The Structure and Stability of Persistence Modules

Frédéric Chazal 1 Steve Y. Oudot 2, 1 Marc Glisse 1 Vin De Silva 3
1 DATASHAPE - Understanding the Shape of Data
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
2 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
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.
Type de document :
Ouvrage (y compris édition critique et traduction)
Springer Verlag, pp.VII, 116, 2016, SpringerBriefs in Mathematics, 978-3-319-42543-6. 〈http://www.springer.com/us/book/9783319425436〉
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Contributeur : Frédéric Chazal <>
Soumis le : dimanche 12 juin 2016 - 14:31:52
Dernière modification le : samedi 18 février 2017 - 01:14:43

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  • HAL Id : hal-01330678, version 1

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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. 〈http://www.springer.com/us/book/9783319425436〉. 〈hal-01330678〉

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