Mathematics of Bioinformatics: Theory, Practice, and Applications

MATHEMATICS OF BIOINFORMATICS......Page 5
CONTENTS......Page 7
PREFACE......Page 11
ABOUT THE AUTHORS......Page 16
1: Bioinformatics and Mathematics......Page 19
1.1 INTRODUCTION......Page 20
1.2 GENETIC CODE AND MATHEMATICS......Page 24
1.3 MATHEMATICAL BACKGROUND......Page 28
1.5 THE BIG PICTURE: INFORMATICS......Page 36
1.6 CHALLENGES AND PERSPECTIVES......Page 39
REFERENCES......Page 40
2: Genetic Codes, Matrices, and Symmetrical Techniques......Page 42
2.1 INTRODUCTION......Page 43
2.2 MATRIX THEORY AND SYMMETRY PRELIMINARIES......Page 46
2.3 GENETIC CODES AND MATRICES......Page 47
2.4 GENETIC MATRICES, HYDROGEN BONDS, AND THE GOLDEN SECTION......Page 59
2.5 SYMMETRICAL PATTERNS, MOLECULAR GENETICS, AND BIOINFORMATICS......Page 67
2.6 CHALLENGES AND PERSPECTIVES......Page 71
REFERENCES......Page 73
3.1 INTRODUCTION......Page 81
3.2 MATHEMATICAL SEQUENCES......Page 82
3.3 SEQUENCE ALIGNMENT......Page 84
3.4 SEQUENCE ANALYSIS AND FURTHER DISCUSSION......Page 99
3.5 CHALLENGES AND PERSPECTIVES......Page 103
REFERENCES......Page 105
4.1 INTRODUCTION......Page 107
4.2 KNOT THEORY PRELIMINARIES......Page 110
4.3 DNA KNOTS AND LINKS......Page 120
4.4 CHALLENGES AND PERSPECTIVES......Page 123
REFERENCES......Page 128
5.1 INTRODUCTION......Page 130
5.2 COMPUTATIONAL GEOMETRY AND TOPOLOGY PRELIMINARIES......Page 131
5.3 PROTEIN STRUCTURES AND PREDICTION......Page 135
5.4 STATISTICAL APPROACH AND DISCUSSION......Page 148
5.5 CHALLENGES AND PERSPECTIVES......Page 150
REFERENCES......Page 151
6.1 INTRODUCTION......Page 154
6.2 GRAPH THEORY PRELIMINARIES AND NETWORK TOPOLOGY......Page 155
6.3 MODELS OF BIOLOGICAL NETWORKS......Page 166
6.4 CHALLENGES AND PERSPECTIVES......Page 170
REFERENCES......Page 173
7.1 INTRODUCTION......Page 175
7.2 FRACTAL GEOMETRY PRELIMINARIES......Page 177
7.3 FRACTAL GEOMETRY IN BIOLOGICAL SYSTEMS......Page 180
7.5 CHALLENGES AND PERSPECTIVES......Page 192
REFERENCES......Page 195
8.1 INTRODUCTION......Page 198
8.2 GENETIC MATRICES AND THE DEGENERACY OF THE GENETIC CODE......Page 199
8.3 THE GENETIC CODE AND HADAMARD MATRICES......Page 212
8.4 GENETIC MATRICES AND MATRIX ALGEBRAS OF HYPERCOMPLEX NUMBERS......Page 219
8.5 SOME RULES OF EVOLUTION OF VARIANTS OF THE GENETIC CODE......Page 232
8.6 CHALLENGES AND PERSPECTIVES......Page 242
REFERENCES......Page 244
9.1 INTRODUCTION......Page 247
9.2 EMERGING PATTERN, DISSIPATIVE STRUCTURE, AND EVOLVING COGNITION......Page 252
9.3 DENOTATIONAL MATHEMATICS AND COGNITIVE COMPUTING......Page 256
9.4 CHALLENGES AND PERSPECTIVES......Page 260
REFERENCES......Page 264
10.1 INTRODUCTION......Page 267
10.2 EVOLUTIONARY TRENDS OF INFORMATION SCIENCES......Page 269
10.3 CENTRAL DOGMA OF INFORMATICS......Page 271
10.4 CHALLENGES AND PERSPECTIVES......Page 276
REFERENCES......Page 277
APPENDIX A: Bioinformatics Notation and Databases......Page 280
APPENDIX B: Bioinformatics and Genetics Time Line......Page 286
APPENDIX C: Bioinformatics Glossary......Page 288
INDEX......Page 315