Preface |
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vii | |
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Chapter 1 Universal Characteristics of Fractal Fluctuations: General Systems Theory |
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1 | (36) |
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1 | (3) |
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1.2 Statistical Methods for Data Analysis |
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4 | (6) |
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1.2.1 Statistical normal distribution |
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4 | (2) |
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1.2.2 Fractal fluctuations and statistical analysis |
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6 | (1) |
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1.2.2.1 Power-laws and fat tails |
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7 | (1) |
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1.2.2.2 Scale-free theory for power-laws with fat, long tails |
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8 | (2) |
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1.3 General Systems Theory for Fractal Fluctuations |
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10 | (10) |
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1.3.1 Dynamic memory (information) circulation network |
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12 | (1) |
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1.3.2 Quasicrystalline structure of the eddy continuum |
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13 | (3) |
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16 | (1) |
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1.3.3.1 Quasiperiodic Penrose tiling pattern |
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16 | (1) |
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17 | (1) |
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17 | (1) |
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1.3.3.4 Berry's phase in quantum systems |
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18 | (1) |
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1.3.3.5 Logarithmic spiral pattern underlying fractal fluctuation |
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18 | (2) |
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1.4 Universal Feigenbaum's Constants and Probability Density Distribution Function for Fractal Fluctuations |
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20 | (17) |
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1.4.1 Same inverse power-law for probability distribution and power spectra of fractal fluctuations |
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24 | (1) |
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1.4.2 Inverse power-law for fractal fluctuations close to Gaussian distribution |
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25 | (2) |
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1.4.3 Fat long tail for probability distribution of fractal fluctuations |
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27 | (1) |
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1.4.4 Power spectra of fractal fluctuations |
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28 | (3) |
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31 | (1) |
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31 | (6) |
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Chapter 2 Nonlinear Dynamics, Chaos and Self-organized Criticality |
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37 | (22) |
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37 | (5) |
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2.2 The DNA Molecule and Heredity |
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42 | (1) |
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43 | (2) |
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2.4 Long-Range Correlations in DNA Base Sequence |
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45 | (3) |
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2.5 Emergence of Order and Coherence in Biology |
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48 | (1) |
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2.6 Multidisciplinary Approach for Modelling Biological Complexity |
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48 | (1) |
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2.7 Fractal Fluctuations and Statistical Normal Distribution |
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49 | (10) |
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50 | (1) |
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50 | (9) |
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Chapter 3 Long-Range Correlations Data 1: Universal Spectrum for DNA Base C+G Frequency Distribution in Human Chromosomes 1--24 |
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59 | (24) |
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59 | (2) |
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3.2 General Systems Theory Concepts |
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61 | (6) |
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3.2.1 Quantum-like chaos in turbulent fluid flows |
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61 | (1) |
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3.2.2 Dynamic memory (information) circulation network |
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61 | (1) |
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3.2.3 Quasicrystalline structure |
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62 | (1) |
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3.2.4 Dominant periodicities |
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63 | (1) |
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3.2.4.1 Emergence of order and coherence in biology |
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64 | (1) |
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3.2.5 Long-range spatiotemporal correlations (coherence) |
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65 | (1) |
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3.2.6 Universal spectrum of fluctuations |
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65 | (1) |
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3.2.7 Quantum mechanics for subatomic dynamics: Apparent paradoxes |
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66 | (1) |
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3.2.7.1 Wave-particle duality |
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66 | (1) |
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3.2.7.2 Non-local connection |
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66 | (1) |
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3.3 Applications of the General Systems Theory Concepts to Genomic DNA Base Sequence Structure |
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67 | (2) |
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69 | (5) |
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69 | (1) |
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3.4.2 Power spectral analyses: Variance and phase spectra |
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69 | (2) |
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3.4.3 Power spectral analyses: Dominant periodicities |
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71 | (1) |
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3.4.3.1 Peak wavelength versus bandwidth |
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72 | (2) |
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74 | (3) |
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77 | (6) |
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78 | (1) |
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78 | (5) |
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Chapter 4 Quantum-like Chaos in the Frequency Distributions of Bases A, C, G, T in Human Chromosome 1 DNA |
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83 | (12) |
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83 | (1) |
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84 | (2) |
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86 | (3) |
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4.4 Results and Conclusions |
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89 | (6) |
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90 | (1) |
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90 | (5) |
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Chapter 5 Universal Spectrum for DNA Base C+G Concentration Variability in Human Chromosome Y |
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95 | (28) |
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95 | (8) |
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5.1.1 General systems theory concepts |
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98 | (1) |
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5.1.2 Quantum-like chaos in turbulent fluid flows |
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98 | (1) |
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5.1.3 Dynamic memory (information) circulation network |
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98 | (1) |
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5.1.4 Quasi-crystalline structure |
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99 | (1) |
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5.1.5 Dominant periodicities |
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100 | (2) |
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5.1.5.1 Emergence of order and coherence in biology |
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102 | (1) |
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5.2 Long-Range Spatiotemporal Correlations (Coherence) |
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103 | (1) |
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5.3 Universal Spectrum of Fluctuations |
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104 | (1) |
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5.4 Quantum Mechanics for Subatomic Dynamics: Apparent Paradoxes |
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104 | (2) |
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5.4.1 Wave-particle duality |
