Multifractal fluctuations in joint angles during infant spontaneous kicking reveal multiplicativity-driven coordination

Chaos, Solitons and Fractals

Volumn 45, Issue 9-10, 2012, Pages 1201-1219

  Stephen, Damian G ^a   Hsu, Wen Hao ^a,b   Young, Diana ^a   Saltzman, Elliot L ^b   Holt, Kenneth G ^b   Newman, Dava J ^c   Weinberg, Marc ^d   Wood, Robert J ^a,e   Nagpal, Radhika ^a,e   Goldfield, Eugene C ^a,f  

^a HARVARD UNIVERSITY   (United States)

^b BOSTON UNIVERSITY   (United States)

^c Massachusetts Institute of Technology   (United States)

^d CHARLES STARK DRAPER LABORATORY   (United States)

^e HARVARD UNIVERSITY   (United States)

^f HARVARD MEDICAL SCHOOL   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIOMECHANICS; CHAOTIC SYSTEMS; COORDINATION REACTIONS; DEGREES OF FREEDOM (MECHANICS); FRACTALS; JOINTS (ANATOMY); PATIENT TREATMENT;

CHAOTIC DYNAMICS; COMPLEX MOVEMENT PATTERNS; DOWNSTREAM EFFECTS; MOTOR CO-ORDINATION; MULTI-JOINT COORDINATIONS; MULTIFRACTAL ANALYSIS; MULTIFRACTAL FLUCTUATIONS; VECTOR AUTOREGRESSIVE MODEL;

PATIENT REHABILITATION;

EID: 84864240216     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2012.06.005     Document Type: Article

References (110)

