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Strong anticipation: Multifractal cascade dynamics modulate scaling in synchronization behaviors

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  • Stephen, Damian G.
  • Dixon, James A.

Abstract

Previous research on anticipatory behaviors has found that the fractal scaling of human behavior may attune to the fractal scaling of an unpredictable signal [Stephen DG, Stepp N, Dixon JA, Turvey MT. Strong anticipation: Sensitivity to long-range correlations in synchronization behavior. Physica A 2008;387:5271–8]. We propose to explain this attunement as a case of multifractal cascade dynamics [Schertzer D, Lovejoy S. Generalised scale invariance in turbulent phenomena. Physico-Chem Hydrodyn J 1985;6:623–5] in which perceptual-motor fluctuations are coordinated across multiple time scales. This account will serve to sharpen the contrast between strong and weak anticipation: whereas the former entails a sensitivity to the intermittent temporal structure of an unpredictable signal, the latter simply predicts sensitivity to an aggregate description of an unpredictable signal irrespective of actual sequence. We pursue this distinction through a reanalysis of Stephen et al.’s data by examining the relationship between the widths of singularity spectra for intertap interval time series and for each corresponding interonset interval time series. We find that the attunement of fractal scaling reported by Stephen et al. was not the trivial result of sensitivity to temporal structure in aggregate but reflected a subtle sensitivity to the coordination across multiple time scales of fluctuation in the unpredictable signal.

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  • Stephen, Damian G. & Dixon, James A., 2011. "Strong anticipation: Multifractal cascade dynamics modulate scaling in synchronization behaviors," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 160-168.
    • Handle: RePEc:eee:chsofr:v:44:y:2011:i:1:p:160-168
    DOI: 10.1016/j.chaos.2011.01.005
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    Cited by:

    1. Raptis, Theophanes E., 2017. "“Viral” Turing Machines, computation from noise and combinatorial hierarchies," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 734-740.
    2. Jun Taek Lee & Damian G. Kelty-Stephen, 2017. "Cascade-Driven Series with Narrower Multifractal Spectra Than Their Surrogates: Standard Deviation of Multipliers Changes Interactions across Scales," Complexity, Hindawi, vol. 2017, pages 1-8, January.
    3. Kelty-Stephen, Damian G., 2017. "Threading a multifractal social psychology through within-organism coordination to within-group interactions: A tale of coordination in three acts," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 363-370.
    4. Stanis{l}aw Dro.zd.z & Rafa{l} Kowalski & Pawe{l} O'swic{e}cimka & Rafa{l} Rak & Robert Gc{e}barowski, 2018. "Dynamical variety of shapes in financial multifractality," Papers 1809.06728, arXiv.org.
    5. Roume, C. & Almurad, Z.M.H. & Scotti, M. & Ezzina, S. & Blain, H. & Delignières, D., 2018. "Windowed detrended cross-correlation analysis of synchronization processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 1131-1150.
    6. Iran R Roman & Auriel Washburn & Edward W Large & Chris Chafe & Takako Fujioka, 2019. "Delayed feedback embedded in perception-action coordination cycles results in anticipation behavior during synchronized rhythmic action: A dynamical systems approach," PLOS Computational Biology, Public Library of Science, vol. 15(10), pages 1-32, October.
    7. Mahmoodi, Korosh & West, Bruce J. & Grigolini, Paolo, 2020. "On the dynamical foundation of multifractality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    8. Delignières, Didier & Marmelat, Vivien, 2014. "Strong anticipation and long-range cross-correlation: Application of detrended cross-correlation analysis to human behavioral data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 47-60.
    9. Stephen, Damian G. & Hsu, Wen-Hao & Young, Diana & Saltzman, Elliot L. & Holt, Kenneth G. & Newman, Dava J. & Weinberg, Marc & Wood, Robert J. & Nagpal, Radhika & Goldfield, Eugene C., 2012. "Multifractal fluctuations in joint angles during infant spontaneous kicking reveal multiplicativity-driven coordination," Chaos, Solitons & Fractals, Elsevier, vol. 45(9), pages 1201-1219.
    10. Pawe{l} O'swik{e}cimka & Stanis{l}aw Dro.zd.z & Mattia Frasca & Robert Gk{e}barowski & Natsue Yoshimura & Luciano Zunino & Ludovico Minati, 2020. "Wavelet-based discrimination of isolated singularities masquerading as multifractals in detrended fluctuation analyses," Papers 2004.03319, arXiv.org.
    11. Okano, Masahiro & Kurebayashi, Wataru & Shinya, Masahiro & Kudo, Kazutoshi, 2019. "Hybrid dynamics in a paired rhythmic synchronization–continuation task," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 625-638.

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