The structure and stability of persistence modules. (2016)

• Record Type: Book
• Further Information: Note: Frédéric Chazal, Vin de Silva, Marc Glisse, Steve Oudot.
• Authors: Chazal, Frédéric, 1971-; De Silva, Vin, 1971-; Glisse, Marc; Oudot, Steve Y, 1979-
• Contents: Preface; Acknowledgments; Contents; 1 Introduction; 1.1 A Brief History of Persistence; 1.2 Main Contributions; 1.3 Application: Stable Descriptors for Metric Spaces; 1.4 Application: Stable Clustering Using Persistence; 1.5 Recommended Reading; 1.6 Organisation; 1.7 Multisets; 2 Persistence Modules; 2.1 Persistence Modules Over a Real Parameter; 2.2 Index Posets; 2.3 Module Categories; 2.4 Interval Modules; 2.5 Interval Decomposition; 2.6 The Decomposition Persistence Diagram; 2.7 Quiver Calculations; 3 Rectangle Measures; 3.1 The Persistence Measure; 3.2 The Persistence Measure (Continued). 3.3 Abstract r-Measures3.4 Equivalence of Measures and Diagrams; 3.5 Non-finite Measures; 3.6 Measures and Diagrams in the Extended Plane; 3.7 The Measure Persistence Diagram; 3.8 Tameness; 3.9 Tameness (Continued); 3.10 Vanishing Lemmas; 3.11 Vanishing Lemmas (Continued); 3.12 Finite Approximations; 4 Interleaving; 4.1 Shifted Homomorphisms; 4.2 Interleaving; 4.3 Interleaving (Continued); 4.4 The Interpolation Lemma; 4.5 The Interpolation Lemma (Continued); 5 The Isometry Theorem; 5.1 The Interleaving Distance; 5.2 The Bottleneck Distance; 5.3 The Bottleneck Distance (Continued). 5.4 The Isometry Theorem5.5 The Converse Stability Theorem; 5.6 The Stability Theorem; 5.7 The Measure Stability Theorem; 5.8 The Measure Stability Theorem (Continued); 6 Variations; 6.1 Partial Interleavings; 6.2 Extended Persistence; References; Index.
• Publisher Details: Switzerland : Springer
• Publication Date: 2016
• Extent: 1 online resource, illustrations
• Subjects: 512/.42; Mathematics; Modules (Algebra); MATHEMATICS -- Algebra -- Intermediate; Modules (Algebra); Mathematics -- Algebra -- General; Mathematics -- Applied; Algebra; Mathematical modelling; Algebraic topology; Algebra; Mathematics -- Topology; Algebraic topology; Electronic books
• Languages: English
• ISBNs: 9783319425450; 3319425455
• Related ISBNs: 9783319425436; 3319425439
• Notes: Note: Includes bibliographical references and index.; Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.