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104 | (1) |
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5.4.2 Non-local connection |
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105 | (1) |
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5.5 Self-Organized Criticality and Quantum-Like Chaos in Computed Model Dynamical Systems |
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106 | (2) |
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5.5.1 Deterministic chaos |
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106 | (1) |
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5.5.2 Universal quantification for deterministic chaos in dynamical systems |
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107 | (1) |
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5.5.3 Universal algorithm for quasi-crystalline structure formation in real world and computed model dynamical systems |
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107 | (1) |
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5.6 Applications of the General Systems Theory Concepts to Genomic DNA Base Sequence Structure |
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108 | (2) |
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110 | (2) |
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110 | (1) |
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5.7.2 Power spectral analyses: Variance and phase spectra |
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111 | (1) |
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5.7.3 Power spectral analyses: Dominant periodicities |
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111 | (1) |
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112 | (3) |
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115 | (8) |
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116 | (1) |
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116 | (7) |
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Chapter 6 Quantum-like Chaos in the Frequency Distributions of the Bases A, C, G, T in Drosophila DNA |
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123 | (40) |
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123 | (8) |
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6.1.1 The DNA molecule and heredity |
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123 | (2) |
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6.1.2 Long-range correlations in DNA base sequence |
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125 | (3) |
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6.1.3 Nonlinear dynamics and chaos |
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128 | (3) |
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6.2 General Systems Theory for Universal Quantification of Fractal Fluctuations of Dynamical Systems |
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131 | (4) |
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135 | (13) |
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6.3.1 Fractal nature of frequency distribution of Drosophila DNA base (A, C, G or T) sequence |
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136 | (1) |
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6.3.2 The frequency distributions of DNA bases A, C, G, T and the statistical normal distribution |
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137 | (2) |
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6.3.3 Continuous periodogram power spectral analyses |
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139 | (1) |
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6.3.4 Power spectral analyses: Summary of results |
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140 | (1) |
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6.3.4.1 Average variance and phase spectra |
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140 | (1) |
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6.3.4.2 Dominant wavebands |
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140 | (2) |
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6.3.4.3 Peak wavelength versus bandwidth |
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142 | (6) |
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6.4 Results and Discussion |
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148 | (3) |
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151 | (12) |
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154 | (1) |
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154 | (9) |
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Chapter 7 Long-Range Correlations Data Set V: Universal Spectrum for DNA Base CG Frequency Distribution in Takifugu Rubripes (Puffer fish) Genome |
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163 | (38) |
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163 | (2) |
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7.1.1 Fractal fluctuations and statistical normal distribution |
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164 | (1) |
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7.2 Multidisciplinary Approach for Modelling Biological Complexity |
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165 | (10) |
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7.2.1 General systems theory for fractal fluctuations in dynamical systems |
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166 | (3) |
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7.2.2 Fractals represent hierarchical communication networks |
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169 | (1) |
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7.2.3 Model predictions (relevance of model predictions to biological networks) |
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170 | (1) |
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7.2.3.1 Quasicrystalline pattern for the network architecture |
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170 | (1) |
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7.2.3.2 Long-range spatiotemporal correlations (coherence) |
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171 | (1) |
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7.2.3.3 Emergence of order and coherence in biology |
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172 | (1) |
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7.2.3.4 Dominant length scales in the quasicrystalline spatial pattern |
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172 | (1) |
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7.2.3.5 DNA sequence and functions |
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173 | (2) |
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175 | (1) |
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175 | (1) |
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7.3.2 Power spectral analyses: Variance and phase spectra |
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175 | (1) |
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7.4 Results and Discussion |
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176 | (9) |
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7.4.1 Data sets and power spectral analyses |
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176 | (3) |
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7.4.2 Model predicted dominant wavebands |
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179 | (3) |
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7.4.3 Peak wavelength versus bandwidth |
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182 | (1) |
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7.4.4 Quasiperiodic Penrose tiling and packing efficiency |
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183 | (2) |
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7.5 Current Status of Basic Concepts in Quantum Mechanics |
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185 | (9) |
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7.5.1 Fractals and quantum theory |
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186 | (2) |
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7.5.2 Quantum mechanics and string theory |
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188 | (1) |
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7.5.3 Fluid mechanics and quantum mechanics |
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189 | (1) |
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7.5.4 General systems theory for fractal space-time fluctuations and quantum-like chaos in atmospheric flows |
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189 | (2) |
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7.5.5 Model predictions and the interpretation of quantum mechanical laws |
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191 | (1) |
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7.5.5.1 Probability and amplitude square: Probability of weather sy stem |
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191 | (1) |
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7.5.5.2 Non-local connection in weather systems |
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192 | (2) |
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7.5.5.3 Non-local connection in quantum systems |
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194 | (1) |
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194 | (7) |
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195 | (1) |
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195 | (6) |
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Chapter 8 Long-Range Correlations in Human Chromosome X DNA Base CG Frequency Distribution: Data Set VI |
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201 | (10) |
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201 | (4) |
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203 | (2) |
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205 | (3) |
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8.3 Results and Conclusions |
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208 | (3) |
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209 | (1) |
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209 | (2) |
Appendix |
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211 | (2) |
Index |
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213 | |