Matthew He, PhD, is Full Professor and Director of the Division of Math, Science, and Technology of Nova Southeastern University, Florida. He is Full Professor and Grand PhD from the World Information Distributed University, Belgium, since 2004. Dr. He has published more than 100 research papers in mathematics, computer science, information theory, and bioinformatics, and is an editor of both International Journal of Biological Systems and International Journal of Cognitive Informatics and Natural Intelligence. Sergey Petoukhov, PhD, is a chief scientist of the Department of Biomechanics, Mechanical Engineering Research Institute of the Russian Academy of Sciences, Moscow, as well as Full Professor and Grand PhD from the World Information Distributed University. He has published more than 150 research papers in biomechanics, bioinformatics, mathematical and theoretical biology, the theory of symmetries and its applications, and mathematics.

• 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 Symmetrical Techniques.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 and Bioinformatics.2.6 Challenges and Perspectives.References.3. Biological Sequences, Sequence Alignment, and Statistics.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 Algebraic Biology.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 Cognitive Informatics.9.1 Introduction.9.2 Emerging Pattern, Dissipative Structure, and Evolving Cognition.9.3 Denotational Mathematics and Cognitive Computing.9.4 Challenges and Perspectives.References.10. Evolutionary Trends and Central Dogma of Informatics.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.

Matthew He, PhD, is Full Professor and Director of the Division of Math, Science, and Technology of Nova Southeastern University, Florida. He is Full Professor and Grand PhD from the World Information Distributed University, Belgium, since 2004. Dr. He has published more than 100 research papers in mathematics, computer science, information theory, and bioinformatics, and is an editor of both International Journal of Biological Systems and International Journal of Cognitive Informatics and Natural Intelligence. Sergey Petoukhov, PhD, is a chief scientist of the Department of Biomechanics, Mechanical Engineering Research Institute of the Russian Academy of Sciences, Moscow, as well as Full Professor and Grand PhD from the World Information Distributed University. He has published more than 150 research papers in biomechanics, bioinformatics, mathematical and theoretical biology, the theory of symmetries and its applications, and mathematics.

• 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 Symmetrical Techniques.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 and Bioinformatics.2.6 Challenges and Perspectives.References.3. Biological Sequences, Sequence Alignment, and Statistics.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 Algebraic Biology.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 Cognitive Informatics.9.1 Introduction.9.2 Emerging Pattern, Dissipative Structure, and Evolving Cognition.9.3 Denotational Mathematics and Cognitive Computing.9.4 Challenges and Perspectives.References.10. Evolutionary Trends and Central Dogma of Informatics.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.

Matthew He, PhD, is Full Professor and Director of the Division of Math, Science, and Technology of Nova Southeastern University, Florida. He is Full Professor and Grand PhD from the World Information Distributed University, Belgium, since 2004. Dr. He has published more than 100 research papers in mathematics, computer science, information theory, and bioinformatics, and is an editor of both International Journal of Biological Systems and International Journal of Cognitive Informatics and Natural Intelligence. Sergey Petoukhov, PhD, is a chief scientist of the Department of Biomechanics, Mechanical Engineering Research Institute of the Russian Academy of Sciences, Moscow, as well as Full Professor and Grand PhD from the World Information Distributed University. He has published more than 150 research papers in biomechanics, bioinformatics, mathematical and theoretical biology, the theory of symmetries and its applications, and mathematics.

• 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 Symmetrical Techniques.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 and Bioinformatics.2.6 Challenges and Perspectives.References.3. Biological Sequences, Sequence Alignment, and Statistics.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 Algebraic Biology.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 Cognitive Informatics.9.1 Introduction.9.2 Emerging Pattern, Dissipative Structure, and Evolving Cognition.9.3 Denotational Mathematics and Cognitive Computing.9.4 Challenges and Perspectives.References.10. Evolutionary Trends and Central Dogma of Informatics.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.