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Fractal and multifractal descriptors restore ergodicity broken by non-Gaussianity in time series. (English) Zbl 1507.37004


MSC:

37A25 Ergodicity, mixing, rates of mixing
28A80 Fractals
37M10 Time series analysis of dynamical systems

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References:

[1] Nickerson, J. V., Anticipatory systems: philosophical, mathematical, and methodological foundations, Int J Gen Syst, 41, 867-871 (2012)
[2] Peirce, C. S., Illustrations of the logic of science (1877), Open Court: Open Court Chicago, IL
[3] Molenaar, P. C.M., On the implications of the classical ergodic theorems: analysis of developmental processes has to focus on intra-individual variation, Dev Psychobiol, 50, 60-69 (2008)
[4] Molenaar, P. C.M.; Ram, N., Dynamic modeling and optimal control of intraindividual variation: a computational paradigm for nonergodic psychological processes, (Stat. Methods Model. Hum. Dyn. An Interdiscip. Dialogue (2010), Routledge/Taylor & Francis Group: Routledge/Taylor & Francis Group New York, NY, US), 13-37
[5] Molenaar, P. C.M.; Sinclair, K. O.; Rovine, M. J.; Ram, N.; Corneal, S. E., Analyzing developmental processes on an individual level using nonstationary time series modeling, Dev Psychol, 45, 260-271 (2009)
[6] Peters, O., The ergodicity problem in economics, Nat Phys, 15, 1216-1221 (2019)
[7] O Peters W Maximilian. A recipe for irreproducible results. ArXiv 2017:1706.07773v1.
[8] Mangalam, M.; Kelty-Stephen, D. G., Point estimates, Simpson’s paradox, and nonergodicity in biological sciences, Neurosci Biobehav Rev, 125, 98-107 (2021)
[9] Fisher, A. J.; Medaglia, J. D.; Jeronimus, B. F., Lack of group-to-individual generalizability is a threat to human subjects research, Proc Natl Acad Sci, 115, E6106-E6115 (2018)
[10] Deng, W.; Barkai, E., Ergodic properties of fractional Brownian-Langevin motion, Phys Rev E, 79, 11112 (2009)
[11] Callender, C., What makes time special? (2017), Oxford University Press: Oxford University Press Oxford, UK · Zbl 1369.00085
[12] Molenaar, P. C.M., A manifesto on psychology as idiographic science: bringing the person back into scientific psychology, this time forever, Meas Interdiscip Res Perspect, 2, 201-218 (2004)
[13] Lewin, K., Defining the “field at a given time”, Psychol Rev, 50, 292-310 (1943)
[14] Stigler, S. M., Regression towards the mean, historically considered, Stat Methods Med Res, 6, 103-114 (1997)
[15] Holden, J. G.; Van Orden, G. C.; Turvey, M. T., Dispersion of response times reveals cognitive dynamics, Psychol Rev, 116, 318-342 (2009)
[16] Stephen, D. G.; Mirman, D., Interactions dominate the dynamics of visual cognition, Cognition, 115, 154-165 (2010)
[17] Reynolds, A. M., Current status and future directions of Lévy walk research, Biol Open, 7, Article bio030106 pp. (2018)
[18] Broido, A. D.; Clauset, A., Scale-free networks are rare, Nat Commun, 10, 1017 (2019)
[19] Clauset, A.; Shalizi, C. R.; Newman, M. E.J., Power-law distributions in empirical data, SIAM Rev, 51, 661-703 (2009) · Zbl 1176.62001
[20] Shlesinger, M. F.; West, B. J.; Klafter, J., Lévy dynamics of enhanced diffusion: application to turbulence, Phys Rev Lett, 58, 1100-1103 (1987)
