Chazal / de Silva / Glisse The Structure and Stability of Persistence Modules

1. Auflage 2016
ISBN: 978-3-319-42545-0
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 120 Seiten, eBook

Reihe: SpringerBriefs in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Chazal, Frédéric

de Silva, Vin

Glisse, Marc

Oudot, Steve

Inhaltsverzeichnis

Introduction.- Persistence Modules.- Rectangle Measures.- Interleaving.- The Isometry Theorem.- Variations.- References.- Index.