Fractal fluctuations and complexity: Current debates and future challenges

Critical Reviews in Biomedical Engineering

Volumn 40, Issue 6, 2012, Pages 485-500

  Delignières, Didier ^a   Marmelat, Vivien ^a  

^a UNIVERSITY OF MONTPELLIER   (France)

Author keywords

1 f fluctuations; Adaptability; Complexity; Degeneracy; Interaction dominant dynamics; Scale invariance; Variability

Indexed keywords

1/F FLUCTUATION; ADAPTABILITY; COMPLEXITY; DEGENERACY; SCALE INVARIANCE; VARIABILITY;

BIOPHYSICS;

FRACTALS;

ADAPTATION; ARTICLE; AUTO REGRESSIVE FRACTIONALLY INTEGRATED MOVING AVERAGE MODEL; COMPLEXITY; CONCEPTUAL FRAMEWORK; CONSCIOUSNESS; CRITICAL THEORY; DEGENERACY; ENERGY TRANSFER; FRACTAL ANALYSIS; HAKEN KELSO BUNZ MODEL; HEALTH; HYPOTHESIS; IDIOSYNCRATIC MODEL; MATHEMATICAL ANALYSIS; MODEL; MONOFRACTAL MODEL; MOTOR COORDINATION; PHYSICAL MEDICINE; PRIORITY JOURNAL; PSYCHOLOGICAL ASPECT; REHABILITATION; TIME SERIES ANALYSIS;

ANIMALS; FORECASTING; FRACTALS; HUMANS; MODELS, BIOLOGICAL; SYSTEMS BIOLOGY;

EID: 84873847421     PISSN: 0278940X     EISSN: None     Source Type: Journal    
DOI: 10.1615/CritRevBiomedEng.2013006727     Document Type: Article

References (81)

