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Topological Data Analysis

The Abel Symposium 2018

  • Conference proceedings
  • © 2020

Overview

Editors:
  1. Nils A. Baas

    1. Department of Mathematical Sciences, NTNU, Trondheim, Norway

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  2. Gunnar E. Carlsson

    1. Department of Mathematics, Stanford University, Stanford, USA

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  3. Gereon Quick

    1. Department of Mathematical Sciences, NTNU, Trondheim, Norway

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  4. Markus Szymik

    1. Department of Mathematical Sciences, NTNU, Trondheim, Norway

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  5. Marius Thaule

    1. Department of Mathematical Sciences, NTNU, Trondheim, Norway

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Part of the book series: Abel Symposia (ABEL, volume 15)

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Table of contents (19 papers)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. A Fractal Dimension for Measures via Persistent Homology

    • Henry Adams, Manuchehr Aminian, Elin Farnell, Michael Kirby, Joshua Mirth, Rachel Neville et al.
    Pages 1-31

  3. DTM-Based Filtrations

    • Hirokazu Anai, Frédéric Chazal, Marc Glisse, Yuichi Ike, Hiroya Inakoshi, Raphaël Tinarrage et al.
    Pages 33-66

  4. Persistence Diagrams as Diagrams: A Categorification of the Stability Theorem

    • Ulrich Bauer, Michael Lesnick
    Pages 67-96

  5. The Persistence Landscape and Some of Its Properties

    • Peter Bubenik
    Pages 97-117

  6. Topological Approaches to Deep Learning

    • Gunnar Carlsson, Rickard Brüel Gabrielsson
    Pages 119-146

  7. Topological Data Analysis of Single-Cell Hi-C Contact Maps

    • Mathieu Carrière, Raúl Rabadán
    Pages 147-162

  8. Neural Ring Homomorphisms and Maps Between Neural Codes

    • Carina Pamela Curto, Nora Youngs
    Pages 163-180

  9. Radius Functions on Poisson–Delaunay Mosaics and Related Complexes Experimentally

    • Herbert Edelsbrunner, Anton Nikitenko, Katharina Ölsböck, Peter Synak
    Pages 181-218

  10. Iterated Integrals and Population Time Series Analysis

    • Chad Giusti, Darrick Lee
    Pages 219-246

  11. Prediction in Cancer Genomics Using Topological Signatures and Machine Learning

    • Georgina Gonzalez, Arina Ushakova, Radmila Sazdanovic, Javier Arsuaga
    Pages 247-276

  12. Topological Adventures in Neuroscience

    • Kathryn Hess
    Pages 277-305

  13. Percolation on Homology Generators in Codimension One

    • Yasuaki Hiraoka, Tatsuya Mikami
    Pages 307-342

  14. Hyperplane Neural Codes and the Polar Complex

    • Vladimir Itskov, Alexander Kunin, Zvi Rosen
    Pages 343-369

  15. Analysis of Dynamic Graphs and Dynamic Metric Spaces via Zigzag Persistence

    • Woojin Kim, Facundo Mémoli, Zane Smith
    Pages 371-389

  16. Canonical Stratifications Along Bisheaves

    • Vidit Nanda, Amit Patel
    Pages 391-403

  17. Inverse Problems in Topological Persistence

    • Steve Oudot, Elchanan Solomon
    Pages 405-433

  18. Sparse Circular Coordinates via Principal \(\mathbb {Z}\)-Bundles

    • Jose A. Perea
    Pages 435-458

  19. Same But Different: Distance Correlations Between Topological Summaries

    • Katharine Turner, Gard Spreemann
    Pages 459-490

  20. Certified Mapper: Repeated Testing for Acyclicity and Obstructions to the Nerve Lemma

    • Mikael Vejdemo-Johansson, Alisa Leshchenko
    Pages 491-515
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Keywords

About this book

This book gathers the proceedings of the 2018 Abel Symposium, which was held in Geiranger, Norway, on June 4-8, 2018. The symposium offered an overview of the emerging field of "Topological Data Analysis". This volume presents papers on various research directions, notably including applications in neuroscience, materials science, cancer biology, and immune response. Providing an essential snapshot of the status quo, it represents a valuable asset for practitioners and those considering entering the field.



Editors and Affiliations

  • Department of Mathematical Sciences, NTNU, Trondheim, Norway

    Nils A. Baas, Gereon Quick, Markus Szymik, Marius Thaule

  • Department of Mathematics, Stanford University, Stanford, USA

    Gunnar E. Carlsson

Bibliographic Information

  • Book Title: Topological Data Analysis

  • Book Subtitle: The Abel Symposium 2018

  • Editors: Nils A. Baas, Gunnar E. Carlsson, Gereon Quick, Markus Szymik, Marius Thaule

  • Series Title: Abel Symposia

  • DOI: https://doi.org/10.1007/978-3-030-43408-3

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2020

  • Hardcover ISBN: 978-3-030-43407-6Published: 26 June 2020

  • Softcover ISBN: 978-3-030-43410-6Published: 26 June 2021

  • eBook ISBN: 978-3-030-43408-3Published: 25 June 2020

  • Series ISSN: 2193-2808

  • Series E-ISSN: 2197-8549

  • Edition Number: 1

  • Number of Pages: XIV, 515

  • Number of Illustrations: 53 b/w illustrations, 146 illustrations in colour

  • Topics: Algebraic Topology, Biomedicine, general, Mathematics of Computing

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