M. Deza's Books

Encyclopedia of Distances

By: Michel Marie Deza,Elena Deza

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Distance metrics and distances have become an essential tool in many areas of pure and applied Mathematics, and this encyclopedia is the first one to treat the subject in full. The book appears just as research intensifies into metric spaces and especially, distance design for applications. These distances are particularly crucial, for example, in computational biology, image analysis, speech recognition, and information retrieval. Here, an assessment of the practical questions arising during selection of a "good'' distance function has been left aside in favor of a comprehensive listing of the main available distances, a useful tool for the distance design community. This reader-friendly reference offers both independent introductions and definitions, while at the same time making cross-referencing easy through hyperlink-like boldfaced references to original definitions. This high-quality publication is a mix of reference resource and coffee-table book.

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Page Count

584

Publisher

Springer Science & Business Media

Published Date

ISBN 10

364200234X

ISBN 13

9783642002342

Geometry of Cuts and Metrics

By: Michel Marie Deza,Monique Laurent

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Geometry of Cuts and Metrics

By: Michel Marie Deza,Monique Laurent

Cuts and metrics are well-known objects that arise - independently, but with many deep and fascinating connections - in diverse fields: in graph theory, combinatorial optimization, geometry of numbers, combinatorial matrix theory, statistical physics, VLSI design etc. This book presents a wealth of results, from different mathematical disciplines, in a unified comprehensive manner, and establishes new and old links, which cannot be found elsewhere. It provides a unique and invaluable source for researchers and graduate students. From the Reviews: "This book is definitely a milestone in the literature of integer programming and combinatorial optimization. It draws from the Interdisciplinarity of these fields [...]. With knowledge about the relevant terms, one can enjoy special subsections without being entirely familiar with the rest of the chapter. This makes it not only an interesting research book but even a dictionary. [...] The longer one works with it, the more beautiful it becomes." Optima 56, 1997.

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Page Count

604

Publisher

Springer Science & Business Media

Published Date

ISBN 10

354061611X

ISBN 13

9783540616115

Dictionary of Distances

By: Elena Deza,M. Deza

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Dictionary of Distances

By: Elena Deza,M. Deza

This book comes out of need and urgency (expressed esp. in areas of Information Retrieval with respect to Image, Audio, Internet and Biology) to have a working tool to compare data. We answer it and much more. The book will provide powerful resource for all researchers using Mathematics as well as for mathematicians themselves. In the time when over-specialization and terminology fences isolate researchers, this Dictionary try to be "centripedal" and "oikoumeni", providing some access and altitude of vision but without taking the route of scientific vulgarisation. This attempted balance is the main philosophy of this Dictionary which defined its structure and style. Key features: - Unicity: it is the first book treating the basic notion of Distance in whole generality. - Interdisciplinarity: this Dictionary is larger in scope than majority of thematic dictionaries. - Encyclopedicity: while an Encyclopedia of Distances seems now too difficult to produce, this book (by its scope, short introductions and organization) provides the main material for it and for future tutorials on some parts of this material. - Applicability: the distances, as well as distance-related notions and paradigms, are provided in ready-to-use fashion. - Worthiness: the need and urgency for such dictionary was great in several huge areas, esp. Information Retrieval, Image Analysis, Speech Recognition and Biology. - Accessibility: the definitions are easy to locate by subject or, in Index, by alphabetic order; the introductions and definitions are reader-friendly and maximally independent one from another; still the text is structured, in the 3D HTML style, by hyperlink-like boldfaced references to similar definitions. - Authors: written by a mathematical couple, authors of about 300 research papers and half dozen successful mathematical books. * Covers a large range of subjects in pure and applied mathematics * Provides almost encyclopedic coverage of each topic, spanning 28 chapters in seven sections * Designed to be easily applied--the distances and distance-related notions and paradigms are ready to use * Helps users quickly locate definitions by subject or in alphabetical order; stand-alone entries include references to other entries and sources for further investigation

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Page Count

391

Publisher

Elsevier Science Limited

Published Date

ISBN 10

0444520872

ISBN 13

9780444520876

Scale-isometric Polytopal Graphs in Hypercubes and Cubic Lattices

Polytopes in Hypercubes and Zn?