[21] Barkai, E.; Garini, Y.; Metzler, R., Strange kinetics of single molecules in living cells, Phys Today, 65, 29 (2012)
[22] Muñoz-Gil, G.; Volpe, G.; Garcia-March, M. A.; Aghion, E.; Argun, A.; Hong, C. B., Objective comparison of methods to decode anomalous diffusion, Nat Commun, 12, 6253 (2021)
[23] Weigel, A. V.; Simon, B.; Tamkun, M. M.; Krapf, D., Ergodic and nonergodic processes coexist in the plasma membrane as observed by single-molecule tracking, Proc Natl Acad Sci, 108, 6438-6443 (2011)
[24] Hu, X.; Hong, L.; Dean Smith, M.; Neusius, T.; Cheng, X.; Smith, J. C., The dynamics of single protein molecules is non-equilibrium and self-similar over thirteen decades in time, Nat Phys, 12, 171-174 (2016)
[25] Fernández, A. D.; Charchar, P.; Cherstvy, A. G.; Metzler, R.; Finnis, M. W., The diffusion of doxorubicin drug molecules in silica nanoslits is non-Gaussian, intermittent and anticorrelated, Phys Chem Chem Phys, 22, 27955-27965 (2020)
[26] Kulkarni, A. M.; Dixit, N. M.; Zukoski, C. F., Ergodic and non-ergodic phase transitions in globular protein suspensions, Faraday Discuss, 123, 37-50 (2003)
[27] Manzo, C.; Torreno-Pina, J. A.; Massignan, P.; Lapeyre, G. J.; Lewenstein, M.; Garcia Parajo, M. F., Weak ergodicity breaking of receptor motion in living cells stemming from random diffusivity, Phys Rev X, 5, 11021 (2015)
[28] Nosonovsky, M.; Roy, P., Allometric scaling law and ergodicity breaking in the vascular system, Microfluid Nanofluidics, 24, 53 (2020)
[29] Masuda, N.; Aihara, K., Ergodicity of spike trains: when does trial averaging make sense?, Neural Comput, 15, 1341-1372 (2003) · Zbl 1085.68642
[30] Medaglia, J. D.; Ramanathan, D. M.; Venkatesan, U. M.; Hillary, F. G., The challenge of non-ergodicity in network neuroscience, Netw Comput Neural Syst, 22, 148-153 (2011)
[31] Harrison, H. S.; Kelty-Stephen, D. G.; Vaz, D. V.; Michaels, C. F., Multiplicative-cascade dynamics in pole balancing, Phys Rev E, 89, 60903 (2014)
[32] Mangalam, M.; Kelty-Stephen, D. G., Multiplicative-cascade dynamics supports whole-body coordination for perception via effortful touch, Hum Mov Sci, 70, Article 102595 pp. (2020)
[33] Mangalam, M.; Carver, N. S.; Kelty-Stephen, D. G., Multifractal signatures of perceptual processing on anatomical sleeves of the human body, J R Soc Interface, 17, 20200328 (2020)
[34] Bloomfield, L.; Lane, E.; Mangalam, M.; Kelty-Stephen, D. G., Perceiving and remembering speech depend on multifractal nonlinearity in movements producing and exploring speech, J R Soc Interface, 18, 20210272 (2021)
[35] Wallot, S.; Kelty-Stephen, D. G., Interaction-dominant causation in mind and brain, and its implication for questions of generalization and replication, Minds Mach, 28, 353-374 (2018)
[36] Mangalam, M.; Chen, R.; McHugh, T. R.; Singh, T.; Kelty-Stephen, D. G., Bodywide fluctuations support manual exploration: fractal fluctuations in posture predict perception of heaviness and length via effortful touch by the hand, Hum Mov Sci, 69, Article 102543 pp. (2020)
[37] Mangalam, M.; Carver, N. S.; Kelty-Stephen, D. G., Global broadcasting of local fractal fluctuations in a bodywide distributed system supports perception via effortful touch, Chaos, SolitonsFractals, 135, Article 109740 pp. (2020)
