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Books Year : 2016

The Structure and Stability of Persistence Modules

Frédéric Chazal
Marc Glisse

Abstract

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.

Dates and versions

hal-01330678 , version 1 (12-06-2016)

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Frédéric Chazal, Steve Y. Oudot, Marc Glisse, Vin de Silva. The Structure and Stability of Persistence Modules. Springer Verlag, pp.VII, 116, 2016, SpringerBriefs in Mathematics, 978-3-319-42543-6. ⟨10.1007/978-3-319-42545-0⟩. ⟨hal-01330678⟩
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