Book
,
Online
in
English
Encyclopedia of Distances
by Michel Marie Deza, Elena Deza.
 Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2016.
 4th ed. 2016.
 XXII, 756 pages 2 illustrations online resource.
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 Summary

 This 4th 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 multisetmetric, algebraic pointconic distance, triangular ratio metric, RossiHamming 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 crossreferencing with easily navigable boldfaced 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 distancerelated notions and paradigms that enable applied mathematicians in other sectors to deploy research tools that nonspecialists 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. ComputerRelated 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. RealWorld Distances: 27 Length Measures and Scales
 28 Distances in Applied Social Sciences
 29 Other Distances.
 Additional form
 ISBN

 9783662528440
 Alternate version: 9783662528433
 Identifying numbers

 doi: 10.1007/9783662528440