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

by West, Bruce J.

• ISBN13: 9789810238360
• ISBN10: 9810238363
• Format: Paperback
• Copyright: 1999-07-01
• Publisher: WORLD SCIENTIFIC PUB CO INC

Summary

This book concerns the development of a theory of complex phenomena, using such concepts as fractals, chaos, & 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 & 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, & 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, & memory in DNA sequences.

Table of Contents

A Tale of Uncertain Knowledge	3	(11)
Systems Perspective of Complexity	11	(9)
Fractal Random Processes	20	(9)
Modeling Random Time Series	29	(8)
On Chance and Necessity	37	(11)
Averages and Expected Values	48	(11)
Variances and Correlations	59	(10)
Power Laws, Dimensional Analysis and Scaling	69	(8)
Bernoulli and Memory	77	(12)
Simple Random Walks and Diffusion	89	(13)
Scaling, Geometry and Memory	102	(8)
Inverse Power-Law Distributions	110	(10)
Fractal Random Walks	120	(11)
Levy Distributions and Scaling	131	(10)
Inverse Power-Law Correlations	141	(10)
Ensembles, Signals and Noise	151	(10)
Spectra and Noise	161	(9)
Generalized Weierstrass Function	170	(8)
How certain can you be?	178	(15)
Scaling in Aggregated Data Sets	193	(13)
Linear Regression	206	(8)
Auto regressive Integrated Moving Average (ARIMA)	214	(10)
Fractional Differences and Inverse Power Laws	224	(13)
Haphazard Human Heart	237	(10)
Willy-nilly Walking	247	(9)
Gamboling Genes	256	(9)
Scaling Sexual Schemes	265	(12)
The Nonlinear Perspective	277	(13)
Dynamics and Geometry	290	(11)
Mapping and Chaos	301	(14)
Memory and Intermittency	315	(9)
Intermittency and Levy Statistics	324	(7)
Strange Dynamics	331	(9)
ART and Teen Births	340	(13)
Brown versus Weierstrass	353	(14)
Fractional Operations	367	(12)
Fractional Calculus Model of Creep	379	(5)
Fractional Relaxation	384	(9)
Fractional Langevin Equation	393	(7)
Fractional Diffusion Equation	400	(7)
The End of Our Tale	407	(7)
References	414	(15)
Index	429