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The Resource The structure and stability of persistence modules, Frédéric Chazal, Vin de Silva, Marc Glisse, Steve Oudot

The structure and stability of persistence modules, Frédéric Chazal, Vin de Silva, Marc Glisse, Steve Oudot

Label
The structure and stability of persistence modules
Title
The structure and stability of persistence modules
Statement of responsibility
Frédéric Chazal, Vin de Silva, Marc Glisse, Steve Oudot
Contributor
Author
Subject
Language
eng
Summary
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
Member of
Cataloging source
N$T
Dewey number
512/.42
Illustrations
illustrations
Index
index present
LC call number
QA247
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorDate
  • 1971-
  • 1971-
  • 1979-
http://library.link/vocab/relatedWorkOrContributorName
  • Chazal, Frédéric
  • De Silva, Vin
  • Glisse, Marc
  • Oudot, Steve Y.
Series statement
SpringerBriefs in mathematics,
http://library.link/vocab/subjectName
Modules (Algebra)
Label
The structure and stability of persistence modules, Frédéric Chazal, Vin de Silva, Marc Glisse, Steve Oudot
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Dimensions
unknown
Extent
1 online resource
File format
unknown
Form of item
online
Isbn
9783319425450
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
illustrations.
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • SPR960458101
  • ocn960458101
Label
The structure and stability of persistence modules, Frédéric Chazal, Vin de Silva, Marc Glisse, Steve Oudot
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Dimensions
unknown
Extent
1 online resource
File format
unknown
Form of item
online
Isbn
9783319425450
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
illustrations.
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • SPR960458101
  • ocn960458101

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