[38] Eke, A.; Herman, P.; Kocsis, L.; Kozak, L. R., Fractal characterization of complexity in temporal physiological signals, Physiol Meas, 23, R1-R38 (2002)
[39] Baxandall, P. J., Noise in transistor circuits. 1. Mainly on fundamental noise concepts, WirelWorld, 74, 388-392 (1968)
[40] Gilden, D. L., Cognitive emissions of 1/f noise, Psychol Rev, 108, 33-56 (2001)
[41] Mangalam, M.; Kelty-Stephen, D. G., Ergodic descriptors of non-ergodic stochastic processes, J R Soc Interface, 19, Article 20220095 pp. (2022)
[42] Van Orden, G. C.; Holden, J. G.; Turvey, M. T., Self-organization of cognitive performance, J Exp Psychol Gen, 132, 331-350 (2003)
[43] Ihlen, E. A.F.; Vereijken, B., Interaction-dominant dynamics in human cognition: beyond 1/f fluctuation, J Exp Psychol Gen, 139, 436-463 (2010)
[44] Dixon, J. A.; Holden, J. G.; Mirman, D.; Stephen, D. G., Multifractal dynamics in the emergence of cognitive structure, Top Cogn Sci, 4, 51-62 (2012)
[45] Kelty-Stephen, D. G.; Lee, I. C.; Carver, N. S.; Newell, K. M.; Mangalam, M., Multifractal roots of suprapostural dexterity, Hum Mov Sci, 76, Article 102771 pp. (2021)
[46] Kloos, H.; Van Orden, G., Voluntary behavior in cognitive and motor tasks, Mind Matter, 8, 19-43 (2010)
[47] Mandelbrot, B. B., Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier, J Fluid Mech, 62, 331-358 (1974) · Zbl 0289.76031
[48] Mutothya, N. M.; Xu, Y.; Li, Y.; Metzler, R., Characterising stochastic motion in heterogeneous media driven by coloured non-Gaussian noise, J Phys A Math Theor, 54, Article 295002 pp. (2021) · Zbl 1519.60119
[49] Häunggi, P.; Jung, P., Colored noise in dynamical systems, (Adv. Chem. Phys (1994), John Wiley & Sons, Inc.: John Wiley & Sons, Inc. Hoboken, NJ), 239-326
[50] Kuehn, N. M.; Abrahamson, N. A., Spatial correlations of ground motion for non-ergodic seismic hazard analysis, Earthq Eng Struct Dyn, 49, 4-23 (2020)
[51] Huang, Z.; Cao, J., Ergodicity and bifurcations for stochastic logistic equation with non-Gaussian Lévy noise, Appl Math Comput, 330, 1-10 (2018) · Zbl 1427.37040
[52] Allez, R.; Rhodes, R.; Vargas, V., Lognormal ⋆-scale invariant random measures, Probab Theory Relat Fields, 155, 751-788 (2013) · Zbl 1278.60083
[53] Bocchini, P.; Deodatis, G., Critical review and latest developments of a class of simulation algorithms for strongly non-Gaussian random fields, ProbabEng Mech, 23, 393-407 (2008)
[54] Farrell, S.; Wagenmakers, E.-J.; Ratcliff, R., 1/f noise in human cognition: is it ubiquitous, and what does it mean?, Psychon Bull Rev, 13, 737-741 (2006)
[55] Wagenmakers, E.-J.; Farrell, S.; Ratcliff, R., Human cognition and a pile of sand: a discussion on serial correlations and self-organized criticality, J Exp Psychol Gen, 134, 108-116 (2005)
[56] Shlesinger, M. F.; Zaslavsky, G. M.; Klafter, J., Strange kinetics, Nature, 363, 31-37 (1993)
[57] Shebalin, J. V., Broken ergodicity and coherent structure in homogeneous turbulence, Phys D Nonlinear Phenom, 37, 173-191 (1989) · Zbl 0687.76052
[58] Shebalin, J. V., Ideal homogeneous magnetohydrodynamic turbulence in the presence of rotation and a mean magnetic field, J Plasma Phys, 72, 507-524 (2006)