1. R.M. Alexander Storange and release of elastic energy in the locomotor system and the stretch-shortening cycle B.M. Nigg, B.R. MacIntosh, J. Mester, Biomechanics and biology of human movement 2000 Human Kinetics Champaign 19 29
2. R.M. Angulo-Kinzler Exploration and selection of intralimb coordination patterns in three-month-old infants J Mot Behav 33 2001 363 376 (Pubitemid 33121881)
3. P. Arena, S. De Fiore, and L. Patané Perception for action in roving robots: a dynamical system approach A. Adamatzky, M. Komosinski, Artificial life models in hardware 2009 Springer London 103 132
4. P. Bak How nature works: the science of self-organized criticality 1996 Copernicus New York
5. F. Baldissera, P. Cavallari, G. Marini, and G. Tassone Differential control of in-phase and anti-phase coupling of rhythmic movements of ipsilateral hand and foot Exp Brain Res 83 1991 375 380
6. A. Bannerjee, J.J. Dolado, J.W. Galbraith, and D.F. Hendry Cointegration, error correction, and the econometric analysis of non-stationary data 1993 Oxford University Press Oxford
7. J.B. Bassingthwaighte, L.S. Liebovitch, and B.J. West Fractal physiology 1994 Oxford University Press New York
8. T. Bohr, M.H. Jensen, G. Paladin, and A. Vulpiani Dynamical systems approach to turbulence 1998 Cambridge University Press Cambridge, UK
9. J.P. Bouchard Power laws and scaling in finance: empirical evidence and simple models M.M. Novak, Emergent nature: patterns, growth and scaling in nature 2002 World Scientific Singapore 157 171
10. H.B. Callen Thermodynamics and an introduction to thermostatics 2nd ed. 1985 Wiley New York
11. F.J. Caniego, M.A. Martín, and F. San José Rényi dimensions of soil pore size distribution Geoderma 112 2003 205 216 (Pubitemid 36189307)
12. A. Chhabra, and R.V. Jensen Direct determination of the f(α) singularity spectrum Phys Rev Lett 62 1989 1327 1330
13. M.A. Daley, G. Felix, and A.A. Biewener Running stability is enhanced by a proximo-distal gradient in joint neuromechanical control J Exp Biol 210 2007 383 394 (Pubitemid 46347910)
14. G. Deco, and M. Corbetta The dynamical balance of the brain at rest The Neuroscientist 17 2011 107 123
15. G. Deco, V.K. Jirsa, and A.R. McIntosh Emerging concepts for the dynamical organization of resting-state activity in the brain Nature Rev Neurosci 12 2011 43 56
16. S.L. Delp, J.P. Loan, M.G. Hoy, F.E. Zajac, E.L. Topp, and J.M. Rosen An interactive graphics-based model of the lower extremity to study orthopaedic surgical procedures IEEE Trans Biomed Eng 37 1990 757 767 (Pubitemid 20324141)
17. S.L. Delp, F.C. Anderson, A.S. Arnold, P. Loan, A. Habib, and C.T. John OpenSim: open-source software to create and analyze dynamic simulations of movement IEEE Trans Biomed Eng 55 2007 1940 1950 (Pubitemid 350006059)
18. J. Dibiasi, and C. Einspieler Load perturbation does not influence spontaneous movements in 3-month-old infants Early Hum Dev 77 2004 37 46 (Pubitemid 38534447)
19. Dixon JA, Holden JG, Mirman D, Stephen DG. Multifractal dynamics in the emergence of cognitive structure. Topics Cognitive Sci 2012.
20. J.A. Dixon, D.G. Stephen, R.A. Boncoddo, and J. Anastas The self-organization of cognitive structure B.H. Ross, The psychology of learning and motivation vol. 52 2010 Academic Press Burlington 343 384
21. J.C. Doyle, and M. Csete Architecture, constraints, and behavior Proc Nat Acad Sci 108 2011 15624 15630
22. D. Durstewitz, and G. Deco Computational significance of transient dynamics in cortical networks Eur J Neurosci 27 2008 217 227
23. C. Einspieler, and H.F.R. Prechtl Fetal movements though they may be spontaneous, yet there is method in them D. Prayer, Fetal MRI Medical radiology 2011 Springer Berlin 177 189
24. L. Fetters, Y.-P. Chen, J. Jonsdottir, and E.Z. Tronick Kicking coordination captures differences between full-term and premature infants with white matter disorder Hum Mov Sci 22 2004 729 748 (Pubitemid 38404809)
25. L. Fetters, I. Sapir, Y.-P. Chen, M. Kubo, and E.Z. Tronick Spontaneous kicking in full-term and preterm infants with and without white matter disorder Developmental Psychobiol 52 2010 524 536
26. M. Forni Using stationarity tests in antitrust market definition Am Law Econ Rev 6 2004 441 464 (Pubitemid 38940426)
