The Structure and Stability of Persistence Modules

Nonfiction, Science & Nature, Mathematics, Topology, Algebra
Cover of the book The Structure and Stability of Persistence Modules by Frédéric Chazal, Vin de Silva, Marc Glisse, Steve Oudot, Springer International Publishing
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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.

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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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