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Topological Data Analysis -

Topological Data Analysis

The Abel Symposium 2018
Buch | Hardcover
XIV, 515 Seiten
2020 | 1st ed. 2020
Springer International Publishing (Verlag)
978-3-030-43407-6 (ISBN)
CHF 299,55 inkl. MwSt
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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.



A fractal dimension for measures via persistent homology.- DTM-based filtrations.- Persistence diagrams as diagrams: a categorification of the stability theorem.- The persistence landscape and some of its properties.- Topological approaches to deep learning.- Topological data analysis of single-cell Hi-C contact maps.- Neural ring homomorphisms and maps between neural codes.- Radius functions on Poisson-Delaunay mosaics and related complexes experimentally.- Iterated integrals and population time series analysis.- Prediction in cancer genomics using topological signatures and machine learning.- Topological adventures in neuroscience.- Percolation on homology generators in codimension one.- Hyperplane neural codes and the polar complex.- Analysis of dynamic graphs and dynamic metric spaces via zigzag persistence.- Canonical stratifications along bisheaves.- Inverse problems in topological persistence.- Sparse circular coordinates via principal Z-bundles.- Same but different: distance correlations between topological summaries.- Certified mapper: repeated testing for acyclicity and obstructions to the nerve lemma. 

Erscheinungsdatum
Reihe/Serie Abel Symposia
Zusatzinfo XIV, 515 p. 199 illus., 146 illus. in color.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Gewicht 955 g
Themenwelt Mathematik / Informatik Informatik Theorie / Studium
Mathematik / Informatik Mathematik Geometrie / Topologie
Medizin / Pharmazie
Schlagworte Data Analysis • Deep learning • Dynamic Graphs • Inverse Problems • nerve lemma • neural codes • neural science • persistence diagrams • Persistent Homology • Poisson-Delaunay mosaics • Poisson–Delaunay mosaics • prediction in cancer genomics • single-cell Hi-C contact maps • stability theorem • topological data analysis
ISBN-10 3-030-43407-9 / 3030434079
ISBN-13 978-3-030-43407-6 / 9783030434076
Zustand Neuware
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