The structure and stability of persistence modules

• 作者： Chazal, Frederic, author.
• 其他作者：
  • Silva, Vin de, author.
  • Glisse, Marc, author.
  • Oudot, Steve, author.
  • SpringerLink (Online service)
• 其他題名：
  • SpringerBriefs in mathematics.
• 出版： Cham : Springer International Publishing :Imprint: Springer
• 叢書名： SpringerBriefs in mathematics,
• 主題： Modules (Algebra) , Mathematics. , Algebraic Topology. , Algebra. , Mathematical Applications in Computer Science.
• ISBN： 9783319425450 (electronic bk.) 、 9783319425436 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: Introduction -- Persistence Modules -- Rectangle Measures -- Interleaving -- The Isometry Theorem -- Variations -- References -- Index.
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• 摘要註: 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.
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