Biology has entered the age of Big Data. A technical revolution has transformed the field, and extracting meaningful information from large biological data sets is now a central methodological challenge. Algebraic topology is a well-established branch of pure mathematics that studies qualitative descriptors of the shape of geometric objects. It aims to reduce comparisons of shape to a comparison of algebraic invariants, such as numbers, which are typically easier to work with. Topological data analysis is a rapidly developing subfield that leverages the tools of algebraic topology to provide robust multiscale analysis of data sets. This book introduces the central ideas and techniques of topological data analysis and its specific applications to biology, including the evolution of viruses, bacteria and humans, genomics of cancer, and single cell characterization of developmental processes. Bridging two disciplines, the book is for researchers and graduate students in genomics and evolutionary biology as well as mathematicians interested in applied topology.
Author(s): Raul Rabadan, Andrew J. Blumberg
Publisher: Cambridge University Press
Year: 2020
Language: English
Pages: 522
Cover......Page 1
Front Matter
......Page 3
TOPOLOGICAL DATA ANALYSIS FOR GENOMICS AND EVOLUTION:
Topology in Biology......Page 5
Copyright
......Page 6
Dedication
......Page 7
Contents
......Page 9
Contributors
......Page 15
Preface......Page 17
Introduction
......Page 21
Part I: Topological Data Analysis
......Page 41
1 Basic Notions of Algebraic Topology......Page 43
2 Topological Data Analysis......Page 142
3 Statistics and Topological Inference......Page 190
4 Dimensionality Reduction, Manifold Learning, and
Metric Geometry......Page 255
Part II: Biological Applications
......Page 291
5 Evolution, Trees, and Beyond......Page 293
6 Cancer Genomics......Page 376
7 Single Cell Expression Data......Page 419
8 Three-Dimensional Structure of DNA......Page 432
9 Topological Data Analysis beyond Genomics
......Page 443
10 Conclusions......Page 463
Appendix A.
Algorithms in Topological Data Analysis......Page 464
Appendix B.
Introduction to Population Genetics......Page 467
Appendix C.
Molecular Phylogenetics......Page 474
References......Page 488
Index......Page 515
