Spatio-temporal complexity in the clusters generated by fractional Brownian paths

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 5471, Issue , 2004, Pages 1-12

  Carbone, Anna ^a   Stanley, H Eugene ^b  

^a POLITECNICO DI TORINO   (Italy)

^b Boston University   (United States)

Author keywords

Complex systems; Fractional Brownian path; Self organized criticality; Systems obeying scaling laws

Indexed keywords

FRACTIONAL BROWNIAN PATHS; POWER LAWS; SELF-ORGANIZED CRITICALITY; SYSTEMS OBEYING SCALING LAWS;

BROWNIAN MOVEMENT; CORRELATION METHODS; FOURIER TRANSFORMS; FRACTALS; FREQUENCY DOMAIN ANALYSIS; FUNCTIONS; KALMAN FILTERING; MATHEMATICAL MODELS; PROBABILITY DISTRIBUTIONS; STOCHASTIC PROGRAMMING;

LARGE SCALE SYSTEMS;

EID: 4344703890     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.548618     Document Type: Conference Paper

References (74)

1. J. Feder, Fractals (Plenum, New York, 1988), p. 172.
2. H.E.Hurst, R.P. Black and Y.M.Simaika Long-term storage: An experimental study (Constable, London, 1965).
3. M.S. Taqqu, V. Teverovsky, and W. Willinger, "Estimators for long-range dependence: an empirical study", Fractals, 3, pp. 785 (1995)
4. S.V. Buldyrev, A.L. Goldberger, S. Havlin, R.N. Mantegna, M.E. Matsa, C.-K. Peng, M. Simons, and H.E. Stanley, "Long-range correlation properties of coding and noncoding DNA sequences: GenBank analysis", Phys. Rev. E, 51, Issue 5, pp. 5084-509 (1993)
5. C.-K. Peng, S.V. Buldyrev, A.L. Goldberger, S. Havlin, M. Simons, and H.E. Stanley, "Finite-size effects on long-range correlations: Implications for analyzing DNA sequences", Phys. Rev. E, 47, pp. 3730-3733 (1993)
6. C.K. Peng, S. V. Buldyrev, S. Havlin, M. Simons, H. E. Stanley, and A. L. Goldberger, "Mosaic organization of DNA nucleotides" Phys. Rev. E 49, 1685 (1994).
7. P. Gopikrishnan., V. Plerou, L. A. N. Amaral, M. Mayer and H. E. Stanley, "Scaling of the distribution of fluctuations of financial market indices", Phys. Rev. E 60, Issue 5, pp. 5305-5316 (1999)
8. H. E. Stanley, V. Afanasyev, L.A.N. Amaral, S.V. Buldyrev, A.L. Goldberger, S.Havlin, H. Leschhorn, P. Maass, R.N. Mantegna, C.-K. Peng, P.A. Prince, M.A. Salinger, M.H.R. Stanley, G.M. Viswanathan, "Anomalous fluctuations in the dynamics of complex systems: from DNA and physiology to econophysics", Physica A, 224, pp. 302-321 (1996)
9. E. Alessio, A. Carbone, G. Castelli, and V. Frappietro "Second-order moving average and scaling of stochastic time series", Eur. Phys. Jour. B 27, 197 (2002).
10. A. Carbone and G. Castelli, "Scaling properties of long-range correlated noisy signals: application to financial markets",in Noise in Complex Systems and Stochastic Dynamics, edited by L. Schimansky-Geier, D. Abbott, A. Neiman, and C. Van den Broeck, Proc. of SPIE 5114 (2003) 406.
11. A. Carbone, G. Castelli, and H. E. Stanley, "Analysis of clusters formed by the moving average of a long-range correlated time series", Phys. Rev. E 69 (2004) 026105.
12. Y. Ashkenazy, M. Lewkowicz, J. Levitan, S. Havlin, K. Saermark, H. Moelgaard, P.E.B. Thomsen, "Discrimination between healthy and sick cardiac autonomic nervous system by detrended heart rate variability analysis", Fractals 7, 85 (1999)
13. G. Rangarajan and M. Ding, "Integrated approach to the assessment of long range correlation in time series data", Phys. Rev. E 61 004991 (2000).
14. N. Vandewalle and M. Ausloos, "Crossing of two mobile averages: A method for measuring the roughness exponent", Phys. Rev. E, 58, Issue 5 pp. 6832-6834, (1998)
15. Kun Hu, Plamen Ch. Ivanov, Zhi Chen, Pedro Carpena, and H. Eugene Stanley, "Effect of trends on detrended fluctuation analysis", Phys. Rev. E 64, 011114, (2001)
16. Z. Chen, P. Ch. Ivanov, K. Hu, and H. E. Stanley, "Effect of Nonstationarities on Detrended Fluctuation Analysis," Phys. Rev. E 65 (2002) 041107.
17. C. Heneghan and G. McDarby, "Coherence and stochastic resonance in a two-state system", Phys. Rev. E, 62, Issue 5, pp. 6103-6110 (2000)
