Encyclopedia of Distances / by Michel Marie Deza, Elena Deza.

Format:

Book

Author/Creator:

Deza, Michel Marie., Author.

Deza, Elena., Author.

Language:

English

Subjects (All):

Geometry, Differential.

Topology.

Computer science--Mathematics.

Computer science.

Applied mathematics.

Engineering mathematics.

Differential Geometry.

Computational Mathematics and Numerical Analysis.

Mathematical and Computational Engineering.

Local Subjects:

Differential Geometry.

Topology.

Computational Mathematics and Numerical Analysis.

Mathematical and Computational Engineering.

Physical Description:

1 online resource (XXII, 756 p. 2 illus.)

Edition:

4th ed. 2016.

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2016.

Summary:

This 4-th edition of the leading reference volume on distance metrics is characterized by updated and rewritten sections on some items suggested by experts and readers, as well a general streamlining of content and the addition of essential new topics. Though the structure remains unchanged, the new edition also explores recent advances in the use of distances and metrics for e.g. generalized distances, probability theory, graph theory, coding theory, data analysis. New topics in the purely mathematical sections include e.g. the Vitanyi multiset-metric, algebraic point-conic distance, triangular ratio metric, Rossi-Hamming metric, Taneja distance, spectral semimetric between graphs, channel metrization, and Maryland bridge distance. The multidisciplinary sections have also been supplemented with new topics, including: dynamic time wrapping distance, memory distance, allometry, atmospheric depth, elliptic orbit distance, VLBI distance measurements, the astronomical system of units, and walkability distance. Leaving aside the practical questions that arise during the selection of a ‘good’ distance function, this work focuses on providing the research community with an invaluable comprehensive listing of the main available distances. As well as providing standalone introductions and definitions, the encyclopedia facilitates swift cross-referencing with easily navigable bold-faced textual links to core entries. In addition to distances themselves, the authors have collated numerous fascinating curiosities in their Who’s Who of metrics, including distance-related notions and paradigms that enable applied mathematicians in other sectors to deploy research tools that non-specialists justly view as arcane. In expanding access to these techniques, and in many cases enriching the context of distances themselves, this peerless volume is certain to stimulate fresh research.

Contents:

Part I. Mathematics of Distances: 1 General Definitions

2 Topological Spaces

3 Generalization of Metric Spaces

4 Metric Transforms

5 Metrics on Normed Structures

Part II. Geometry and Distances: 6 Distances in Geometry

7 Riemannian and Hermitian Metrics

8 Distances on Surfaces and Knots

9 Distances on Convex Bodies, Cones and Simplicial Complexes

Part III. Distances in Classical Mathematics: 10 Distances in Algebra

11 Distances on Strings and Permutations

12 Distances on Numbers, Polynomials and Matrices

13 Distances in Functional Analysis

14 Distances in Probability Theory

Part IV. Distances in Applied Mathematics: 15 Distances in Graph Theory

16 Distances in Coding Theory

17 Distances and Similarities in Data Analysis

18 Distances in Systems and Mathematical Engineering

Part V. Computer-Related Distances: 19 Distances on Real and Digital Planes

20 Voronoi Diagram Distances

21 Image and Audio Distances

22 Distances in Networks

Part VI. Distances in Natural Sciences: 23 Distances in Biology

24 Distances in Physics and Chemistry

25 Distances in Earth Science and Astronomy

26 Distances in Cosmology and Theory of Relativity

Part VII. Real-World Distances: 27 Length Measures and Scales

28 Distances in Applied Social Sciences

29 Other Distances.

Notes:

Includes bibliographical references and index.

ISBN:

3-662-52844-4