Sequences of predictive eye movements form a fractional Brownian series - Implications for self-organized criticality in the oculomotor system

Biological Cybernetics

Volumn 93, Issue 1, 2005, Pages 43-53

  Shelhamer, Mark ^a  

^a JOHNS HOPKINS UNIVERSITY SCHOOL OF MEDICINE   (United States)

Author keywords

Power law scaling; Prediction; Saccade

Indexed keywords

BRAIN; BROWNIAN MOVEMENT; DATA REDUCTION; FREQUENCIES; OSCILLATIONS; PHASE TRANSITIONS;

FLUCTUATION ANALYSIS; FRACTIONAL BROWNIAN SERIES; OCULOMOTOR SYSTEMS; THRESHOLD FREQUENCY;

EYE MOVEMENTS;

ARTICLE; BIOLOGICAL MODEL; COMPARATIVE STUDY; DEPTH PERCEPTION; HUMAN; METHODOLOGY; MOVEMENT PERCEPTION; NONLINEAR SYSTEM; PHOTOSTIMULATION; PHYSIOLOGY; PREDICTION AND FORECASTING; REACTION TIME; SACCADIC EYE MOVEMENT; VISUAL SYSTEM FUNCTION;

HUMANS; MODELS, NEUROLOGICAL; MOTION PERCEPTION; NONLINEAR DYNAMICS; OCULAR PHYSIOLOGY; PHOTIC STIMULATION; PREDICTIVE VALUE OF TESTS; REACTION TIME; SACCADES; SPACE PERCEPTION;

EID: 23044469643     PISSN: 03401200     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00422-005-0584-9     Document Type: Article

References (34)

1. Addison PS (1997) Fractals and chaos, an illustrated course. Institute of Physics Publishing, Philadelphia
2. Bak P (1996) How nature works: the science of self-organized criticality. Copernicus Books, New York
3. Bak P, Tang C, Wiesenfeld K (1987) Self-organized criticality : an explanation of the 1/f noise. Phys Rev Lett 59:381-384
4. Bak P, Tang C, Wiesenfeld K (1988) Self-organized criticality. Phys Rev A 38:364-374
5. Bassingthwaighte JB, Liebovitch LS, West BJ (1994) Fractal physiology. Oxford University Press, New York
6. Becker W (1991) In: Carpenter RHS (ed) Eye movements. Macmillan, London, pp 95-137
7. Chakraborti SR, Barnes GR, Collins CJ (2002) Factors affecting the longevity of a short-term velocity store for predictive oculomotor tracking. Exp Brain Res 144:152-158
8. Chialvo DR, Bak P (1999) Learning from mistakes. Neurosci 90:1137-1148
9. Ding M, Chen Y, Kelso JA (2002) Statistical analysis of timing errors. Brain Cogn 48:98-106
10. Farmer JD, Sidorowich JJ (1987) Predicting chaotic time series. Phys Rev Lett 59:845-848
11. Freeman WJ (2004) Origin, structure, and role of background EEG activity, part 2. Analytic phase. Clin Neurophysiol 115:2089-2107
12. Gagnon D, O'Driscoll GA, Petrides M, Pike GB (2002) The effect of spatial and temporal information on saccades and neural activity in oculomotor structures. Brain 125:123-139
13. Gaymard B, Ploner CJ, Rivaud S, Vermersch AI, Pierrot-Deseilligny C (1998) Cortical control of saccades. Exp Brain Res 123:159-163
14. Hausdorff JM, Peng C-K, Ladin Z, Wei JY, Goldberger AL (1995) Is walking a random walk? Evidence for long-range correlations in stride interval of human gait. J Appl Physiol 78:349-358
15. Ivry RB, Spencer RM (2004) The neural representation of time. Curr Opin Neurobiol 14:225-232
16. Joiner WM, Shelhamer M (2004) An investigation of the relative stability of reactive and predictive oculomotor tracking. J Vestibular Res 14:209
17. Kelso JAS, Southard DL, Goodman D (1979) On the nature of human interlimb coordination. Science 203:1029-1031
18. Linkenkaer-Hansen K, Nikouline VV, Palva JM, Ilmoniemi RJ (2001) Long-range temporal correlations and scaling behavior in human brain oscillations. J Neurosci 21:1370-1377
19. Mandelbrot BB (1983) The fractal geometry of nature. W.H. Freeman and Company, New York
20. Packard NH, Crutchfield JP, Farmer JD, Shaw RS (1980) Geometry from a time series. Phys Rev Lett 45:712-716
21. Peng C-K, Hausdorff JM, Goldberger AL (2000) In: Walleczek J (ed) Self-organized biological dynamics & nonlinear control. Cambridge University Press, New York, pp 66-96
22. Peng C-K, Havlin S, Stanley HE, Goldberger AL (1995) Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos 5:82-87
23. Roberts S, Eykholt R, Thaut MH (2000) Analysis of correlations and search for evidence of deterministic chaos in rhythmic motor control by the human brain. Phys Rev E 62:2597-2607
24. Ruelle D (1990) Deterministic chaos: the science and the fiction. Proc Royal Soc Lond A 427:241-248
25. Shelhamer M (2005) Sequences of predictive saccades are correlated over a span of approximately two seconds, and produce a fractal time series. J Neurophysiol 93:2002-2011
26. Shelhamer M, Gross CD (1998) Prediction of the sequence of optokinetic nystagmus eye movements reveals deterministic structure in reflexive oculomotor behavior. IEEE Trans Biomed Eng 45:668-670
27. Shelhamer M, Joiner WM (2003) Saccades exhibit abrupt transition between reactive and predictive; predictive saccade sequences have long-term correlations. J Neurophysiol 90:2763-2769
28. Skarda CA, Freeman WJ (1987) How brains make chaos in order to make sense of the world. Behav Brain Sci 10:161-195
29. Sklavos S, Porrill J, Kaneko CR, Dean P (2005) Evidence for wide range of time scales in oculomotor plant dynamics: Implications for models of eye-movement control. Vision Res 45:1525-1542
30. Stam CJ, de Bruin EA (2004) Scale-free dynamics of global functional connectivity in the human brain. Hum Brain Mapp 22:97-109
31. Teich MC (1989) Fractal character of the auditory neural spike train. IEEE Trans Biomed Eng 36:150-160
32. Theiler J, Eubank S, Longtin A, Galdrikian B, Farmer JD (1992) Testing for nonlinearity in time series: the method of surrogate data. Physica D 58:77-94
33. Trillenberg P, Gross C, Shelhamer M (2001) Random walks, random sequences, and nonlinear dynamics in human optokinetic nystagmus. J Appl Physiol 91:1750-1759
34. Tsonis AA, Elsner JB (1992) Nonlinear prediction as a way of distinguishing chaos from random fractal sequences. Nature 358:217-220