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Topological Data Analysis for Genomics and Evolution

Topological Data Analysis for Genomics and Evolution
Topology in Biology

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  • Publication planned for: September 2019
  • availability: Not yet published - available from September 2019
  • format: Hardback
  • isbn: 9781107159549

Price is not yet set
Hardback

Not yet published - available from September 2019
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  • Biology has entered the age of Big Data. The 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 questions to a comparison of algebraic invariants, such as numbers, which are typically easier to solve. 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 alongside 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
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    Product details

    • Publication planned for: September 2019
    • format: Hardback
    • isbn: 9781107159549
    • availability: Not yet published - available from September 2019
  • Table of Contents

    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.

  • Authors

    Raúl Rabadán, Columbia University, New York

    Andrew J. Blumberg, University of Texas, Austin

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