Generating surrogates from recurrences

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 366, Issue 1865, 2008, Pages 545-557

  Thiel, M ^a,b   Romano, M C ^a,b   Kurths, J ^a   Rolfs, M ^a   Kliegl, R ^a  

^a UNIVERSITY OF POTSDAM   (Germany)

^b UNIVERSITY OF ABERDEEN   (United Kingdom)

Author keywords

Hypothesis test; Phase synchronization; Recurrence plots; Surrogate data

Indexed keywords

BINOCULAR VISION; BRAIN; SYNCHRONIZATION;

BINOCULAR FIXATIONAL MOVEMENTS; HYPOTHESIS TEST; PHASE SYNCHRONIZATION; RECURRENCE PLOTS; TWIN SURROGATE (TS);

MULTIVARIABLE SYSTEMS;

ALGORITHM; ARTICLE; BIOLOGICAL MODEL; BIOPHYSICS; DEPTH PERCEPTION; EYE MOVEMENT; HUMAN; PHYSIOLOGY; STATISTICAL MODEL;

ALGORITHMS; BIOPHYSICS; EYE MOVEMENTS; HUMANS; MODELS, BIOLOGICAL; MODELS, STATISTICAL; VISION DISPARITY;

EID: 38149050682     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2007.2109     Document Type: Conference Paper

References (33)