27. U. Frisch Turbulence: the legacy of A.N. Kolmogorov 1996 Cambridge University Press Cambridge
28. J.C. Galloway, and E. Thelen Feet first: object exploration in young infants Infant Behav Dev 27 2004 107 112 (Pubitemid 38153021)
29. J.J. Gibson The senses considered as perceptual systems 1966 Houghton Mifflin Boston
30. E.C. Goldfield Emergent forms: origins and early development of human action and performance 1995 Oxford University Press New York
31. E.C. Goldfield Development of infant action systems and exploratory activity: a tribute to Edward S. Reed Ecological Psychol 12 2000 303 318
32. E.C. Goldfield, and P.H. Wolff A dynamical systems perspective on infant action and its development G. Bremner, A. Slater, Theories of infant development 2004 Blackwell Malden 3 29
33. S. Grillner, and P. Wallén On peripheral control mechanisms acting on central pattern generators for swimming in the dogfish J Exp Biol 98 1982 1 22
34. H. Grönqvist, K. Strand Brodd, and C. von Hofsten Rearching strategies of very preterm infants at 8 months corrected age Exp Brain Res 209 2011 225 233
35. M. Hadders-Algra The neuronal group selection theory: promising principles for understanding and treating developmental motor disorders Dev Medicine Child Neurol 42 2000 707 715
36. M. Hadders-Algra General movements: a window for early identification of children at high risk of developmental disorders J Pediatr 145 2004 S12 S18
37. T.C. Halsey, M.H. Jensen, L.P. Kadanoff, I. Procaccia, and B.I. Shraiman Fractal measures and their singularities: the characterization of strange sets Phys Rev A 33 1986 1141 1151
38. T.C. Hestenberg, D.S. Moore, S. Monaghan, A. Clipson, and R. Epstein Bootstrap methods and permutation tests 2005 W.H. Freeman New York
39. α fluctuation J Exp Psychol Gen 139 2010 436 463
40. P.Ch. Ivanov, L.A.N. Amaral, A.L. Goldberger, S. Havlin, M.G. Rosenblum, and H.E. Stanley From 1/f noise to multifractal cascades in heartbeat dynamics Chaos 11 2001 641 652
41. J.L. Jensen, B.D. Ulrich, E. Thelen, K. Schneider, and R.F. Zernicke Adaptive dynamics in the leg movement patterns of human infants: I. The effects of posture on spontaneous kicking J Mot Behav 26 1994 303 312
42. J.L. Jensen, B.D. Ulrich, E. Thelen, K. Schneider, and R.F. Zernicke Adaptive dynamics of the leg movement patterns of human infants: III. Age-related differences in limb control J Mot Behav 27 1995 366 374 (Pubitemid 26057947)
43. J.W. Kantelhardt, S.A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, and H.E. Stanley Multifractal detrended fluctuation analysis of nonstationary time series Physica A 316 2002 87 114 (Pubitemid 35385237)
44. D. Kwiatkowski, P.C.B. Phillips, P. Schmidt, and Y. Shin Testing the null hypothesis of stationarity against the alternative of a unit root J Econometr 54 1992 159 178
45. H.M. Lee, A. Bhat, J.P. Scholz, and J.C. Galloway Toy-oriented changes during early arm movements IV: shoulder-elbow coordination Infant Behav Dev 31 2008 447 469
46. H. Lütkepohl New introduction to multiple time series analysis 2005 Springer New York
47. B.B. Mandelbrot Fractals and scaling in finance: discontinuity, concentration, risk 1997 Springer Berlin
48. B.B. Mandelbrot Fractal and chaos: the Mandelbrot set and beyond 2004 Springer New York
49. B.B. Mandelbrot, and J.W. Van Ness Fractional Brownian motions, fractional noises, and applications SIAM Rev 10 1968 422 437
50. J.F. Muzy, E. Bacry, and A. Arneodo The multifractal formalism revisited with wavelets Int J Bifurc Chaos Appl Sci Eng 4 1994 245 302
51. P. Petersson, A. Waldenstrom, C. Fahreaus, and J. Schouenborg Spontaneous muscle twitches during sleep guide spinal self-organization Nature 424 2003 72 75 (Pubitemid 36834843)
52. J.P. Piek The role of variability in early motor development Infant Behav Dev 25 2002 452 465 (Pubitemid 36105320)
53. R.E. Plotnick, and J.J. Sepkoski A multiplicative multifractal model for originations and extinctions Paleobiol 27 2001 126 139 (Pubitemid 32386384)
54. A.A. Priplata, B.L. Patritti, J.B. Niemi, R. Hughes, D.C. Gravelle, and L.A. Lipsitz Noise-enhanced balance control in patients with diabetes and patients with stroke Ann Neurol 59 2006 4 12 (Pubitemid 43042865)
