Topological Data Analysis for Genomics and Evolution
Topology in Biology

An introduction to geometric and topological methods to analyze large scale biological data; includes statistics and genomic applications.

Raul Rabadan (Author), Andrew J. Blumberg (Author)

9781107159549, Cambridge University Press

Hardback, published 19 December 2019

324 pages, 277 colour illus.
25.2 x 17.8 x 2.8 cm, 1.12 kg

'… has been a useful strategy, it is ill-equipped to deal with the very high dimensionality of genomic data. The book will be of interest to biologists and mathematicians ranging from advanced undergraduates to experienced researchers seeking to add new analytic strategies in their work, or to establish collaborations across disciplines.' D. P. Genereux, Choice

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.

Introduction
Part I. Topological Data Analysis: 1. Basic notions of algebraic topology
2. Topological data analysis
3. Statistics and topological inference
4. Manifold learning and metric geometry
Part II. Biological Applications: 5. Evolution, trees, and beyond
6. Cancer genomics
7. Single cell expression data
8. Three dimensional structure of DNA
9. Topological data analysis beyond genomics
10. Conclusions.

Subject Areas: Genetics [non-medical PSAK]