Mathematics of Bioinformatics

Mathematics of Bioinformatics: Theory, Methods, and Applications provides a comprehensive format for connecting and integrating information derived from mathematical methods and applying it to the understanding of biological sequences, structures, and networks. Each chapter is divided into a number of sections based on the bioinformatics topics and related mathematical theory and methods. Each topic of the section is comprised of the following three parts: an introduction to the biological problems in bioinformatics; a presentation of relevant topics of mathematical theory and methods to the bioinformatics problems introduced in the first part; an integrative overview that draws the connections and interfaces between bioinformatics problems/issues and mathematical theory/methods/applications.

Mathematics of Bioinformatics: Theory, Methods, andApplications provides a comprehensive format forconnecting and integrating information derived from mathematicalmethods and applying it to the understanding of biologicalsequences, structures, and networks. Each chapter is divided into anumber of sections based on the bioinformatics topics and relatedmathematical theory and methods. Each topic of the section iscomprised of the following three parts: an introduction to thebiological problems in bioinformatics; a presentationof relevant topics of mathematical theory and methods to thebioinformatics problems introduced in the first part; anintegrative overview that draws the connections and interfacesbetween bioinformatics problems/issues and mathematicaltheory/methods/applications.

Preface.About the Authors.1. Bioinformatics and Mathematics.1.1 Introduction.1.2 Genetic Code and Mathematics.1.3 Mathematical Background.1.4 Converting Data to Knowledge.1.5 Big Picture: Informatics.1.6 Challenges and Perspectives.References.2. Genetic Codes, Matrices, and SymmetricalTechniques.2.1 Introduction.2.2 Matrix Theory and Symmetry Preliminaries.2.3 Genetic Codes and Matrices.2.4 Genetic Matrices, Hydrogen Bonds and the Golden Section.2.5 Symmetrical Patterns, Molecular Genetics andBioinformatics.2.6 Challenges and Perspectives.References.3. Biological Sequences, Sequence Alignment, andStatistics.3.1 Introduction.3.2 Mathematical Sequences.3.3 Sequence Alignment.3.4 Sequence Analysis and Further Discussions.3.5 Challenges and Perspectives.References.4. Structures of DNA and Knot Theory.4.1 Introduction.4.2 Knot Theory Preliminaries.4.3 DNA Knots and Links.4.4 Challenges and Perspectives.References.5. Protein Structures, Geometry, and Topology.5.1 Introduction.5.2 Computational Geometry and Topology Preliminaries.5.3 Protein Structures and Prediction.5.4 Statistical Approach and Discussions.5.5 Challenges and Perspectives.References.6. Biological Networks and Graph Theory.6.1 Introduction.6.2 Graph Theory Preliminaries and Network Topology.6.3 Models of Biological Networks.6.4 Challenges and Perspectives.References.7. Biological Systems, Fractals, and Systems Biology.7.1 Introduction.7.2 Fractal Geometry Preliminaries.7.3 Fractal Geometry in Biological Systems.7.4 Systems Biology and Perspectives.7.5 Challenges and Perspectives.References.8. Matrix Genetics, Hadamard Matrix, and AlgebraicBiology.8.1 Introduction.8.2 Genetic Matrices and the Degeneracy of the Genetic Code.8.3 The Genetic Code and Hadamard Matrices.8.4 Genetic Matrices and Matrices of Hypercomplex Numbers.8.5 Some Rules of Evolution of Variants of the Genetic Code.8.6 Challenges and Perspectives.References.9. Bioinformatics, Living Systems and CognitiveInformatics.9.1 Introduction.9.2 Emerging Pattern, Dissipative Structure, and EvolvingCognition.9.3 Denotational Mathematics and Cognitive Computing.9.4 Challenges and Perspectives.References.10. Evolutionary Trends and Central Dogma ofInformatics.10.1 Introduction.10.2 Evolutionary Trends of Information Sciences.10.3 Central Dogma of Informatics.10.4 Challenges and Perspectives.References.Appendix A. Bioinformatics Notation and Databases.Appendix B. Bioinformatics/Genetics/Timeline.Appendix C. Bioinformatics Glossary.Index.