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The Structure and Stability of Persistence Modules
Frédéric ChazalVin de SilvaMarc GlisseSteve Oudot
出版Springer, 2016-10-08
主題Mathematics / TopologyMathematics / Algebra / GeneralMathematics / AppliedMathematics / Geometry / General
ISBN33194254559783319425450
URLhttp://books.google.com.hk/books?id=0QM6DQAAQBAJ&hl=&source=gbs_api
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註釋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.