Complexity and Fisher information

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 61, Issue 4, 2000, Pages R3303-R3305

  Binder, P M ^a  

^a UNIVERSIDAD DE LOS ANDES   (Colombia)

Author keywords

[No Author keywords available]

Indexed keywords

FISHER INFORMATION MATRIX;

FISHER INFORMATION; HIERARCHICAL CLASSIFICATION; OBSERVER-BASED; THEORY OF MEASUREMENT; TRAJECTORY SPACE;

HIERARCHICAL SYSTEMS;

EID: 4243227939     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.61.R3303     Document Type: Article

References (21)

1. B. R. Frieden, Physics from Fisher Information: A Unification (Cambridge University Press, Cambridge, England, 1998).
2. B. R. Frieden, A. Plastino, A. R. Plastino, and B. H. Soffer, Phys. Rev. E 60, 48 (1999).
3. R. Badii and A. Politi, Complexity: Hierarchical Structure and Scaling in Physics (Cambridge University Press, Cambridge, England, 1997).
4. R. Badii and A. Politi, Phys. Rev. Lett. 78, 444 (1997).
5. R. A. Fisher, Philos. Trans. R. Soc. London 222, 309 (1922).
6. S. Kullback, Information Theory and Statistics (Wiley, New York, 1959).
7. G. V. Vstovsky, Phys. Rev. E 51, 975 (1995).
8. P. J. Brockwell and R. A. Davis, Introduction to Time Series and Forecasting (Springer, New York, 1996). Fisher information is related to the properties of maximum likelihood estimators.
9. L. Brillouin, Science and Information Theory (Academic Press, New York, 1956).
10. L. Jaeger and H. Kantz, Physica D 105, 79 (1997)
11. L. JaegerH. KantzJ. Phys. A 30, L567 (1997), and references therein.
12. F. Christiansen and A. Politi, Phys. Rev. E 51, 3811 (1995).
13. M. Mézard, G. Parisi, and M. A. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1986).
14. R. Rammal, G. Toulouse, and M. A. Virasoro, Rev. Mod. Phys. 58, 765 (1986).
15. See I. A. Campbell and L. de Arcangelis, Europhys. Lett. 13, 587 (1990) for a study of the configuration space of an Ising spin glass and its relation to its dynamics and dynamical phase transitions.
16. P. Grassberger, Z. Naturforsch. Teil A 43a, 671 (1988).
17. J. P. Crutchfield and K. Young, Phys. Rev. Lett. 63, 105 (1989).
18. J. P. Crutchfield and C. R. Shalizi, Phys. Rev. E 59, 275 (1999);C. R. Shalizi and J. P. Crutchfield, Santa Fe Institute, Working Paper No. WP-99-07-044, 1999 (unpublished). In these papers it is proved that epsilon-machines optimize prediction of the future, that the causal states of a process are a sufficient statistic for predicting the process, that they are simpler than any rival model which is as good at predicting, and that they have higher internal determinism than any rival model.
19. N. Perry and P.-M. Binder, Phys. Rev. E 60, 459 (1999).
20. J. P. Crutchfield, in Inside vs. Outside, edited by H. Atmanspacher (Springer, Berlin, 1994), pp. 234–272.
21. R. Badii, Europhys. Lett. 13, 599 (1990).