Power-law distribution in a learning process: Competition, learning and natural selection

Physica A: Statistical Mechanics and its Applications

Volumn 345, Issue 1-2, 2005, Pages 267-274

  Gupta, Hari M ^a   Campanha, José R ^a  

^a SÃO PAULO STATE UNIVERSITY UNESP   (Brazil)

Author keywords

Learning; Natural selection; Power law

Indexed keywords

COMPETITION; ECONOMIC AND SOCIAL EFFECTS; LARGE SCALE SYSTEMS; NATURAL SCIENCES; SELECTION; STATISTICAL METHODS;

HOLISTIC PROPERTIES; LEARNING; NATURAL SELECTION; POWER-LAW;

LEARNING SYSTEMS;

EID: 8344257289     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4371(04)00986-0     Document Type: Review

References (41)

1. P. Bak, How Nature Works, Oxford University Press, Oxford, 1997.
2. B.B. Mandelbrot, The Fractal Geometry of Nature, Freeman, New York, 1982.
3. B.B. Mandelbrot, Science 156 (1967) 637.
4. D.L. Ruderman, Network: Comput. Neural Systems 5 (1994) 517.
5. L. Poon, C. Grebogi, Phys. Rev. Lett. 75 (1995) 4023.
6. R. Badii, A. Politi, Complexity - Hierarchical Structures and Scaling in Physics, Cambridge, UK, 1997.
7. P. Lévy, Théorie de lAddition des Variables Aléatories, Gauthier-Villars, Paris, 1937.
8. V. Pareto, Cours d'Économie Politique. Reprinted as a volume of Oeuvres Complétes, Droz, Geneva, 1896-1965.
9. C.K. Peng, et al., Phys. Rev. Lett. 70 (1993) 1343.
10. G.F. Zebende, P.M.C. de Oliveira, T.J. Penna, Phys. Rev. E 57 (1998) 3311.
11. J.B. Bassingthwaighte, L.S. Liebovitch, B.J. West, Fractal Physiology, Oxford University Press, New York, 1994.
12. U. Frish, M.F. Shlesinger, G. Zaslavasky, Lévy Flights and Related Phenomena in Physics, Springer, Berlin, 1994.
13. T.H. Solomon, E.R. Weeks, H.L. Swinney, Phys. Rev. Lett. 71 (1993) 3975.
14. M. Nelkin, Adv. Phys. 43 (1994) 143.
15. A. Ott, J.P. Bouchard, D. Langevin, W. Urbach, Phys. Rev. Lett. 65 (1990) 2201.
16. Z. Olami, H.J.S. Feder, K. Christensen, Phys. Rev. Lett. 68 (1992) 1244.
17. B. Chabaud, et al., Phys. Rev. Lett. 73 (1994) 3227.
18. E. Weeks, J. Urbach, H.L. Swinney, Physica D 97 (1996) 291.
19. T.H. Solomon, E.R. Weeks, H.L. Swinney, Physica D 76 (1994) 70.
20. H.E. Hurst, Trans. Am. Soc. Civil Eng. 116 (1951) 770.
21. Proceedings of First International Conference on High Frequency Data in Finance, Olsen & Associates, Zurich, 1995.
22. R.N. Mantegna, H.E. Stanley, Nature 376 (1995) 46.
23. G. Ghashghaie, et al., Nature 381 (1996) 767; A. Arneodo, et al., preprint cond-mat/9607120.
24. G. Ghashghaie, et al., Nature 381 (1996) 767; A. Arneodo, et al., preprint cond-mat/9607120.
25. E.F. Fama, Manage. Sci. 11 (1965) 404.
26. A.L. Tucker, J. Bus. Econ. Statist. 10 (1992) 73.
27. J.P. Bouchaud, M. Potters Theorie des risques financieres, Alea Saclay, 1997.
28. A. Arneodo, J.F. Muzy, D. Sornette, Eur. Phys. J. B 2 (1998) 227.
29. T. Lux, M. Marches, Nature 397 (1999) 498.
30. H.M. Gupta, J.R. Campanha, F.R. Chavarette, Int. J. Mod. Phys. C 14 (2003) 449.
31. A. Einstein, L. Infeld, The Evolution of Physics: From Early Concepts to Relativity and Quanta, Simon & Schuster, USA, 1976.
32. L.A.N. Amaral, et al., Phys. Rev. Lett. 80 (1998) 1385.
33. L.D. Hulst, G.J. Rodgers, Eur. Phys. J. B 21 (2001) 447.
34. C. Tsallis, J. Stat. Phys. 52 (1988) 479.
35. C. Tsallis, Braz. J. Phys. 29 (1999) 1.
36. P. Bak, C. Tang, K. Wiesenfeld, Phys. Rev. Lett. 59 (1987) 381.
37. K.G. Zipf, Human Behavior and the Principle of Least Effort, Addison-Wesley, Cambridge, MA, 1949.
38. R.R. Bush, in: D. Luce (Ed.), Developments in Mathematical Psychology, The Free Press of Glencoe, IL, 1960, pp. 123-165.
39. C. Tsallis, M.P. Albuquerque, Eur. Phys. J. B 13 (2000) 777.
40. H.M. Gupta, J.R. Campanha, Physica A 268 (1999) 231.
41. H.M. Gupta, J.R. Campanha, Physica A 275 (2000) 531.