55. A.A. Priplata, J.B. Niemi, J.D. Harry, L.A. Lipsitz, and J.J. Collins Vibrating insoles and balance control in elderly people Lancet 362 2003 1123 1124 (Pubitemid 37222339)
56. A.A. Priplata, J. Niemi, M. Salen, J. Harry, L.A. Lipsitz, and J.J. Collins Noise-enhanced human balance control Phys Rev Lett 89 2002 238101
57. M.E. Raichle, and A.Z. Snyder A default mode of brain function: a brief history of an evolving idea NeuroImage 37 2007 1083 1090 (Pubitemid 47385262)
58. D. Schertzer, and S. Lovejoy Uncertainty and predictability in geophysics: chaos and multifractal insights R.S.J. Sparks, C.J. Hawkesworth, State of the planet, frontiers and challenges in geophysics 2004 AGU Washington, DC 317 334
59. K. Schneider, and R.F. Zernicke Mass, center of mass, and moment of inertia estimates for infant limb segments J Biomech 25 1992 145 148
60. T. Schreiber, and A. Schmitz Improved surrogate data for nonlinearity tests Phys rev Lett 1996 635 638 (Pubitemid 126624517)
61. C.A. Sims Macroeconomics and reality Econometrica 48 1980 1 48
62. O. Sporns, and G.M. Edelman Solving Bernstein's problem: a proposal for the development of coordinated movement by selection Child Dev 64 1993 960 981
63. R.B. Stein Peripheral control of movement Physiol Rev 54 1974 215 243
64. S. Steingrube, M. Timme, F. Wörgötter, and P. Manoonpong Self-organized adaptation of a simple neural circuit enables complex robot behaviour Nature Phys 6 2010 224 230
65. D.G. Stephen, and J. Anastas Fractal fluctuations in gaze speed visual search Attention Percept Psychophys 73 2011 666 677
66. D.G. Stephen, and J.A. Dixon The self-organization of insight: entropy and power laws in problem solving J Problem Solving 2 2009 72 101
67. D.G. Stephen, and J.A. Dixon Strong anticipation: multifractal cascade dynamics modulate scaling in synchronization behaviors Chaos Solitons Fract 44 2011 160 168
68. D.G. Stephen, and A. Hajnal Transfer of calibration from hand to foot: functional equivalence and fractal fluctuations Attention Percept Psychophys 73 2011 1302 1328
69. D.G. Stephen, J.R. Anastas, and J.A. Dixon Scaling in executive control reflects multiplicative multifractal cascade dynamics Front Physiol 3 2012 102
70. D.G. Stephen, R. Arzamarski, and C.F. Michaels The role of fractality in perceptual learning: exploration in dynamic touch J Exp Psychol Hum Percept Perform 36 2010 1161 1173
71. E. Thelen Developmental origins of motor coordination: leg movements in human infants Dev Psychobiol 18 1985 1 22 (Pubitemid 15106462)
72. E. Thelen The (re)discovery of motor development: learning new things from an old field Dev Psychol 25 1989 946 949
73. E. Thelen Three-month-old infants can learn task-specific patterns of interlimb coordination Psychol Sci 5 1994 280 285
74. E. Thelen, and B. Ulrich Hidden skills: a dynamic systems analysis of treadmill stepping during the first year Monographs Soc Res Child Dev 56 1991 1 98
75. E. Thelen, D. Corbetta, K. Kamm, J.P. Spencer, K. Schneider, and R.F. Zernicke The transition to reaching: mapping intention and intrinsic dynamics Child Dev 64 1993 1058 1098
76. J. Timmer Power of surrogate data testing with respect to nonstationarity Phys Rev E 58 1998 5153 5156 (Pubitemid 128596455)
77. B.D. Ulrich, J.L. Jensen, E. Thelen, K. Schneider, and R.F. Zernicke Adaptive dynamics in leg movement patterns of human infants: II. Treadmill stepping in infants and adults J Mot Behav 26 1994 313 324
78. J. Vaal, A.J. van Soest, B. Hopkins, L.T. Sie, and M.S. van der Knaap Development of spontaneous leg movements in infants with and without periventricular leukomalacia Exp Brain Res 135 2000 94 105
79. D. Veneziano, G.E. Moglen, and R.L. Bras Multifractal analysis: pitfalls of standard procedures and alternatives Phys Rev E 52 1995 1387 1398
80. T. Vicsek Fractal growth phenomena 1992 World Scientific Singapore
81. E.-J. Wagenmakers, H.L.J. van der Maas, and S. Farrell Abstract concepts require concrete models: why cognitive scientists have not yet embraced nonlinearly-coupled, dynamical, self-organized critical, synergistic, scale-free, exquisitely context-sensitive, interaction-dominant, multifractal, interdependent brain-body-niche systems Topics Cognitive Sci 4 2012 87 93