18. J.S.Leu and A.Papamarcou, "On estimating the spectral exponent of fractional Brownian motion", IEEE Trans.Inf.Theory 41, 233 (1995)
19. S.Thurner, M.C.Feurstein, and M.C.Teich "Multiresolution Wavelet Analysis of Heartbeat Intervals Discriminates Healthy Patients from Those with Cardiac Pathology" Phys. Rev. Lett. 80 (1998) 1544.
20. S.B.Lowen and M.C.Teich,"Fractal renewal processes generate 1/f noise", Phys. Rev.E 47 (1993) 992
21. M.C.Teich, C.Heneghan, S.B. Lowen, and R.G. Turcott"Wavelets in Medicine and in Biology", edited by A.Aldroubi and M.Unser (CRC Press, Boca Raton, FL, (1996))
22. Michel M. Dacorogna, Ramazan Genay, Ulrich Mller, Richard B. Olsen, Olivier V. Pictet, "An Introduction to High-Frequency Finance", Academic Press, (2001)
23. R.N. Mantegna and H.E. Stanley, "An Introduction to Econophysics: Correlations and Complexity in Finance", Cambridge University Press, 2000
24. R. F. Engle, "Autoregressive Conditional Heteroskedaticity with Estimates of the Variance of United Kingdom Inflation", Econometrica 50 (1982) 987.
25. T. Bollerslev, T. "Generalized Autoregressive Conditional Heteroskedasticity", J. Econometrics 31 (1986) 307.
26. R. F. Engle, "New Frontiers for ARCH Models", J. Appl. Econometrics 17 (2002) 425.
27. R. T. Baillie, T. Bollerslev, and H. O. Mikkelsen, "Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity", J. Econometrics 74 (1996) 3.
28. R. N. Mantegna and H. E. Stanley, "Scaling Behaviour in the Dynamics of an Economic Index", Nature 376 (1996) 46.
29. X. Gabaix, P. Gopikrishnan, V. Plerou, and H. E. Stanley, "A Theory of Power-Law Distributions in Financial Market Fluctuations",Nature 423 (2003) 267.
30. B. B. Mandelbrot, A. Fisher, and L. Calvet, "A Multifractal Model of Asset Returns," [mimeo] Cowles Foundation for Research in Economics (1997).
31. L. Calvet and A. Fisher, "Multifractality in Asset Returns: Theory and Evidence," Rev. Econ. Stat. 84 (2002) 381-406.
32. T. Lux, "Turbulence in Financial Markets: The Surprising Explanatory Power of Simple Cascade Models," Quantitative Finance 1 (2001) 632-640.
33. E. F. Fama and K. R. French, "Permanent and Temporary Components of Stock Prices", J. Political Economy 96 (1988) 246.
34. J. Y. Campbell, "A Variance Decomposition of the Stock Returns", Econ. J. 101 (1991) 157.
35. J. Y. Campbell, "Why Long Horizons? A Study of Power against Persistent Alternatives", J. Empirical Finance 8 (2001) 459.
36. R. Priestly, "Time-Varying Persistence in Expected Returns", J. Banking and Finance, 101 (2001) 157.
37. U. Frisch and G. Parisi, G. in Turbulence and Predictability in Geophysical Fluid Dynamics, edited by M.Ghil (Kluwer North-Holland, Amsterdam, 1985), pp. 84-88.
38. A. Carbone. G. Castelli, and H. E. Stanley, "Time-Dependent Hurst Exponent in Financial Time Series", Physica A, in press, (2004).
39. A. Arneodo, E. Bacry, and J. F. Muzy, "The Thermodynanics of Fractals Revisited with Wavelets," Physica A 213 (1993) 232-275.
40. G. C. Papanicolaou and K. E. Sølna, "Wavelet Based Estimation of Local Kolmogorov Turbulence," in Theory and Applications of Long-Range Dependence, edited by P. Doukham, G. Oppenheim and M. S. Taqqu (Birkhauser, Berlin, 2003), p. 473.
41. S. W. Smith, "Digital Filters," in Digital Signal Processing: A Practical Guide for Engineers and Scientists (Elsevier Science, Burlington MA, 2003), pp. 261-343.
42. R. H. Voss, "Random Fractal Forgeries," in NATO ASI series, Vol. F17 Fundamental Algorithm for Computer Graphics, edited by R. A. Earnshaw (Springer-Verlag, Berlin/Heidelberg, 1985).
43. O. Biham, Z.-F. Huang, O. Malcai, S. Solomon, "Long-time fluctuations in a dynamical model of stock market indices", Phys. Rev. E, 64, 026101, (2001).
44. J. D. Hamilton, "State-Space Models", in Handbook of Econometrics, Vol. IV, edited by R. F. Engle and D. L. McFadden (Elsevier, Amsterdam, 1995), p. 3039.