1. Morin E. La Méthode. Paris: Seuil; 2008.
2. Morin E, Le Moigne JL. L'intelligence de la complexité. Paris: L'Harmattan; 1999.
3. Descartes R. Discours de la méthode. Leyde: Ian Maire; 1637.
4. Schmidt RA. A schema theory of discrete motor skill learning. Exerc. Sport Sci Rev. 1975;4:229- 61.
5. Bernstein N. Biodynamics of locomotion. In: Whiting HTA, editor. Human motor actions-Bernstein reassessed. Amsterdam: North-Holland; 1984. p. 171-221.
6. Kelso JAS. Phase transitions and critical behavior in human bimanual coordination. Am J Physiol Regul Integr Comp Physiol. 1984;15:R1000-R1004.
7. Kelso JAS. Dynamic patterns: the self-organization of brain and behavior. Cambridge: MIT Press; 1995.
8. Haken H. Advanced synergetics. Berlin: Springer Verlag; 1983.
9. Beek PJ, Peper CE, Stegeman DF. Dynamical models of movement coordination. Hum Mov Sci. 1995;14:573-608.
10. Atlan H. Entre le cristal et la fumée. Paris: Seuil; 1979.
11. Mandelbrot B., van Ness JW. Fractional Brownian motions, fractional noises and applications. SIAM Rev. 1968;10:422-37.
12. α noise in human cognition. Psychon Bull Rev. 2004;11:579-615.
13. Peng CK, Mietus J, Hausdorff JM, Havlin S, Stanley HE, Goldberger AL. Long-range anti-correlations and non-Gaussian behavior of the heartbeat. Phys Rev Lett. 1993;70:1343-6.
14. Delignières D, Torre K, Lemoine L. Methodological issues in the application of monofractal analyses in psychological and behavioral research. Nonlinear Dynamics Psychol Life Sci. 2005;9:435-62.
15. Delignières D, Ramdani S, Lemoine L, Torre K, Fortes M, Ninot, G. Fractal analysis for short time series: a reassessment of classical methods. J Math Psychol. 2006;50:525-44.
16. Delignières D, Marmelat V. Theoretical and methodological issues in serial correlation analysis. Adv Exp Med Biol. 2013;782:127-148.
17. Hurst HE. Long-term storage capacity of reservoirs. Trans Am Soc Civ Eng. 1951;116:770-99.
18. Matsuzaki M. Fractals in earthquakes. Philos Trans Phys Sci Eng. 1994;348:449-57.
19. Leland WE, Taqqu MS, Willinger W, Wilson DV. On the self-similar nature of ethernet traffic (extended version). IEEE ACM T Network. 1994;2:1- 15.
20. Delignières D, Fortes M, Ninot G. The fractal dynamics of self-esteem and physical self. Nonlinear Dynamics Psychol Life Sci. 2004;8:479-510.
21. Gilden DL. Fluctuations in the time required for elementary decisions. Psychol Sci. 1997;8:296-301.
22. Van Orden GC, Holden JC, Turvey MT. Self-organization of cognitive performance. J Exp Psychol Gen. 2003;132:331-350.
23. Gilden DL, Thornton T, Mallon MW. 1/f noise in human cognition. Science. 1995;267:1837-9.
24. Lemoine L, Torre K, Delignières, D. Testing for the presence of 1/f noise in continuation tapping data. Can J Exp Psychol. 2006;60:247-57.
25. Hausdorff JM, Peng C-K, Ladin Z, Wei JY, Goldberger AL. Is walking a random walk? Evidence for long-range correlations in stride interval of human gait. J Appl Physiol. 1995;78:349-358.
26. β fluctuations in bimanual coordination: an additional challenge for modeling. Exp Brain Res. 2007;183:225- 34.
27. Hausdorff JM, Mitchell SL, Firtion R, Peng CK, Cudkowicz ME, Wei JY, Goldberger AL. Altered fractal dynamics of gait: reduced stride-interval correlations with aging and Huntington's disease. J Appl Physiol. 1997;82:262-9.
28. Hausdorff JM. Gait dynamics in Parkinson's disease: common and distinct behavior among stride length, gait variability, and fractal-like scaling. Chaos. 2009;19:026113.
29. Goldberger AL, Amaral LAN, Hausdorff JM, Ivanov PCh, Peng CK, Stanley HE. Fractal dynamics in physiology: alterations with disease and aging. PNAS. 2002;99:2466-72.
30. Lipsitz LA, Goldberger MD. Loss of 'complexity' and aging. J Am Med Assoc. 1992;267:1806-9.
31. Vaillancourt DE, Newell KM. Changing complexity in human behavior and physiology through aging and disease. Neurobiol Aging. 2002;23:1-11.
32. Ward L. Dynamical cognitive science. Cambridge, MA: MIT Press; 2002.
33. Delignières D, Torre K, Lemoine L. Fractal models for event-based and dynamical timers. Acta Psychol. 2008;127:382-97.
34. α type) in human coordination. Phys Rev Lett. 1997;79:4501-4.
35. Kello CT, Beltz BC, Holden, JG, Van Orden GC. The emergent coordination of cognitive function. J Exp Psychol Gen. 2007;136:551-68.
36. Granger CWJ. Long memory relationships and aggregation of dynamic models. J Econ. 1980;14:227- 38.
37. Chong TT, Wong KT. Time series properties of aggregated AR(2) processes. Econ Lett. 2001;73:325- 32.
38. Pressing J. Sources of 1/f noise effects in human cognition and performance. Paideusis. 1999;2:42-59.
39. Hausdorf JM, Peng CK. Multiscaled randomness: a possible source of 1/f noise in biology. Phys Rev E. 1996;54:2154-7.
40. Diniz A, Barreiros J, Crato N. Parameterized estimation of long-range correlation and variance components in human serial interval production. Motor Control. 2010;14:26-43.
41. Kaulakys B. On the intrinsic origin of 1/f noise. Microelectron Reliab. 2000;40:1787-90.
42. Beltz BB, Kello CT. On the intrinsic fluctuations of human behavior. In: Vanchevsky M, editor. Focus on Cognitive Psychology Research. Hauppauge, NY: Nova Science Publishers; 2006. p. 25-41.
43. Bak P. How nature works. New York: Springer-Verlag; 1996.
