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＜電子ブック＞
Topological Data Analysis : The Abel Symposium 2018 / edited by Nils A. Baas, Gunnar E. Carlsson, Gereon Quick, Markus Szymik, Marius Thaule
(Abel Symposia. ISSN:21978549 ; 15)

版	1st ed. 2020.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2020
大きさ	XIV, 515 p. 199 illus., 146 illus. in color : online resource
著者標目	Baas, Nils A editor Carlsson, Gunnar E editor Quick, Gereon editor Szymik, Markus editor Thaule, Marius editor SpringerLink (Online service)
件　名	LCSH:Algebraic topology LCSH:Medicine—Research LCSH:Biology—Research LCSH:Computer science—Mathematics FREE:Algebraic Topology FREE:Biomedical Research FREE:Mathematics of Computing
一般注記	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. 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 HTTP:URL=https://doi.org/10.1007/978-3-030-43408-3

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