45. K. Ivanova, M. Ausloos, "Low order variability diagrams for short range correlation evidence in financial data: BGL-USD exchange rate, Dow-Jones Industrial Average, Gold ounce price", Physica A, 265, pp. 279-291 (1999)
46. P. Grau-Carles, "Long-range power-law correlations in stock returns", Physica A, 299, 521, (2001).
47. P. Bak, C. Tang, and K. Wiesenfeld, "Self-organized criticality: An explanation of the 1/f noise", Phys. Rev. Lett. 59 (1987) 381.
48. P. Bak, C. Tang, and K. Wiesenfeld, "Self-organized criticality", Phys. Rev. A 38 (1988) 364.
49. C. Tang, K. Wiesenfeld, P. Bak, S. Coppersmith, and P. Littlewood, "Phase organization", Phys. Rev. Lett. 58, 1161-1164 (1987)
50. H. J. Jensen, Self-Organized Criticality: Emergent Complex Behavior in Physical and Biological Systems (Cambridge Univ. Press. Cambridge, 2000).
51. L. P. Kadanoff, S. R. Nagel, L. Wu, and S. Zhou, "Scaling and universality in avalanches", Phys. Rev. A 39 (1989) 6524.
52. Y. C. Zhang, "Scaling theory of self-organized criticality", Phys. Rev. Lett. 63 (1989) 470.
53. D. Dhar and R. Ramaswamy, "Exactly solved model of self-organized critical phenomena". Phys. Rev. Lett. 63 (1989) 1659.
54. D. Dhar, "Self-Organized Critical State of Sandpile Automation Models", Phys. Rev. Lett. 64 (1990) 1613.
55. K. Sneppen," Self-organized pinning and interface growth in a random medium", Phys. Rev. Lett. 69 (1992) 3539.
56. P. Bak and K. Sneppen, "Punctuated equilibrium and criticality in a simple model of evolution", Phys. Rev. Lett. 71 (1993) 4083.
57. K. Christensen, Z. Olami, and P. Bak, "Deterministic 1/f noise in nonconserative models of self-organized criticality", Phys. Rev. Lett. 68 (1992) 2417.
58. D.L.Turcotte, "Self-organized criticality", Rep. Prog. Phys. 62 (1999) 1377.
59. S. Maslov, M. Paczuski, and P. Bak, "Avalanches and 1/f Noise in Evolution and Growth Models", Phys. Rev. Lett. 73 (1994) 2162.
60. M. Paczuski, S. Maslov, and P. Bak, "Avalanche dynamics in evolution, growth, and depinning models", Phys. Rev. E 53 (1996) 414.
61. S. S. Manna,"Two state model of self-organized criticality", J. Phys. A: Math. Gen. 24 (1991) L363.
62. B. Tadic, and D. Dhar,"Emergent Spatial Structures in Critical Sandpiles", Phys. Rev. Lett. 79 (1997) 1519.
63. M. Paczuski and K. E. Bassler, " Theoretical results for sandpile models of self-organized criticality with multiple topplings", Phys. Rev. E 62 (2000) 5347.
64. R. Pastor-Satorras and A. Vespignani, "Critical behavior and conservation in directed sandpiles", Phys. Rev. E 62 (2000) 6195.
65. D. Dhar,"Some results and a conjecture for Manna's stochastic sandpile model", Physica A 270 (1999) 69.
66. A. Chessa, H. E. Stanley, A. Vespignani, and S. Zapperi, "Universality in sandpiles" Phys. Rev. E 59 (1999) R12.
67. A. Vespignani, R. Dickman, M. A. Munoz, and S. Zapperi, "Absorbing-state phase transitions in fixedenergy sandpiles", Phys. Rev. E 62 (2000) 4564.
68. R. Dogaru Universality and Emergent Computation in Cellular Neural Networks (World Scientific Series in Nonlinear science, Singapore, 2003).
69. J.P. Boon Ed. Lattice gas automata: Theory, simulation, implementation J. Stat. Phys. 68 (1992).
70. J. R. Weimar and J.-P. Boon, "Class of cellular automata for reaction-diffusion systems", Phys. Rev. E 49, 1749 (1994).
71. E. Domany and W. Kinzel, "Directed Percolation in Two Dimensions: Numerical Analysis and an Exact Solution", Phys. Rev. Lett. 47 (1981) 5.
72. E. Domany and W. Kinzel, "Equivalence of Cellular Automata to Ising Models and Directed Percolation", Phys. Rev. Lett. 53 (1984) 311.
73. F.Y. Wu and H.E.Stanley, "Domany-Kinzel Model of Directed Percolation: Formulation as a RandomWalk Problem and Some Exact Results", Phys. Rev. Lett. 48 (1982) 775.
74. A. Carbone and H. E. Stanley, "Directed Self-Organized Critical Patterns Emerging from Fractional Brownian Paths", Physica A, (2004), in press