Probability Theory of Classical Euclidean Optimization Problems
Probability Theory of Classical Euclidean Optimization Problems

Author: Joseph E. Yukich

Publisher: Springer

Published: 2006-11-14

Total Pages: 162

ISBN-13: 354069627X

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This monograph describes the stochastic behavior of the solutions to the classic problems of Euclidean combinatorial optimization, computational geometry, and operations research. Using two-sided additivity and isoperimetry, it formulates general methods describing the total edge length of random graphs in Euclidean space. The approach furnishes strong laws of large numbers, large deviations, and rates of convergence for solutions to the random versions of various classic optimization problems, including the traveling salesman, minimal spanning tree, minimal matching, minimal triangulation, two-factor, and k-median problems. Essentially self-contained, this monograph may be read by probabilists, combinatorialists, graph theorists, and theoretical computer scientists.

Algorithms and Data Structures
Algorithms and Data Structures

Author: Frank Dehne

Publisher: Springer

Published: 2011-07-18

Total Pages: 730

ISBN-13: 3642223001

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This book constitutes the refereed proceedings of the 12th Algorithms and Data Structures Symposium, WADS 2011, held in New York, NY, USA, in August 2011. The Algorithms and Data Structures Symposium - WADS (formerly "Workshop on Algorithms and Data Structures") is intended as a forum for researchers in the area of design and analysis of algorithms and data structures. The 59 revised full papers presented in this volume were carefully reviewed and selected from 141 submissions. The papers present original research on the theory and application of algorithms and data structures in all areas, including combinatorics, computational geometry, databases, graphics, parallel and distributed computing.

Loeb Measures in Practice: Recent Advances
Loeb Measures in Practice: Recent Advances

Author: Nigel J. Cutland

Publisher: Springer

Published: 2004-10-11

Total Pages: 118

ISBN-13: 3540445315

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This expanded version of the 1997 European Mathematical Society Lectures given by the author in Helsinki, begins with a self-contained introduction to nonstandard analysis (NSA) and the construction of Loeb Measures, which are rich measures discovered in 1975 by Peter Loeb, using techniques from NSA. Subsequent chapters sketch a range of recent applications of Loeb measures due to the author and his collaborators, in such diverse fields as (stochastic) fluid mechanics, stochastic calculus of variations ("Malliavin" calculus) and the mathematical finance theory. The exposition is designed for a general audience, and no previous knowledge of either NSA or the various fields of applications is assumed.

Flows on 2-dimensional Manifolds
Flows on 2-dimensional Manifolds

Author: Igor Nikolaev

Publisher: Springer Science & Business Media

Published: 1999-07-15

Total Pages: 324

ISBN-13: 9783540660804

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Time-evolution in low-dimensional topological spaces is a subject of puzzling vitality. This book is a state-of-the-art account, covering classical and new results. The volume comprises Poincaré-Bendixson, local and Morse-Smale theories, as well as a carefully written chapter on the invariants of surface flows. Of particular interest are chapters on the Anosov-Weil problem, C*-algebras and non-compact surfaces. The book invites graduate students and non-specialists to a fascinating realm of research. It is a valuable source of reference to the specialists.

Beyond the Worst-Case Analysis of Algorithms
Beyond the Worst-Case Analysis of Algorithms

Author: Tim Roughgarden

Publisher: Cambridge University Press

Published: 2021-01-14

Total Pages: 705

ISBN-13: 1108494315

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Introduces exciting new methods for assessing algorithms for problems ranging from clustering to linear programming to neural networks.

Quantization and Non-holomorphic Modular Forms
Quantization and Non-holomorphic Modular Forms

Author: André Unterberger

Publisher: Springer Science & Business Media

Published: 2000-08-28

Total Pages: 266

ISBN-13: 9783540678618

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This is a new approach to the theory of non-holomorphic modular forms, based on ideas from quantization theory or pseudodifferential analysis. Extending the Rankin-Selberg method so as to apply it to the calculation of the Roelcke-Selberg decomposition of the product of two Eisenstein series, one lets Maass cusp-forms appear as residues of simple, Eisenstein-like, series. Other results, based on quantization theory, include a reinterpretation of the Lax-Phillips scattering theory for the automorphic wave equation, in terms of distributions on R2 automorphic with respect to the linear action of SL(2,Z).

Elliptic Genera and Vertex Operator Super-Algebras
Elliptic Genera and Vertex Operator Super-Algebras

Author: Hirotaka Tamanoi

Publisher: Springer Science & Business Media

Published: 1999-06-21

Total Pages: 404

ISBN-13: 9783540660064

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This monograph deals with two aspects of the theory of elliptic genus: its topological aspect involving elliptic functions, and its representation theoretic aspect involving vertex operator super-algebras. For the second aspect, elliptic genera are shown to have the structure of modules over certain vertex operator super-algebras. The vertex operators corresponding to parallel tensor fields on closed Riemannian Spin Kähler manifolds such as Riemannian tensors and Kähler forms are shown to give rise to Virasoro algebras and affine Lie algebras. This monograph is chiefly intended for topologists and it includes accounts on topics outside of topology such as vertex operator algebras.

Differentiability of Six Operators on Nonsmooth Functions and P-Variation
Differentiability of Six Operators on Nonsmooth Functions and P-Variation

Author: R. M. Dudley

Publisher: Springer Science & Business

Published: 1999-06-21

Total Pages: 300

ISBN-13: 9783540659754

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The book is about differentiability of six operators on functions or pairs of functions: composition (f of g), integration (of f dg), multiplication and convolution of two functions, both varying, and the product integral and inverse operators for one function. The operators are differentiable with respect to p-variation norms with optimal remainder bounds. Thus the functions as arguments of the operators can be nonsmooth, possibly discontinuous, but four of the six operators turn out to be analytic (holomorphic) for some p-variation norms. The reader will need to know basic real analysis, including Riemann and Lebesgue integration. The book is intended for analysts, statisticians and probabilists. Analysts and statisticians have each studied the differentiability of some of the operators from different viewpoints, and this volume seeks to unify and expand their results.

Real Enriques Surfaces
Real Enriques Surfaces

Author: Alexander Degtyarev

Publisher: Springer Science & Business Media

Published: 2000-10-26

Total Pages: 284

ISBN-13: 9783540410881

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Deformation classes. p. 89.

Geometric Aspects of Functional Analysis
Geometric Aspects of Functional Analysis

Author: V.D. Milman

Publisher: Springer

Published: 2007-05-09

Total Pages: 296

ISBN-13: 354045392X

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This volume of original research papers from the Israeli GAFA seminar during the years 1996-2000 not only reports on more traditional directions of Geometric Functional Analysis, but also reflects on some of the recent new trends in Banach Space Theory and related topics. These include the tighter connection with convexity and the resulting added emphasis on convex bodies that are not necessarily centrally symmetric, and the treatment of bodies which have only very weak convex-like structure. Another topic represented here is the use of new probabilistic tools; in particular transportation of measure methods and new inequalities emerging from Poincaré-like inequalities.