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Beschreibung
This book is a comprehensive treatment of the theory of persistence modules over the real line. It presents a set of mathematical tools to analyse the structure and to establish the stability of such modules, providing a sound mathematical framework for the study of persistence diagrams. Completely self-contained, this brief introduces the notion of persistence measure and makes extensive use of a new calculus of quiver representations to facilitate explicit computations.
Appealing to both beginners and experts in the subject, The Structure and Stability of Persistence Modules provides a purely algebraic presentation of persistence, and thus complements the existing literature, which focuses mainly on topological and algorithmic aspects.
This book is a comprehensive treatment of the theory of persistence modules over the real line. It presents a set of mathematical tools to analyse the structure and to establish the stability of such modules, providing a sound mathematical framework for the study of persistence diagrams. Completely self-contained, this brief introduces the notion of persistence measure and makes extensive use of a new calculus of quiver representations to facilitate explicit computations.
Appealing to both beginners and experts in the subject, The Structure and Stability of Persistence Modules provides a purely algebraic presentation of persistence, and thus complements the existing literature, which focuses mainly on topological and algorithmic aspects.
Inhaltsverzeichnis
Introduction.- Persistence Modules.- Rectangle Measures.- Interleaving.- The Isometry Theorem.- Variations.- References.- Index.
Details
Erscheinungsjahr: 2016
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: x
120 S.
2 s/w Illustr.
15 farbige Illustr.
120 p. 17 illus.
15 illus. in color.
ISBN-13: 9783319425436
ISBN-10: 3319425439
Sprache: Englisch
Herstellernummer: 978-3-319-42543-6
Einband: Kartoniert / Broschiert
Autor: Chazal, Frédéric
de Silva, Vin
Glisse, Marc
Oudot, Steve
Auflage: 1st ed. 2016
Hersteller: Springer
Springer, Berlin
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Abbildungen: X, 120 p. 17 illus., 15 illus. in color.
Maße: 237 x 161 x 8 mm
Von/Mit: Frédéric Chazal (u. a.)
Erscheinungsdatum: 17.10.2016
Gewicht: 0,213 kg
Artikel-ID: 107530443