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Measure (mathematics)

About: Measure (mathematics) is a(n) research topic. Over the lifetime, 23563 publication(s) have been published within this topic receiving 417328 citation(s).

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Journal ArticleDOI
Abstract: The authors present a new molecular dynamics algorithm for sampling the canonical distribution. In this approach the velocities of all the particles are rescaled by a properly chosen random factor. The algorithm is formally justified and it is shown that, in spite of its stochastic nature, a quantity can still be defined that remains constant during the evolution. In numerical applications this quantity can be used to measure the accuracy of the sampling. The authors illustrate the properties of this new method on Lennard-Jones and TIP4P water models in the solid and liquid phases. Its performance is excellent and largely independent of the thermostat parameter also with regard to the dynamic properties.

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8,777 citations


Proceedings Article
24 Jul 1998-
TL;DR: This work presents an informationtheoretic definition of similarity that is applicable as long as there is a probabilistic model and demonstrates how this definition can be used to measure the similarity in a number of different domains.

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Abstract: Similarity is an important and widely used concept Previous definitions of similarity are tied to a particular application or a form of knowledge representation We present an informationtheoretic definition of similarity that is applicable as long as there is a probabilistic model We demonstrate how our definition can be used to measure the similarity in a number of different domains

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4,239 citations


Journal ArticleDOI
Guifre Vidal, Reinhard F. Werner1Institutions (1)
22 Feb 2002-Physical Review A
TL;DR: A measure of entanglement that can be computed effectively for any mixed state of an arbitrary bipartite system is presented and it is shown that it does not increase under local manipulations of the system.

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Abstract: We present a measure of entanglement that can be computed effectively for any mixed state of an arbitrary bipartite system. We show that it does not increase under local manipulations of the system, and use it to obtain a bound on the teleportation capacity and on the distillable entanglement of mixed states.

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3,287 citations


Journal ArticleDOI
01 Mar 1976-Econometrica
Abstract: The primary aim of this paper is to propose a new measure of poverty, which should avoid some of the shortcomings of the measures currently in use. An axiomatic approach is used to derive the measure. The conception of welfare in the axiom set is ordinal. The information requirement for the new measure is quite limited, permitting practical use.

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2,521 citations


Journal ArticleDOI
A. Lempel1, Jacob Ziv1Institutions (1)
TL;DR: A new approach to the problem of evaluating the complexity ("randomness") of finite sequences is presented, related to the number of steps in a self-delimiting production process by which a given sequence is presumed to be generated.

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Abstract: A new approach to the problem of evaluating the complexity ("randomness") of finite sequences is presented. The proposed complexity measure is related to the number of steps in a self-delimiting production process by which a given sequence is presumed to be generated. It is further related to the number of distinct substrings and the rate of their occurrence along the sequence. The derived properties of the proposed measure are discussed and motivated in conjunction with other well-established complexity criteria.

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2,208 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202233
20211,503
20201,358
20191,254
20181,173
20171,058

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Topic's top 5 most impactful authors

Nageswari Shanmugalingam

31 papers, 587 citations

Luigi Ambrosio

27 papers, 1.2K citations

Sadao Tomizawa

22 papers, 102 citations

Daniel Lenz

21 papers, 513 citations

Michael Baake

18 papers, 252 citations