Application of computational mechanics to the analysis of natural data: An example in geomagnetism

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 67, Issue 1 2, 2003, Pages 162031-1620315

  Clarke, Richard W ^a   Freeman, Mervyn P ^a   Watkins, Nicholas W ^a  

^a BRITISH ANTARCTIC SURVEY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRIC CURRENTS; SPURIOUS SIGNAL NOISE; SUN; TIME SERIES ANALYSIS;

COMPUTATIONAL MECHANICS;

GEOMAGNETISM;

EID: 0038056057     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (28)

1. R. Badii and A. Politi, Complexity-Hierarchical Structures and Scaling in Physics (Cambridge University Press, Cambridge, UK, 1999).
2. J.P. Crutchfield and K.A. Young, Phys. Rev. Lett. 63, 105 (1989).
3. C.R. Shalizi and J.P. Crutchfield, J. Stat. Phys. 104, 819 (2001).
4. J.P. Crutchfield, Physica D 75, 11 (1994).
5. C.R. Shalizi and J.P. Crutchfield, e-print arXiv.org/abs/cs.LG/0001027.
6. A.J. Palmer, C.W. Fairall, and W.A. Brewer, IEEE Trans. Geosci. Remote Sens. GE-38, 2056 (2000).
7. J.D. Pelletier and D.L. Turcotte, Adv. Geophys. 40, 91 (1999).
8. D. P. Feldman, Ph. D. thesis, University of California, Davis, 1998.
9. S.B. Lowen and M.C. Teich, Phys. Rev. E 47, 992 (1993).
10. M.B. Weissmann, Rev. Mod. Phys. 60, 537 (1988).
11. J.E. Borovsky, R.J. Nemzek, and R.D. Belian, J. Geophys. Res. 98, 3807 (1993).
12. 2n is required to prevent statistical fluctuations from dominating the identification of equivalence classes.
13. A. Witt, J. Kurths, F. Krause, and K. Fischer, Geophys. Astrophys. Fluid Dyn. 77, 79 (1994).
14. J.P. Crutchfield and K.A. Young, in Complexity, Entropy and the Physics of Information, edited by W.H. Zurek (Addison-Wesley, Reading, MA, 1990), p. 223.
15. J.P. Crutchfield, in Modeling Complex Phenomena, edited by L. Lam and V. Naroditsky (Springer-Verlag, Berlin, 1992), p. 66.
16. J.E. Hanson, Ph. D. thesis, University of California, Berkeley, 1993.
17. N. Perry and P.-M. Binder, Phys. Rev. E 60, 459 (1999).
18. K.A. Young, Ph. D, thesis, University of California, Santa Cruz, 1991.
19. H. Poirier, Science et Vie 1003, 56 (2001).
20. W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes, 2nd ed. (Cambridge University Press, Cambridge, 1996).
21. For the unbiased Poisson switch, see the discussions of the "random telegraph" in J. S. Bendat, Principles and Applications of Random Noise Theory (Wiley, New York, 1958); and of the Poisson switch in H.J. Jensen, Self-Organized Criticality (Cambridge University Press, Cambridge, 1998).
22. For the unbiased Poisson switch, see the discussions of the "random telegraph" in J. S. Bendat, Principles and Applications of Random Noise Theory (Wiley, New York, 1958); and of the Poisson switch in H.J. Jensen, Self-Organized Criticality (Cambridge University Press, Cambridge, 1998).
23. S.-I. Akasofu and S. Chapman, Solar-Terrestrial Physics (Oxford University Press, New York, 1972).
24. See H.J. Jensen, K. Christensen, and H.C. Fogedby, Phys. Rev. B 40, 7425 (1989), and also Ref. [21].
25. A.J. Smith, M.P. Freeman, M.G. Wickett, and B.D. Cox, J. Geophys. Res. 104, 12 351 (1999).
26. If we had been considering infinite sofic sequences this zone would be always be infinitely big because all structure would be resolved after a certain word length, and would continue to be resolvable. This does not usually apply to finite sofic sequences because beyond a certain threshold word length statistical fluctuations in the profiles are able to destroy the equivalence classes.
27. In an engineering context, one would usually settle for that model constructed by the highest level of analysis, whether or not it is on a plateau. This is not acceptable from a scientific perspective because there is no way to justify that such models are not totally arbitrary.
28. G.J. Chaitin, IEEE Trans. Inf. Theory IT-20, 10 (1974).