Physiology, Promiscuity and Prophecy at the Millennium:A Tale of Tails

    This 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.

Lecture 1：A Tale of Uncertain Knowledge
Lecture 2：Systems Perspective of Complexity
Lecture 3：Fractal Random Processes
Lecture 4：Modeling Random Time Series
Lecture 5：On Chance and Necessity
Lecture 6：Averages and Expected Values
Lecture 7：Variances and Correlations
Lecture 8：Power Laws, Dimensional Analysis and Scaling
Lecture 9：Bernoulli and Memory
Lecture 10：Simple Random Walks and Diffusion
Lecture 11：Scaling, Geometry and Memory
Lecture 12：Inverse Power-Law Distributions
Lecture 13：Fractal Random Walks
Lecture 14：Levy Distributions and Scaling
Lecture 15：Inverse Power-Law Correlations
Lecture 16：Ensembles, Signals and Noise
Lecture 17：Spectra and Noise
Lecture 18：Generalized Weierstrass Function
Lecture 19：How Certain Can You Be?
Lecture 20：Scaling in Aggregated Data Sets
Lecture 21：Linear Regression
Lecture 22：Auto Regressive Integrated Moving Average (ARIMA)
Lecture 23：Fractional Differences and Inverse Power Laws
Lecture 24：Haphazard Human Heart
Lecture 25：Willy-Nilly Walking
Lecture 26：Gamboling Genes
Lecture 27：Scaling Sexual Schemes
Lecture 28：The Nonlinear Perspective
Lecture 29：Dynamics and Geometry
Lecture 30：Mapping and Chaos
Lecture 31：Memory and Intermittency
Lecture 32：Intermittency and L関y Statistics
Lecture 33：Strange Dynamics
Lecture 34：ART and Teen Births
Lecture 35：Brown versus Weierstrass
Lecture 36：Fractional Operations
Lecture 37：Fractional Calculus Model of Creep
Lecture 38：Fractional Relaxation
Lecture 39：Fractional Langevin Equation
Lecture 40：Fractional Diffusion Equation
Lecture 41：The End of Our Tale
REFERENCES
INDEX