Topological Data Analysis

The Abel Symposium 2018

Nils A. Baas, Gunnar E. Carlsson, Gereon Quick , Markus Szymik

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English

Springer Nature Switzerland AG
26 June 2020

Medical research; Algebraic topology; Maths for computer scientists

Series: Abel Symposia

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.

Edited by: Nils A. Baas, Gunnar E. Carlsson, Gereon Quick, Markus Szymik, Marius Thaule
Imprint: Springer Nature Switzerland AG
Country of Publication: Switzerland
Edition: 2020 ed.
Volume: 15
Dimensions: Height: 235mm, Width: 155mm,
Weight: 957g
ISBN: 9783030434076
ISBN 10: 3030434079
Series: Abel Symposia
Pages: 515
Publication Date: 26 June 2020
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.