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Topological data analysis. Proceedings of the Abel symposium 2018, Geiranger, Norway, June 4–8, 2018. (English) Zbl 1448.62008
Abel Symposia 15. Cham: Springer (ISBN 978-3-030-43407-6/hbk; 978-3-030-43408-3/ebook). xiv, 515 p. (2020).

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Publisher’s description: 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.
The articles of this volume will be reviewed individually. For the preceding symposium see [Zbl 1411.14002].
Indexed articles:
Adams, Henry; Aminian, Manuchehr; Farnell, Elin; Kirby, Michael; Mirth, Joshua; Neville, Rachel; Peterson, Chris; Shonkwiler, Clayton, A fractal dimension for measures via persistent homology, 1-31 [Zbl 1448.62211]
Anai, Hirokazu; Chazal, Frédéric; Glisse, Marc; Ike, Yuichi; Inakoshi, Hiroya; Tinarrage, Raphaël; Umeda, Yuhei, DTM-based filtrations, 33-66 [Zbl 1448.62212]
Bauer, Ulrich; Lesnick, Michael, Persistence diagrams as diagrams: a categorification of the stability theorem, 67-96 [Zbl 1453.55004]
Bubenik, Peter, The persistence landscape and some of its properties, 97-117 [Zbl 1453.62807]
Carlsson, Gunnar; Gabrielsson, Rickard Brüel, Topological approaches to deep learning, 119-146 [Zbl 1441.68220]
Carrière, Mathieu; Rabadán, Raúl, Topological data analysis of single-cell Hi-C contact maps, 147-162 [Zbl 1448.62213]
Curto, Carina Pamela; Youngs, Nora, Neural ring homomorphisms and maps between neural codes, 163-180 [Zbl 1448.62214]
Edelsbrunner, Herbert; Nikitenko, Anton; Ölsböck, Katharina; Synak, Peter, Radius functions on Poisson-Delaunay mosaics and related complexes experimentally, 181-218 [Zbl 1448.62215]
Giusti, Chad; Lee, Darrick, Iterated integrals and population time series analysis, 219-246 [Zbl 1448.62216]
Gonzalez, Georgina; Ushakova, Arina; Sazdanovic, Radmila; Arsuaga, Javier, Prediction in cancer genomics using topological signatures and machine learning, 247-276 [Zbl 1448.62165]
Hess, Kathryn, Topological adventures in neuroscience, 277-305 [Zbl 1451.92071]
Hiraoka, Yasuaki; Mikami, Tatsuya, Percolation on homology generators in codimension one, 307-342 [Zbl 1448.62217]
Itskov, Vladimir; Kunin, Alexander; Rosen, Zvi, Hyperplane neural codes and the polar complex, 343-369 [Zbl 1451.92019]
Kim, Woojin; Mémoli, Facundo; Smith, Zane, Analysis of dynamic graphs and dynamic metric spaces via zigzag persistence, 371-389 [Zbl 1448.55008]
Nanda, Vidit; Patel, Amit, Canonical stratifications along bisheaves, 391-403 [Zbl 1448.55006]
Oudot, Steve; Solomon, Elchanan, Inverse problems in topological persistence, 405-433 [Zbl 1447.55006]
Perea, Jose A., Sparse circular coordinates via principal \(\mathbb{Z}\)-bundles, 435-458 [Zbl 1450.62140]
Turner, Katharine; Spreemann, Gard, Same but different: distance correlations between topological summaries, 459-490 [Zbl 1450.62141]
Vejdemo-Johansson, Mikael; Leshchenko, Alisa, Certified mapper: repeated testing for acyclicity and obstructions to the nerve lemma, 491-515 [Zbl 1450.62142]
MSC:
62-06 Proceedings, conferences, collections, etc. pertaining to statistics
55-06 Proceedings, conferences, collections, etc. pertaining to algebraic topology
62R40 Topological data analysis
62P10 Applications of statistics to biology and medical sciences; meta analysis
55N31 Persistent homology and applications, topological data analysis
92B05 General biology and biomathematics
00B25 Proceedings of conferences of miscellaneous specific interest
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