Matthew He & Sergey Petoukhov 
Mathematics of Bioinformatics 
Theory, Methods and Applications

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.

สารบัญ

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.

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Matthew He, Ph D, is Full Professor and Director of the
Division of Math, Science, and Technology of Nova Southeastern
University, Florida. He is Full Professor and Grand Ph D 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, Ph D, 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 Ph D 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.