By: M. Deza,Viatcheslav Grishukhin,Mikhail Shtogrin

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Scale-isometric Polytopal Graphs in Hypercubes and Cubic Lattices

Polytopes in Hypercubes and Zn?

By: M. Deza,Viatcheslav Grishukhin,Mikhail Shtogrin

This monograph identifies polytopes that are ?combinatorially ?1-embeddable?, within interesting lists of polytopal graphs, i.e. such that corresponding polytopes are either prominent mathematically (regular partitions, root lattices, uniform polytopes and so on), or applicable in chemistry (fullerenes, polycycles, etc.). The embeddability, if any, provides applications to chemical graphs and, in the first case, it gives new combinatorial perspective to ??2-prominent? affine polytopal objects.The lists of polytopal graphs in the book come from broad areas of geometry, crystallography and graph theory. The book concentrates on such concise and, as much as possible, independent definitions. The scale-isometric embeddability ? the main unifying question, to which those lists are subjected ? is presented with the minimum of technicalities.

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Page Count

186

Publisher

World Scientific

Published Date

ISBN 10

1860944213

ISBN 13

9781860944215

Figurate Numbers

By: Elena Deza,M. Deza

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Figurate Numbers

By: Elena Deza,M. Deza

Plane figurate numbers -- Space figurate numbers -- Multidimensional figurate members -- Areas of number theory including figurate numbers -- Fermat's polygonal number theorem.

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Page Count

475

Publisher

World Scientific

Published Date

ISBN 10

9814355488

ISBN 13

9789814355483

Combinatorics and Computer Science

8th Franco-Japanese and 4th Franco-Chinese Conference, Brest, France, July 3 - 5, 1995 Selected Papers

By: M. Deza,Reinhardt Euler

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Combinatorics and Computer Science

8th Franco-Japanese and 4th Franco-Chinese Conference, Brest, France, July 3 - 5, 1995 Selected Papers

By: M. Deza,Reinhardt Euler

This book presents a collection of 33 strictly refereed full papers on combinatorics and computer science; these papers have been selected from the 54 papers accepted for presentation at the joint 8th Franco-Japanese and 4th Franco-Chinese Conference on Combinatorics in Computer Science, CCS '96, held in Brest, France in July 1995. The papers included in the book have been contributed by authors from 10 countries; they are organized in sections entitled graph theory, combinatorial optimization, selected topics, and parallel and distributed computing.

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Page Count

436

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540615768

ISBN 13

9783540615767

Generalizations of Finite Metrics and Cuts

By: Elena Deza,M. Deza,Elena Mitchel,Mathieu Dutour Sikirić

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Generalizations of Finite Metrics and Cuts

By: Elena Deza,M. Deza,Elena Mitchel,Mathieu Dutour Sikirić

This book introduces oriented version of metrics and cuts and their multidimensional analogues, as well as partial metrics and weighted metrics. It is a follow-up of Geometry of Cuts and Metrics by Deza and Laurent which presents rich theory of classical binary and symmetric objects — metrics and cuts. Many research publications on this subject are devoted to different special aspects of the theory of generalized metrics. However, they are disconnected one from other, often written in different mathematical language, consider the same objects from different points of view without analysis of possible connections, etc. In this book we will construct full theory of main classes of finite generalized metrics and their polyhedral aspects."--

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Page Count

303

Published Date

ISBN 10

9814740403

ISBN 13

9789814740401

Book's by M. Deza

Encyclopedia of Distances

Encyclopedia of Distances

Geometry of Cuts and Metrics

Geometry of Cuts and Metrics

Dictionary of Distances

Dictionary of Distances

Scale-isometric Polytopal Graphs in Hypercubes and Cubic Lattices

Scale-isometric Polytopal Graphs in Hypercubes and Cubic Lattices

Figurate Numbers

Figurate Numbers

Combinatorics and Computer Science

Combinatorics and Computer Science

Generalizations of Finite Metrics and Cuts

Generalizations of Finite Metrics and Cuts

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