-07-10 Ulf-G. Meißner

Measurements play a crucial role in doing physics: Their results provide the basis on which we adopt or reject physical theories. In this note, we examine the effect of subjecting measurements themselves to our experience. We require that…

Quantum Physics · Physics 2020-01-28 Arne Hansen , Stefan Wolf

We emphasize the difficulties of an experiment that can definitely discriminate between local realistic hidden variables theories and quantum mechanics using the Bell CHSH inequalities and a real measurement apparatus. In particular we…

Quantum Physics · Physics 2009-11-07 A. Feoli , S. Rampone

We analytically study proximity and distance properties of various kernels and similarity measures on graphs. This helps to understand the mathematical nature of such measures and can potentially be useful for recommending the adoption of…

Combinatorics · Mathematics 2018-08-17 Konstantin Avrachenkov , Pavel Chebotarev , Dmytro Rubanov

In many contexts it is extremely costly to perform enough high quality experimental measurements to accurately parameterize a predictive quantitative model. However, it is often much easier to carry out large numbers of experiments that…

Data Analysis, Statistics and Probability · Physics 2017-11-22 Alpha A. Lee , Michael P. Brenner , Lucy J. Colwell

Besides the classical distinction of correlation and dependence, many dependence measures bear further pitfalls in their application and interpretation. The aim of this paper is to raise and recall awareness of some of these limitations by…

Methodology · Statistics 2020-04-17 Björn Böttcher

Quark and lepton flavor physics presents us with a basic question: Can we understand the pattern of masses and mixings of the known quarks and leptons, and how do present and proposed measurements help to advance that goal? Topics discussed…

High Energy Physics - Phenomenology · Physics 2013-10-02 Jonathan L. Rosner

A quantum field model for an experiment describes thermal fluctuations explicitly and quantum fluctuations implicitly, whereas a comparable continuous random field model would describe both thermal and quantum fluctuations explicitly. An…

Quantum Physics · Physics 2008-11-26 Peter Morgan

Judging the significance and reproducibility of quantitative research requires a good understanding of relevant uncertainties, but it is often unclear how well these have been evaluated and what they imply. Reported scientific uncertainties…

Applications · Statistics 2017-01-20 David C. Bailey

This paper describes measures for evaluating the three determinants of how well a probabilistic classifier performs on a given test set. These determinants are the appropriateness, for the test set, of the results of (1) feature selection,…

cmp-lg · Computer Science 2008-02-03 Rebecca Bruce , Janyce Wiebe , Ted Pedersen

We investigate for which metric spaces the performance of distance labeling and of $\ell_\infty$-embeddings differ, and how significant can this difference be. Recall that a distance labeling is a distributed representation of distances in…

Data Structures and Algorithms · Computer Science 2023-09-21 Arnold Filtser , Lee-Ad Gottlieb , Robert Krauthgamer

Precise measurements of the lepton properties provide stringent tests of the Standard Model structure and accurate determinations of its parameters. We overview the present status of a few selected topics: lepton universality, QCD tests and…

High Energy Physics - Phenomenology · Physics 2009-11-07 A. Pich