Mathematics of Bioinformatics Theory, Methods and Applications

by He, Matthew; Petoukhov, Sergey

• ISBN13: 9780470404430
• ISBN10: 0470404434
• Edition: 1st
• Format: Hardcover
• Copyright: 2011-01-04
• Publisher: Wiley-Interscience

Summary

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.

Author Biography

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.

Table of Contents

Preface	p. ix
About the Authors	p. xiv
Bioinformatics and Mathematics	p. 1
Introduction	p. 2
Genetic Code and Mathematics	p. 6
Mathematical Background	p. 10
Converting Data to Knowledge	p. 18
The Big Picture: Informatics	p. 18
Challenges and Perspectives	p. 21
References	p. 22
Genetic Codes, Matrices, and Symmetrical Techniques	p. 24
Introduction	p. 25
Matrix Theory and Symmetry Preliminaries	p. 28
Genetic Codes and Matrices	p. 29
Genetic Matrices, Hydrogen Bonds, and the Golden Section	p. 41
Symmetrical Patterns, Molecular Genetics, and Bioinformatics	p. 49
Challenges and Perspectives	p. 53
References	p. 55
Biological Sequences, Sequence Alignment, and Statistics	p. 63
Introduction	p. 63
Mathematical Sequences	p. 64
Sequence Alignment	p. 66
Sequence Analysis and Further Discussion	p. 81
Challenges and Perspectives	p. 85
References	p. 87
Structures of DNA and Knot Theory	p. 89
Introduction	p. 89
Knot Theory Preliminaries	p. 92
DNA Knots and Links	p. 102
Challenges and Perspectives	p. 105
References	p. 110
Protein Structures, Geometry, and Topology	p. 112
Introduction	p. 112
Computational Geometry and Topology Preliminaries	p. 113
Protein Structures and Prediction	p. 117
Statistical Approach and Discussion	p. 130
Challenges and Perspectives	p. 132
References	p. 133
Biological Networks and Graph Theory	p. 136
Introduction	p. 136
Graph Theory Preliminaries and Network Topology	p. 137
Models of Biological Networks	p. 148
Challenges and Perspectives	p. 152
References	p. 155
Biological Systems, Fractals, and Systems Biology	p. 157
Introduction	p. 157
Fractal Geometry Preliminaries	p. 159
Fractal Geometry in Biological Systems	p. 162
Systems Biology	p. 174
Challenges and Perspectives	p. 174
References	p. 177
Matrix Genetics, Hadamard Matrices, and Algebraic Biology	p. 180
Introduction	p. 180
Genetic Matrices and the Degeneracy of the Genetic Code	p. 181
The Genetic Code and Hadamard Matrices	p. 194
Genetic Matrices and Matrix Algebras of Hypercomplex Numbers	p. 201
Some Rules of Evolution of Variants of the Genetic Code	p. 214
Challenges and Perspectives	p. 224
References	p. 226
Bioinformatics, Denotational Mathematics, and Cognitive Informatics	p. 229
Introduction	p. 229
Emerging Pattern, Dissipative Structure, and Evolving Cognition	p. 234
Denotational Mathematics and Cognitive Computing	p. 238
Challenges and Perspectives	p. 242
References	p. 246
Evolutionary Trends and Central Dogma of Informatics	p. 249
Introduction	p. 249
Evolutionary Trends of Information Sciences	p. 251
Central Dogma of Informatics	p. 253
Challenges and Perspectives	p. 258
References	p. 259
Bioinformatics Notation and Databases	p. 262
Bioinformatics and Genetics Time Line	p. 268
Bioinformatics Glossary	p. 270
Index	p. 297
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