Stochastic Models, Information Theory, and...

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Beschreibung

The subjects of stochastic processes, information theory, and Lie groups are usually treated separately from each other. This unique two-volume set presents these topics in a unified setting, thereby building bridges between fields that are rarely studied by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of stochastic, geometric, and group-theoretic concepts in the modeling of physical phenomena.

Volume 2 builds on the fundamentals presented in Volume 1, delving deeper into relationships among stochastic geometry, geometric aspects of the theory of communications and coding, multivariate statistical analysis, and error propagation on Lie groups. Extensive exercises, motivating examples, and real-world applications make the work suitable as a textbook for use in courses that emphasize applied stochastic processes or differential geometry.

Stochastic Models, Information Theory, and Lie Groups will be of interest to advanced undergraduate and graduate students, researchers, and practitioners working in applied mathematics, the physical sciences, and engineering.

Zusammenfassung

Unique work: the only book to use tools and concepts from several mathematical areas usually treated in separate books-stochastic processes, information theory, and Lie theory-thereby building bridges between topics rarely studied by the same individuals

Extensive exercises and numerous examples used to motivate concepts with an emphasis on modeling physical phenomena

Concrete presentation makes it easy for readers to obtain numerical solutions for their own problems

Applications to a variety of areas, including conformational fluctuations of DNA, infotaxis, statistical mechanics, and biomolecular information theory

Suitable as a textbook for advanced undergraduate and graduate courses in applied stochastic processes or differential geometry

For a broad audience of advanced undergraduate and graduate students, researchers, and practitioners in applied mathematics, the physical sciences, and engineering

Includes supplementary material: [...]

Inhaltsverzeichnis

Lie Groups I: Introduction and Examples.- Lie Groups II: Differential Geometric Properties.- Lie Groups III: Integration, Convolution, and Fourier Analysis.- Variational Calculus on Lie Groups.- Statistical Mechanics and Ergodic Theory.- Parts Entropy and the Principal Kinematic Formula.- Estimation and Multivariate Analysis in R^n.- Information, Communication, and Group Therapy.- Algebraic and Geometric Coding Theory.- Information Theory on Lie Groups.- Stochastic Processes on Lie Groups.- Locomotion and Perception as Communication over Principal Fiber Bundles; and A Survey of Additional Applications.

Details

Erscheinungsjahr:	2011
Fachbereich:	Topologie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Seiten:	464
Reihe:	Applied and Numerical Harmonic Analysis
Inhalt:	xxvii 435 S.
ISBN-13:	9780817649432
ISBN-10:	0817649433
Sprache:	Englisch
Herstellernummer:	12757039
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Chirikjian, Gregory S.
Auflage:	1st Edition.
Hersteller:	Birkhuser Boston Birkhäuser Boston Applied and Numerical Harmonic Analysis
Maße:	260 x 183 x 31 mm
Von/Mit:	Gregory S. Chirikjian
Erscheinungsdatum:	15.11.2011
Gewicht:	1,063 kg

preigu-id: 106897880