1. Allaria, E., Arecchi, F. T., Di Garbo, A. & Meucci, R. 2001 Synchronization of homoclinic chaos. Phys. Rev. Lett. 86, 791-794. (doi:10.1103/PhysRevLett.86.791)
2. Allefeld, C. & Kurths, J. 2004 Testing for phase synchronization. Int. J. Bifurc. Chaos 14, 405-416. (doi:10.1142/S021812740400951X)
3. Blasius, B., Huppert, A. & Stone, L. 1999 Complex dynamics and phase synchronization in spatially extended ecological systems. Nature 399, 354-359. (doi:10.1038/20676)
4. Bohr, J., Bohr, H., Brunak, S., Cotterill, R. M., Fredholm, H., Lautrup, B. & Petersen, S. B. 1993 Protein structures from distance inequalities. J. Mol. Biol. 231, 861-869. (doi:10.1006/jmbi.1993.1332)
5. Ciuffreda, K. J. & Tannen, B. 1995 Eye movement basics for the clinician. St. Louis, MO: Mosby.
6. Coppola, D. & Purves, D. 1996 The extraordinarily rapid disappearance of entopic images. Proc. Natl Acad. Sci. USA 93, 8001-8004. (doi:10.1073/pnas.93.15.8001)
7. Eckmann, J.-P., Kamphorst, S. O. & Ruelle, D. 1987 Recurrence plots of dynamical systems. Europhys. Lett. 4, 973-977. (doi:10.1209/0295-5075/4/9/004)
8. Engbert, R. & Kliegl, R. 2003 Microsaccades uncover the orientation of covert attention. Vision Res. 43, 1035-1045. (doi:10.1016/S0042-6989(03)00084-1)
9. Engbert, R. & Kliegl, R. 2004 Microsaccades keep the eyes' balance. Psychol. Sci. 15, 431-436. (doi:10.1111/j.0956-7976.2004.00697.x)
10. Katok, A. & Hasselblatt, B. 1995 Introduction to the modern theory of dynamical systems. Cambridge, UK: Cambridge University Press.
11. Laubrock, J., Engbert, R. & Kliegl, R. 2005 Microsaccade dynamics during covert attention. Vision Res. 45, 721-730. (doi:10.1016/j.visres.2004.09.029)
12. Lorenz, E. N. 1963 Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130-141. (doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2)
13. Marwan, N., Wessel, N., Meyerfeldt, U., Schirdewan, A. & Kurths, J. 2002a Recurrence-plot-based measures of complexity and their application to heart-rate-variability data. Phys. Rev. E 66, 026702, 1-8. (doi:10.1103/PhysRevE.66.026702)
14. Marwan, N., Thiel, M. & Nowaczyk, N. R. 2002b Cross recurrence plot based synchronization of time series. Nonlin. Process. Geophys. 9, 325-331.
15. Mormann, F., Andrzejak, R. G., Kreuz, T., Rieke, C., David, P., Elger, C. E. & Lehnertz, K. 2003 Automated detection of a preseizure state based on a decrease in synchronization in intracranial electroencephalogram recordings from epilepsy patients. Phys. Rev. E 67, 021912, 1-10. (doi:10.1103/PhysRevE.67.021912)
16. Ott, E. 1993 Chaos in dynamical systems. Cambridge, UK: Cambridge University Press.
17. Palus, M. 1997 Detecting phase synchronization in noisy systems. Phys. Lett. A 235, 341-351. (doi:10.1016/S0375-9601(97)00635-X)
18. Palus, M. & Stefanovska, A. 2003 Direction of coupling from phases of interacting oscillators: an information-theoretic approach. Phys. Rev. E 67, 055201. (doi:10.1103/PhysRevE.67.055201)
19. Pikovsky, A., Rosenblum, M. & Kurths, J. 2001 Synchronization. Cambridge nonlinear science series, vol. 12. Cambridge, UK: Cambridge University Press.
20. Riggs, L. A., Ratliff, F., Cornsweet, J. C. & Cornsweet, T. N. 1953 The disappearance of steadily fixated visual test objects. J. Opt. Soc. Am. 43, 495-501.
21. Rodriguez, E., George, N., Lachaux, J.-P., Martinerie, J., Renault, B. & Varela, F. 1999 Perception's shadow: long-distance synchronization of human brain activity. Nature 397, 430-133. (doi:10.1038/17002)
22. Rolfs, M., Engbert, R. & Kliegl, R. 2005 Crossmodal coupling of oculomotor control and spatial attention in vision and audition. Exp. Brain Res. 166, 427-439. (doi:10.1007/s00221-005-2382-y)
23. Romano, M. C., Thiel, M., Kurths, J., Kiss, I. Z. & Hudson, J. L. 2005 Detection of synchronization for non-phase-coherent and non-stationary data. Europhys. Lett. 71, 466-472. (doi:10.1209/epl/i2005-10095-1)
24. Schäfer, C., Rosenblum, M., Kurths, J. & Abel, H.-H. 1998 Heartbeat synchronized with ventilation. Nature 392, 239-240. (doi:10.1038/32567)
25. Sowa, R., Chernihovskyi, A., Mormann, F. & Lehnertz, K. 2005 Estimating phase synchronization in dynamical systems using cellular neural networks. Phys. Rev. E 71, 061926, 1-6. (doi:10.1103/PhysRevE.71. 061926)
26. Sparks, D. L. 2002 The brainstem control of saccadic eye movements. Nat. Rev. Neurosci. 3, 952-964. (doi:10.1038/nrn986)
27. Tass, P., Rosenblum, M., Weule, J., Kurths, J., Pikovsky, A., Volkmann, J., Schnitzler, A. & Freund, H.-J. 1998 Detection of n : m phase locking from noisy data: application to magnetoencephalography. Phys. Rev. Lett. 81, 3291-3294. (doi:10.1103/PhysRevLett.81.3291)
28. Thiel, M., Romano, M. C., Kurths, J. & Read, P. 2004a Estimation of dynamical invariants without embedding by recurrence plots. Chaos 14, 234-243. (doi:10.1063/1.1667633)
29. Thiel, M., Romano, M. C. & Kurths, J. 2004b How much information is contained in a recurrence plot? Phys. Lett. A 330, 343-349. (doi:10.1016/j.physleta.2004.07.050)
30. Thiel, M., Romano, M. C., Kurths, J., Rolfs, M. & Kliegl, R. 2006 Twin surrogates to test for complex synchronisation. Eur. Phys. Lett. 75, 535-541. (doi:10.1209/epl/i2006-10147-0)
31. Van Leeuwen, P., Geue, D., Lange, S., Cysarz, D., Bettermann, H. & Grönemeyer, D. 2003 Is there evidence of fetal-maternal heart rate synchronization? BMC Physiol. 3, 2. (doi: 10.1186/1472-6793-3-2)
32. Weber Jr, C. L. & Zbilut, J. P. 1994 Dynamical assessment of physiological systems and states using recurrence plot strategies. J. Appl. Physiol. 76, 965-973.
33. Zhou, W. & King, W. M. 1998 Promotor commands encode monocular eye movements. Nature 393, 692-695. (doi:10.1038/31489)