Topological Data Analysis for Genomics and Evolution

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.
Concisely introduces algebraic topology and the concepts behind topological data analysis for the non-professional mathematician, visually illustrating key ideas
Provides an overview of biological ideas through the lens of genomics for mathematically-advanced readers interested in applied topology, including reconstructing evolutionary processes from genomic data, how cancers evolve or why patients responds to different therapies
Includes an introduction to statistics in topological data analysis, crucial for potential practitioners and end-users applying the methodology to biological questions