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.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.

Mathematical methods that illuminate fundamental problems related to the genetic code and bioinformatics

Mathematics of Bioinformatics: Theory, Practice, and Applications provides a comprehensive blueprint for connecting and integrating information derived from mathematical methods and applying it to the understanding of biological sequences, structures, and networks. It offers valuable knowledge about mathematical tools, phenomenological results, and interdisciplinary connections in the fields of molecular genetics, bioinformatics, and informatics.

Each chapter is divided into sections based on bioinformatics topics and related mathematical theory and methods. Each topic is comprised of an introduction to the biological problems in bioinformatics; a presentation of topics in mathematical theory and methods relevant to the problems; and an integrative overview that draws the connections and interfaces between the problems, theory, methods, and applications. This practical resource:

• Covers genetic codes, sequences, structures, functions, biological networks/systems, and interfaces with mathematics, making connections between mathematics and bioinformatics for the bioinformatics specialist
• Provides integrative models for potential simulations, modeling, and implementation utilizing algorithms and analysis for the computer scientist
• Details recent research covering other branches of mathematics such as linear algebra, topology, differential geometry, fractals, and chaos theory that have found useful applications in bioinformatics
• Emphasizes applications of mathematics in bioinformatics while eschewing mathematical proofs and deep theories

Mathematics of Bioinformatics is intended for scientists, researchers, and upper-level undergraduate and graduate students in bioinformatics, mathematics, computer informatics, theoretical biology, mathematical biology, and biotechnology who seek information on the possibilities and challenges of interface between mathematics and bioinformatics. Readers with a foundation in calculus can also adapt to the mathematical topics introduced throughout.