[59] Scale-by-scale simplicity: An introduction to multiplicative cascades, (Schertzer, D.; Lovejoy, S., Weather Clim. Emergent Laws Multifractal Cascades (2013), Cambridge University Press: Cambridge University Press Cambridge), 59-82 · Zbl 1378.86002
[60] Kelty-Stephen, D. G.; Palatinus, K.; Saltzman, E.; Dixon, J. A., A tutorial on multifractality, cascades, and interactivity for empirical time series in ecological science, Ecol Psychol, 25, 1-62 (2013)
[61] Bacry, E.; Delour, J.; Muzy, J. F., Multifractal random walk, Phys Rev E, 64, 26103 (2001) · Zbl 0974.91045
[62] Arneodo, A.; Bacry, E.; Muzy, J. F., Random cascades on wavelet dyadic trees, J Math Phys, 39, 4142-4164 (1998) · Zbl 0931.28008
[63] Kiyono, K.; Struzik, Z. R.; Yamamoto, Y., Estimator of a non-Gaussian parameter in multiplicative log-normal models, Phys Rev E, 76, 41113 (2007)
[64] Peng, C.-K.; Buldyrev, S. V.; Havlin, S.; Simons, M.; Stanley, H. E.; Goldberger, A. L., Mosaic organization of DNA nucleotides, Phys Rev E, 49, 1685-1689 (1994)
[65] Peng, C.-K.; Havlin, S.; Stanley, H. E.; Goldberger, A. L., Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series, Chaos, 5, 82-87 (1995)
[66] Chhabra, A.; Jensen, R. V., Direct determination of the f(α) singularity spectrum, Phys Rev Lett, 62, 1327-1330 (1989)
[67] Mandelbrot, B. B., The fractal geometry of nature (1982), W H Freeman: W H Freeman New York, NY · Zbl 0504.28001
[68] Mandelbrot, B. B., Fractals and scaling in finance (1997), Springer: Springer New York, NY · Zbl 1005.91001
[69] Halsey, T. C.; Jensen, M. H.; Kadanoff, L. P.; Procaccia, I.; Shraiman, B. I., Fractal measures and their singularities: the characterization of strange sets, Phys Rev A, 33, 1141-1151 (1986) · Zbl 1184.37028
[70] Ihlen, E., Introduction to multifractal detrended fluctuation analysis in Matlab, Front Physiol, 3, 141 (2012)
[71] Schreiber, T.; Schmitz, A., Improved surrogate data for nonlinearity tests, Phys Rev Lett, 77, 635-638 (1996)
[72] Kelty-Stephen, D. G.; Lane, E.; Bloomfield, L.; Mangalam, M., Multifractal test for nonlinearity of interactions across scales in time series, Behav Res Methods (2022)
[73] Thirumalai, D.; Mountain, R. D.; Kirkpatrick, T. R., Ergodic behavior in supercooled liquids and in glasses, Phys Rev A, 39, 3563-3574 (1989)
[74] Jacobson, N.; Berleman-Paul, Q.; Mangalam, M.; Kelty-Stephen, D. G.; Ralston, C., Multifractality in postural sway supports quiet eye training in aiming tasks: a study of golf putting, Hum Mov Sci, 76, Article 102752 pp. (2021)
[75] Carver, N. S.; Bojovic, D.; Kelty-Stephen, D. G., Multifractal foundations of visually-guided aiming and adaptation to prismatic perturbation, Hum Mov Sci, 55, 61-72 (2017)
[76] Kelty-Stephen, D. G.; Dixon, J. A., Interwoven fluctuations during intermodal perception: fractality in head sway supports the use of visual feedback in haptic perceptual judgments by manual wielding, J Exp Psychol Hum Percept Perform, 40, 2289-2309 (2014)
[77] Kantelhardt, J. W.; Ashkenazy, Y.; Ivanov, P. Ch.; Bunde, A.; Havlin, S.; Penzel, T., Characterization of sleep stages by correlations in the magnitude and sign of heartbeat increments, Phys Rev E, 65, Article 051908 pp. (2002)
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