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Mathematics of Bioinformatics: Theory, Methods and Applications

Mathematics of Bioinformatics: Theory, Methods and Applications

Matthew He, Sergey Petoukhov

ISBN: 978-0-470-90464-0

Oct 2010

350 pages


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.

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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


Appendix A. Bioinformatics Notation and Databases.

Appendix B. Bioinformatics/Genetics/Timeline.

Appendix C. Bioinformatics Glossary.