Algebraic topology is particularly suited for the analysis of high dimensional large data sets, including those in modern biology. The book introduces geometric and topological methods, including statistics, as well as applications to biology - including cancer genetics, single cell studies and reconstructing evolutionary relationships from genomic data.
Algebraic topology is particularly suited for the analysis of high dimensional large data sets, including those in modern biology. The book introduces geometric and topological methods, including statistics, as well as applications to biology - including cancer genetics, single cell studies and reconstructing evolutionary relationships from genomic data.
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.
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.
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