44. Jensen HJ. Self-organized criticality. Cambridge, England: Cambridge University Press; 1998.
45. Wagenmakers EJ, Farrell S, Ratcliff R. Human cognition and a pile of sand: a discussion on serial correlations and self-organized criticality. J Exp Psychol Gen. 2005;134:108-16.
46. α fluctuation in cognitive performance. J Exp Psychol Gen. 2010;139:436-63.
47. Stephen DG, Anastas JR, Dixon JA. Scaling in executive control reflects multiplicative multifractal cascade dynamics. Front Fract Physiol. 2012;3:102.
48. Mandelbrot B. Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier. J Fluid Mech. 1974;62:331- 58.
49. Scafetta N, Griffin L, West BJ. Hölder exponent spectra for human gait. Physica A. 2003;328:561- 83.
50. Scafetta N, Marchi D, West BJ. Understanding the complexity of human gait dynamics. Chaos. 2009;19:026108.
51. Whitacre JM, Bender, A. Degeneracy: a design principle for robustness and evolvability. J Theor Biol. 2010;263:143-53.
52. Tononi G, Sporns O, Edelman GM. Measures of degeneracy and redundancy in biological networks. PNAS. 1999;96:3257-62.
53. Edelman GM, Gally JA. Degeneracy and complexity in biological systems. PNAS. 2001;98:13763-8.
54. Carlson JM, Doyle J. Complexity and robustness. PNAS. 2002;99:2538-45.
55. West BJ, Scafetta N. Nonlinear dynamical model of human gait. Phys Rev E. 2003;67:051917.
56. Delignières D, Marmelat V, Torre K. Degeneracy and long-range correlation: a simulation study. BIO Web of Conferences. 2011;1:00020. Available from: http://dx.doi.org/10.1051/bioconf/20110100020
57. Torre K, Delignières D, Lemoine L. Detection of long-range dependence and estimation of fractal exponents through ARFIMA modeling. Br J Math Stat Psychol. 2007;60:85-106.
58. Delignières D, Lemoine L, Torre K. Time intervals production in tapping and oscillatory motion. Hum Mov Sci. 2004;23:87-103.
59. Wing A., Kristofferson AB. The timing of interresponse intervals. Percept Psychophys. 1973;13:455-60.
60. β noise in self-paced and synchronized tapping: A unifying mechanistic model. Biol Cyber. 2008;99:159-70.
61. Vorberg D, Wing A. Modeling variability and dependence in timing. In: H. Heuer H, Keele SW, editors. Handbook of perception and action, vol 2. London: Academic Press; 1996. p. 181-262.
62. Torre K, Balasubramaniam R, Delignières D. Oscillating in synchrony with a metronome: serial dependence, limit cycle dynamics, and modeling. Motor Control. 2010;14:323-43.
63. Delignières D, Torre K. Fractal dynamics of human gait: a reassessment of the 1996 data of Hausdorff et al. J Appl Physiol. 2009;106:1272-9.
64. Diniz A, Wijnants ML, Torre K, Barreiros J, Crato N, Bosman AMT, Hasselman F, Cox RFA, Van Orden GC, Delignières D. Contemporary theories of 1/f noise in motor control. Hum Mov Sci. 2011;30:889-905.
65. Slifkin AB, Newell KM. Is variability in human performance a reflection of system noise? Curr Dir Psychol Sci. 1998;7:170-7.
66. Correll J. 1/f noise and effort on implicit measures of bias. J Pers Soc Psychol. 2008;94:48-59.
67. Correll J. Order from chaos? 1/f noise predicts performance on reaction time measures. J Exp Soc Psychol. 2011;47:830-5.
68. Wijnants, ML, Bosman, AMT, Hasselman F, Cox RFA, Van Orden GC. 1/f scaling in movement time changes with practice in precision aiming. Nonlinear Dynamics Psychol Life Sci. 2009;13:79-98.
69. Aks DJ. 1/f dynamic in complex visual search: Evidence for self-organized criticality in human perception. In: Riley MA, Van Orden GC, editors. Tutorials in contemporary nonlinear methods for the behavioral sciences; 2005. p. 319-352. Available from: http://www.nsf.gov/sbe/bcs/pac/nmbs/nmbs.jsp
70. West B, Griffin L. Allometric control, inverse power law and human gait. Chaos, Soliton Fract. 1999;10:1519-27.
71. Torre K, Delignières D. Distinct ways for timing movements in bimanual coordination tasks: The contribution of serial correlation analysis and implications for modelling. Acta Psychol. 2008;129:284-96.
72. Helmuth L, Ivry RB. When two hands are better than one: reduced timing variability during bimanual movements. J Exp Psychol Hum Percept Perf. 1996;22:278-93.
73. Haken H, Kelso JAS, Bunz H. A theoretical model of phase transition in human hand movement. Biol Cyber. 1985;51:347-56.
74. Mandelbrot B. Les objets fractals. Paris: Flammarion; 1995.
75. Marmelat V, Delignières D. Strong anticipation: Complexity matching in interpersonal coordination. Exp Brain Res. 2012;222:137-48.
76. Repp BH. Sensorimotor synchronization: a review of the tapping literature. Psychon Bull Rev. 2005;12:969-92.
77. Stephen DG, Stepp N, Dixon J, Turvey MT. Strong anticipation: sensitivity to long-range correlations in synchronization behavior. Physica A. 2008;387:5271-8.
78. Dubois DM. Mathematical foundations of discrete and functional systems with strong and weak anticipations. Lect Notes Comput Sc. 2003;2684:110- 32.
79. Stepp N, Turvey MT. On strong anticipation. Cog Syst Res. 2010;11:148-64.
80. Stephen DG, Dixon J. Strong anticipation: multifractal cascade dynamics modulate scaling in synchronization behaviors. Chaos Soliton Fract. 2011;44:160-8.
81. West BJ, Geneston EL, Grigolini P. Maximizing information exchange between complex networks. Phys Rep. 2008;468:1-99.