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＜電子ブック＞
The Structure and Stability of Persistence Modules / by Frédéric Chazal, Vin de Silva, Marc Glisse, Steve Oudot
(SpringerBriefs in Mathematics. ISSN:21918201)

版	1st ed. 2016.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2016
大きさ	X, 120 p. 17 illus., 15 illus. in color : online resource
著者標目	*Chazal, Frédéric author de Silva, Vin author Glisse, Marc author Oudot, Steve author SpringerLink (Online service)
件　名	LCSH:Algebraic topology LCSH:Algebra LCSH:Computer science—Mathematics FREE:Algebraic Topology FREE:Algebra FREE:Mathematical Applications in Computer Science
一般注記	Introduction -- Persistence Modules -- Rectangle Measures -- Interleaving -- The Isometry Theorem -- Variations -- References -- Index 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 HTTP:URL=https://doi.org/10.1007/978-3-319-42545-0

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