Ebook: Encyclopedia of Distances

This updated and revised second edition of the leading reference volume on distance metrics includes a wealth of new material that reflects advances in a field now regarded as an essential tool in many areas of pure and applied mathematics.

The publication of this volume coincides with intensifying research efforts into metric spaces and especially distance design for applications. Accurate metrics have become a crucial goal in computational biology, image analysis, speech recognition and information retrieval.

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.

This updated and revised second edition of the leading reference volume on distance metrics includes a wealth of new material that reflects advances in a field now regarded as an essential tool in many areas of pure and applied mathematics.

The publication of this volume coincides with intensifying research efforts into metric spaces and especially distance design for applications. Accurate metrics have become a crucial goal in computational biology, image analysis, speech recognition and information retrieval.

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.

This updated and revised second edition of the leading reference volume on distance metrics includes a wealth of new material that reflects advances in a field now regarded as an essential tool in many areas of pure and applied mathematics.

The publication of this volume coincides with intensifying research efforts into metric spaces and especially distance design for applications. Accurate metrics have become a crucial goal in computational biology, image analysis, speech recognition and information retrieval.

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.

Content:
Front Matter....Pages I-XVIII
Front Matter....Pages 1-1
General Definitions....Pages 3-58
Topological Spaces....Pages 59-66
Generalizations of Metric Spaces....Pages 67-78
Metric Transforms....Pages 79-87
Metrics on Normed Structures....Pages 89-99
Front Matter....Pages 101-101
Distances in Geometry....Pages 103-123
Riemannian and Hermitian Metrics....Pages 125-155
Distances on Surfaces and Knots....Pages 157-168
Distances on Convex Bodies, Cones, and Simplicial Complexes....Pages 169-180
Front Matter....Pages 181-181
Distances in Algebra....Pages 183-195
Distances on Strings and Permutations....Pages 197-208
Distances on Numbers, Polynomials, and Matrices....Pages 209-221
Distances in Functional Analysis....Pages 223-232
Distances in Probability Theory....Pages 233-245
Front Matter....Pages 247-247
Distances in Graph Theory....Pages 249-278
Distances in Coding Theory....Pages 279-290
Distances and Similarities in Data Analysis....Pages 291-305
Distances in Systems and Mathematical Engineering....Pages 307-320
Front Matter....Pages 321-321
Distances on Real and Digital Planes....Pages 323-338
Voronoi Diagram Distances....Pages 339-347
Front Matter....Pages 321-321
Image and Audio Distances....Pages 349-369
Distances in Networks....Pages 371-384
Front Matter....Pages 385-385
Distances in Biology....Pages 387-434
Distances in Physics and Chemistry....Pages 435-464
Distances in Earth Science and Astronomy....Pages 465-496
Distances in Cosmology and Theory of Relativity....Pages 497-526
Front Matter....Pages 527-527
Length Measures and Scales....Pages 529-543
Distances in Applied Social Sciences....Pages 545-586
Other Distances....Pages 587-617
Back Matter....Pages 619-650

This updated and revised second edition of the leading reference volume on distance metrics includes a wealth of new material that reflects advances in a field now regarded as an essential tool in many areas of pure and applied mathematics.

The publication of this volume coincides with intensifying research efforts into metric spaces and especially distance design for applications. Accurate metrics have become a crucial goal in computational biology, image analysis, speech recognition and information retrieval.

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.

Content:
Front Matter....Pages I-XVIII
Front Matter....Pages 1-1
General Definitions....Pages 3-58
Topological Spaces....Pages 59-66
Generalizations of Metric Spaces....Pages 67-78
Metric Transforms....Pages 79-87
Metrics on Normed Structures....Pages 89-99
Front Matter....Pages 101-101
Distances in Geometry....Pages 103-123
Riemannian and Hermitian Metrics....Pages 125-155
Distances on Surfaces and Knots....Pages 157-168
Distances on Convex Bodies, Cones, and Simplicial Complexes....Pages 169-180
Front Matter....Pages 181-181
Distances in Algebra....Pages 183-195
Distances on Strings and Permutations....Pages 197-208
Distances on Numbers, Polynomials, and Matrices....Pages 209-221
Distances in Functional Analysis....Pages 223-232
Distances in Probability Theory....Pages 233-245
Front Matter....Pages 247-247
Distances in Graph Theory....Pages 249-278
Distances in Coding Theory....Pages 279-290
Distances and Similarities in Data Analysis....Pages 291-305
Distances in Systems and Mathematical Engineering....Pages 307-320
Front Matter....Pages 321-321
Distances on Real and Digital Planes....Pages 323-338
Voronoi Diagram Distances....Pages 339-347
Front Matter....Pages 321-321
Image and Audio Distances....Pages 349-369
Distances in Networks....Pages 371-384
Front Matter....Pages 385-385
Distances in Biology....Pages 387-434
Distances in Physics and Chemistry....Pages 435-464
Distances in Earth Science and Astronomy....Pages 465-496
Distances in Cosmology and Theory of Relativity....Pages 497-526
Front Matter....Pages 527-527
Length Measures and Scales....Pages 529-543
Distances in Applied Social Sciences....Pages 545-586
Other Distances....Pages 587-617
Back Matter....Pages 619-650
....