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.
Raul Rabadan is a Professor at Columbia University, New York. He is Director of the Program for Mathematical Genomics at Columbia University, New York, and the NCI Physics and Oncology Center for Topology of Cancer Evolution and Heterogeneity. Dr Rabadan received his Ph.D. in Theoretical Physics in 2001 and went on to conduct research at the European Laboratory for Particle Physics (CERN) in Switzerland, and at the Institute for Advanced Study (IAS), Princeton, New Jersey. At Columbia University, he leads a highly interdisciplinary laboratory with researchers from the fields of mathematics, physics, computer science, engineering, and medicine, with the common goal of solving biomedical problems through quantitative computational models.
Inhaltsangabe
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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