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

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World Scientific, Jan 1, 1999 - Philosophy - 443 pages
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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.
 

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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
REFERENCES
414
INDEX
429
Copyright

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About the author (1999)

Bruce J. West is Chief Mathematical Scientist with the Information Science Directorate at the Army Research Office, a position he has held for the last 10 years. After receiving his Ph.D. in Physics from the University of Rochester in 1970, he was Associate Director of a small private research institute (La Jolla Institute) for almost twenty years and a Professor at the University of North Texas for a decade. His research interests are in the nonlinear dynamics of complex networks. He has over 350 scientific publications, including 11 books and 8500 citations, and he has received multiple academic and government awards for his research and publications.

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