The Structure and Stability of Persistence Modules
Nonfiction, Science & Nature, Mathematics, Topology, Algebra
| Author: | Frédéric Chazal, Vin de Silva, Marc Glisse, Steve Oudot | ISBN: | 9783319425450 |
| Publisher: | Springer International Publishing | Publication: | October 8, 2016 |
| Imprint: | Springer | Language: | English |
| Author: | Frédéric Chazal, Vin de Silva, Marc Glisse, Steve Oudot |
| ISBN: | 9783319425450 |
| Publisher: | Springer International Publishing |
| Publication: | October 8, 2016 |
| Imprint: | Springer |
| Language: | English |
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.
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.
