M. Deza – Encyclopedia of Distances (2016)
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Автор: M. Deza
Название книги: Encyclopedia of Distances (2016)
Формат: PDF
Жанр: Математика
Страницы: 757
Качество: Изначально компьютерное, E-book
In 2016,one decade after the publication of our Dictionary of Distances, the number of WWW entries offered by Google on the topics “distance” and “distance metric” has grown from 300 million (about 4% of all entries) and 12 million to 1:35 billion (about 5:4% of all entries) and 114 million.
This fourth edition is characterized by updated and rewritten sections on some items suggested by experts and readers, as well as 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.
Contents
Mathematics of Distances
General Definitions
Topological Spaces
Generalizations of Metric Spaces
Metric Transforms
Geometry and Distances
Distances in Geometry
Riemannian and Hermitian Metrics
Distances on Surfaces and Knots
Distances on Convex Bodies, Cones, and Simplicial Complexes
Distances in Classical Mathematics
Distances in Algebra
Distances on Strings and Permutations
Distances on Numbers, Polynomials, and Matrices
Distances in Functional Analysis
Distances in Probability Theory
Distances in Applied Mathematics
Distances in Graph Theory
Distances in Coding Theory
Distances and Similarities in Data Analysis
Distances in Systems and Mathematical Engineering
Computer-Related Distances
Distances on Real and Digital Planes
Voronoi Diagram Distances
Image and Audio Distances
Distances in Networks
Distances in Natural Sciences
Distances in Biology
Distances in Physics and Chemistry
Distances in Earth Science and Astronomy
Distances in Cosmology and Theory of Relativity
Real-World Distances
Length Measures and Scales
Distances in Applied Social Sciences
Other Distances
Описание
Encyclopedia of Distances Мишеля Деза — это фундаментальный справочник, в котором собраны и систематизированы сотни различных понятий расстояния из математики, информатики, физики, биологии, лингвистики и других дисциплин.
Книга рассматривает метрики и расстояния в самых разных контекстах: от классических евклидовых и манхэттенских метрик до экзотических расстояний в графах, генетике, химии, когнитивных науках и теории данных. Автор приводит определения, основные свойства, примеры применения и взаимосвязи между различными типами расстояний.
- математикам и специалистам по дискретной геометрии
- исследователям в области машинного обучения и анализа данных
- студентам и преподавателям, изучающим метрические пространства
- специалистам по компьютерному зрению, биоинформатике и лингвистике
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