## Physiology, Promiscuity, and Prophecy at the Millennium: A Tale of TailsThis book concerns the development of a theory of complex phenomena, using such concepts as fractals, chaos, and fractional derivatives; but, most important, the idea of an allometric control process is developed. In summary the theory attempts to explain why the distribution in the intensity of wars is the same as the relative frequency of the number of words used in languages and the number of species evolved over time from one or a few remote ancestors. The theory also describes the similarity in the variability of the number of births to teens in Texas to the number of sexual partners in homosexual liaisons. The data in both of the aforementioned categories are shown to have long-term memory, and it is this memory that also gives rise to inverse power laws in such physiological phenomena as the interbeat interval distribution of the human heart, the interstride interval distribution in the human gait, and memory in DNA sequences. |

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### Contents

A Tale of Uncertain Knowledge | 3 |

Lecture | 4 |

Lecture | 5 |

Lecture | 6 |

Lecture | 7 |

Lecture | 8 |

Lecture | 9 |

Systems Perspective of Complexity | 11 |

Scaling in Aggregated Data Sets | 193 |

Linear Regression | 206 |

Auto regressive Integrated Moving Average ARIMA214 | 214 |

Fractional Differences and Inverse Power Laws | 224 |

Haphazard Human Heart | 237 |

Willynilly Walking | 247 |

Gamboling Genes | 256 |

Scaling Sexual Schemes | 265 |

Fractal Random Processes | 19 |

Modeling Random Time Series | 29 |

On Chance and Necessity | 37 |

Averages and Expected Values | 48 |

Variances and Correlations | 59 |

Power Laws Dimensional Analysis and Scaling | 69 |

Bernoulli and Memory | 77 |

Simple Random Walks and Diffusion | 89 |

Scaling Geometry and Memory | 102 |

Inverse PowerLaw Distributions | 110 |

Fractal Random Walks | 120 |

Levy Distributions and Scaling | 131 |

Inverse PowerLaw Correlations | 141 |

Ensembles Signals and Noise | 151 |

Spectra and Noise | 161 |

Generalized Weierstrass Function | 170 |

How certain can you be? | 178 |

The Nonlinear Perspective | 277 |

Dynamics and Geometry | 290 |

Mapping and Chaos | 301 |

Memory and Intermittency | 315 |

Intermittency and Levy Statistics | 324 |

Strange Dynamics | 331 |

ART and Teen Births | 340 |

Brown versus Weierstrass | 353 |

Fractional Operations | 367 |

Fractional Calculus Model of Creep | 379 |

Fractional Relaxation | 384 |

Fractional Langevin Equation | 393 |

Fractional Diffusion Equation | 400 |

The End of Our Tale | 407 |

414 | |

429 | |

### Common terms and phrases

aggregation allometric allometric control ARIMA asymptotic attractor average behavior Brownian motion chaos chaotic complex phenomena correlation function curve data points data set defined denote depicted in Figure described determine deterministic differential equations diffusion diffusion equation discussion dynamical equations dynamical systems ensemble erratic evolution example exponent finite fixed point fluctuations Fourier transform fractal dimension fractal random fractional derivative fractional difference fractional integral frequency Gaussian given independent indicated initial interbeat interval inverse power inverse power-law large number Lecture Levy distribution linear logarithm Lyapunov exponent mathematical mean measure memory normal distribution number of births number of steps observed obtain orbit parameter phase space phenomenon physical predicted probability density quantity random process random shocks random walk random walk process regression relation relative dispersion sample sciences self-similar social solution spectrum statistical statistically independent stochastic process structure teen-birth data trajectories variable variance Weierstrass function Wiener process yields zero

### References to this book

Where Medicine Went Wrong: Rediscovering the Path to Complexity Bruce J. West No preview available - 2006 |