Thoughts on modeling complexity

Complexity

Volumn 11, Issue 3, 2006, Pages 33-43

  West, Bruce J ^a  

^a U S ARMY RESEARCH OFFICE   (United States)

Author keywords

Allometric control; Fractional Langevin equation; Fractional random walks; Multifractal

Indexed keywords

EID: 33645331291     PISSN: 10762787     EISSN: 10990526     Source Type: Journal    
DOI: 10.1002/cplx.20114     Document Type: Article

References (30)

1. Lévy, P. Theorie de l'addition des variables aleatoires; Gauthier-Villars: Paris, 1937.
2. Montroll, E.W.; West, B.J. An enriched collection of stochastic processes. In: Fluctuation Phenomena, 2nd Ed.; Montroll, E.W., Lebowitz, J.L., Eds.; North-Holland: Amstersdam, 1987; pp 61-195;
3. Montroll E.W.; Shlesinger M.F. A wonderful world of random walks. In: Fluctuation Phenomena II; Montroll, E.W.; Lebowitz, J.L., Eds.; North-Holland: Amstersdam, 1984.
4. West, B.J.; Seshadri, V. Linear systems with Lévy fluctuations. Physica A 1982, 113, 203.
5. Hosking, J.T.M. Fractional differencing. Biometrika 1981, 68, 165-178.
6. West, B.J. Physiology, promiscuity and prophecy at the millennium: A tale of tails, In: Studies of Nonlinear Phenomena in the Life Sciences, Vol. 7; World Scientific: Singapore, 1999;
7. West, B.J.; Deering, W. Fractal physiology for physicists: Lévy statistics. Phys Rep 1994, 246, 1.
8. West, B.J.; Bickel, D.R. Fractional-difference stochastic model of evolutionary substitutions in DNA sequences. Phys Lett A 1999, 256, 188.
9. Perrin, J. Mouvement brownien et réalité moléculaire, Annales de chimie et de physique, VIII 18; 5-114;
10. translated by F. Soddy as Brownian Movement and Molecular Reality, Taylor and Francis: London, 1925.
11. Montroll, E.W.; Weiss, Random walks on lattices II. G. J Math Phys 1965, 6, 178.
12. Lindenberg, K.; West, B.J. The Nonequilibrium Statistical Mechanics of Open and Closed Systems; VCH, Berlin, 1990.
13. Pareto, V. Cours d'Economie Politique; Laussane, 1897.
14. Lotka, A.J. Elements of Mathematical Biology; Dover: New York, 1956; first published by Williams and Wilkins in 1924.
15. Zipf, G.K. Human Behavior and the Principle of Least Effort; Addison-Wesley: New York, 1949.
16. West, B.J., Bargava, V.; Goldberger, A.L. Beyond the principle of similtude: Renormalization in the bronchial tree. J Appl Physiol 60, 1089-1098, 1986.
17. Mandelbrot, B.B.; van Ness, J.W. Fractional Brownian motions, fractional noises and applications. SIAM Rev 1968, 10, 422.
18. West, B.J.; Bologna, M.; Grigolini, P. Physics of Fractal Operators; Springer: New York, (2003.
19. West, B.J.; Grigolini, P.; Metzler, R.; Nonnenmacher, T.F. Fractional diffusion and Levy stable processes. Phys Rev E 1997, 55, 99;
20. Allegrini P.; Grigolini P.; West, B.J. Dynamical approach to Lévy processes. Phys Rev E 1996, 54, 4760.
21. Samko, S.G.; Kilbas, A.A.; Marichev, O.I. Fractional Integrals and Derivatives; Gordon and Breach Science Publishers: Switzerland, 1993.
22. Zaslavsky, G.M. In: Lévy Flights and Related Topics in Physics; Shlesinger, M.F..; Zaslavsky, G.M.; Fisch, U., Eds.; Springer: Berlin, 1994.
23. Taylor, L.R. Aggregation, variance and mean. Nature 1961, 189, 732.
24. Huxley, J.S. Problems of Relative Growth; The Dial Press: New York, 1932.
25. Hausdorff, J.M.; Purdon, P.L.; Peng, C.K.; Ladin, Z.; Wei, J.Y.; Goldberger, A.L. Is walking a random walk? Evidence for long-range correlations in stride interval of human gait. J Appl Physiol 1995, 78, 349.
26. West, B.J.; Griffin, L. Allometric control of human gait. Fractals 1998, 6, 101.
27. West, B.J.; Griffin, L.A.; Frederick, H.J.; Moon, R.E. The independently fractal nature of respiration and heart rate during exercise under normobaric and hyperbaric conditions. Respir Physiol Neurobiol 2005, 145, 219-233.
28. West, B.J.; Latka, M.; Glaubic-Latka M.; Latka D. Multifractality of cerebral blood flow. Physica A 2003, 318, 453-460.
29. Peng, C.K.; Mietus, J.; Hausdorff, J.M.; Havlin, S.; Stanley, H.G.; Goldberger, A.L. Long-range anti-correlations and non-Gaussian behavior of the heartbeat, Phys Rev Lett 1993, 70, 1343.
30. Cannon, W.B. The Wisdom of the Body; Norton & Co.: New York, 1932.