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An introduction to probability theory and its applications
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The article was published on 1950-01-01 and is currently open access. It has received 31532 citations till now. The article focuses on the topics: Probability and statistics & Imprecise probability.read more
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An efficient k-means clustering algorithm: analysis and implementation
Tapas Kanungo,David M. Mount,Nathan S. Netanyahu,Christine D. Piatko,Ruth Silverman,Angela Y. Wu +5 more
TL;DR: This work presents a simple and efficient implementation of Lloyd's k-means clustering algorithm, which it calls the filtering algorithm, and establishes the practical efficiency of the algorithm's running time.
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Measuring the Strangeness of Strange Attractors
TL;DR: In this paper, the correlation exponent v is introduced as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise, and algorithms for extracting v from the time series of a single variable are proposed.
Book
Probability: Theory and Examples
TL;DR: In this paper, a comprehensive introduction to probability theory covering laws of large numbers, central limit theorem, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion is presented.
Journal ArticleDOI
Molecular dynamics simulations at constant pressure and/or temperature
TL;DR: In this paper, it is shown that time averages of properties of the simulated fluid are equal to averages over the isoenthalpic-isobaric, canonical, and isothermal-isboric ensembles.
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Ergodic theory of chaos and strange attractors
Jean-Pierre Eckmann,David Ruelle +1 more
TL;DR: A review of the main mathematical ideas and their concrete implementation in analyzing experiments can be found in this paper, where the main subjects are the theory of dimensions (number of excited degrees of freedom), entropy (production of information), and characteristic exponents (describing sensitivity to initial conditions).