82. B.J. West Where medicine went wrong: rediscovering the path to complexity 2006 World Scientific Teaneck
83. B. Wild, M. Eichler, H.-C. Friedrich, M. Hartmann, S. Zipfel, and W. Herzog A graphical vector autoregressive modeling approach to the analysis of electronic diary data BMC Med Res Method 10 2010 28
84. D.A. Winter Biomechanics and motor control of human movement 2005 Wiley Hoboken, NJ
85. M. Wolf Evidence for the first-order phase transition in the multifractal spectrum for diffusion-limited aggregation J Phys A Math Gen 23 1990 L1287 L1291
86. X.D. Yang, A.J. He, Y. Zhou, and X.B. Ning Multifractal mass exponent spectrum of complex physiological time series Chinese Sci Bull 55 2010 1996 2003
87. M. Zamir Critique of the test of multifractality as applied to biological data J Theor Biol 225 2003 407 412 (Pubitemid 37353063)
88. K.E. Bassler, G.H. Gunaratne, and J.L. McCauley Markov processes, Hurst exponents, and nonlinear diffusion equations: with application to finance Physica A 369 2006 343 353
89. D. Chappell, and J. Scalo Multifractal scaling, geometrical diversity, and hierarchical structure in the cool interstellar medium Astrophys J 551 2001 712 729
90. C.V. Chianca, A. Ticona, and T.J.P. Penna Fourier-detrended fluctuation analysis Physica A 357 2005 447 454 (Pubitemid 41285200)
91. P. Douhkan, G. Oppenheim, and M.S. Taqqu Theory and applications of long-range dependence 2003 Birkhauser Boston Cambridge, MA
92. P. Grigolini, G. Aquino, M. Bologna, M. Lukovic, and B.J. West A theory of 1/f-noise in human cognition Physica A 388 2009 4192 4204
93. A. Grinsted, J.C. Moore, and S. Jevrejeva Application of the cross wavelet transform and wavelet coherence to geophysical time series Nonlin Process Geophys 2004
94. J.G. Holden, G. Van Orden, and M.T. Turvey Dispersion of response times reveals cognitive dynamics Psychol Rev 116 2009 318 342
95. C.T. Kello, G.D.A. Brown, R. Ferrer-i-Cancho, J.G. Holden, K. Linkenkaer-Hansen, and T. Rhodes Scaling laws in cognitive sciences Trends Cogn Sci 14 2010 223 232
96. R. Magrans, P. Gomis, P. Caminal, and G. Wagner Multifractal and nonlinear assessment of autonomous nervous system response during transient myocardial ischaemia Physiol Meas 31 2010 565 580
97. I. Main Statistical physics, seismogenesis, and seismic hazard Rev Geophys 34 1996 433 462
98. B.B. Mandelbrot How long is the coast of Britain? Statistical self-similarity and fractional dimension Science 156 1967 636 638
99. D. Maraun, H. Rust, and J. Timmer Tempting long-memory - on the interpretation of DFA results Nonlin Process Geophys 11 2004 495 503 (Pubitemid 39660861)
100. E.W. Montroll, and M.F. Shlesinger On 1/f noise and other distributions with long tails Proc Nat Acad Sci 79 1982 3380 3383
101. C.J. Morales, and E.D. Kolaczyk Wavelet based multifractal analysis of human balance Ann Biomed Eng 30 2002 588 597 (Pubitemid 34726345)
102. J.F. Muzy, J. Delour, and E. Bacry Modelling fluctuations of financial time series: from cascade process to stochastic volatility model Eur Phys J B 17 2000 537 548
103. J.A. Reyes, M.E. Mendoza, J.L. Carrillo, and Z.G. Ye Domain wall dynamics near the phase transition in PZN-9%PT Integr Ferroelectr 126 2011 166 170
104. A.M. Reynolds, and C.J. Rhodes The Lévy flight paradigm: random search patterns and mechanisms Ecol 90 2009 877 887
105. T. Rhodes, and M.T. Turvey Human memory retrieval as Lévy foraging Physica A 385 2007 255 260 (Pubitemid 47374432)
106. M.F. Shlesinger, G.M. Zaslavsky, and J. Klafter Strange kinetics Nature 363 1993 31 37
107. D.G. Stephen, D. Mirman, J.S. Magnuson, and J.A. Dixon Lévy-like diffusion in eye movements during spoken-language comprehension Phys Rev E 79 2009 056114
108. P.J. Treffner, and J.A.S. Kelso Dynamic encounters: long-memory during functional stabilization Ecol Psychol 11 1999 103 137
109. G. Van Orden, J.G. Holden, and M.T. Turvey Self-organization of cognitive performance J Exp Psychol Gen 132 2003 331 350 (Pubitemid 37110314)
110. G. Van Orden, C.T. Kello, and J.G. Holden Situated behavior and the place of measurement in psychological theory Ecol Psychol 22 2010 24 43