Moving frames of reference, relativity and invariance in transfer entropy and information dynamics

Entropy

Volumn 15, Issue 1, 2013, Pages 177-197

  Lizier, Joseph T ^a,b,c   Mahoney, John R ^d,e  

^a CSIRO   (Australia)

^b UNIVERSITY OF SYDNEY   (Australia)

^c MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

^d UNIVERSITY OF CALIFORNIA   (United States)

^e UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Cellular automata; Complex systems; Information dynamics; Information storage; Information theory; Information transfer; Transfer entropy

Indexed keywords

EID: 84873141556     PISSN: None     EISSN: 10994300     Source Type: Journal    
DOI: 10.3390/e15010177     Document Type: Article

References (36)

1. Halliday, D.; Resnick, R.; Walker, J. Fundamentals of Physics, 4th ed.; John Wiley & Sons: New York, NY, USA, 1993.
2. Cover, T.M.; Thomas, J.A. Elements of Information Theory; John Wiley & Sons: New York, NY, USA, 1991.
3. MacKay, D.J. Information Theory, Inference, and Learning Algorithms; Cambridge University Press: Cambridge, UK, 2003.
4. Lizier, J.T.; Prokopenko, M.; Zomaya, A.Y. Detecting Non-trivial Computation in Complex Dynamics. In Proceedings of the 9th European Conference on Artificial Life (ECAL 2007), Lisbon, Portugal, 10-14 September 2007; Almeidae Costa, F., Rocha, L.M., Costa, E., Harvey, I., Coutinho, A., Eds.; Springer: Berlin/Heidelberg, 2007; Vol. 4648, Lecture Notes in Computer Science, pp. 895-904.
5. Lizier, J.T.; Prokopenko, M.; Zomaya, A.Y. Local information transfer as a spatiotemporal filter for complex systems. Phys. Rev. E 2008, 77, 026110+.
6. Lizier, J.T.; Prokopenko, M.; Zomaya, A.Y. Information modification and particle collisions in distributed computation. Chaos 2010, 20, 037109+.
7. Lizier, J.T.; Prokopenko, M.; Zomaya, A.Y. Local measures of information storage in complex distributed computation. Inform. Sciences 2012, 208, 39-54.
8. Lizier, J.T. The local information dynamics of distributed computation in complex systems; Springer Theses, Springer: Berlin/Heidelberg, Germany, 2013.
9. Schreiber, T. Measuring Information Transfer. Phys. Rev. Lett. 2000, 85, 461-464.
10. Smith, M.A. Cellular automata methods in mathematical physics. PhD thesis, Massachusetts Institute of Technology, 1994.
11. Mitchell, M. Computation in Cellular Automata: A Selected Review. In Non-Standard Computation; Gramss, T., Bornholdt, S., Gross, M., Mitchell, M.; Pellizzari, T., Eds.; VCH Verlagsgesellschaft: Weinheim, Germany, 1998; pp. 95-140.
12. Wolfram, S. A New Kind of Science; Wolfram Media: Champaign, IL, USA, 2002.
13. Hanson, J.E.; Crutchfield, J.P. The Attractor-Basin Portait of a Cellular Automaton. J. Stat. Phys. 1992, 66, 1415-1462.
14. Grassberger, P. New mechanism for deterministic diffusion. Phys. Rev. A 1983, 28, 3666.
15. Grassberger, P. Long-range effects in an elementary cellular automaton. J. Stat. Phys. 1986, 45, 27-39.
16. Hanson, J.E.; Crutchfield, J.P. Computational mechanics of cellular automata: An example. Physica D 1997, 103, 169-189.
17. Wuensche, A. Classifying cellular automata automatically: Finding gliders, filtering, and relating space-time patterns, attractor basins, and the Z parameter. Complexity 1999, 4, 47-66.
18. Helvik, T.; Lindgren, K.; Nordahl, M.G. Local information in one-dimensional cellular automata. Proceedings of the International Conference on Cellular Automata for Research and Industry, Amsterdam; Sloot, P.M., Chopard, B., Hoekstra, A.G., Eds.; Springer: Berlin/Heidelberg, Germany, 2004; Vol. 3305, Lecture Notes in Computer Science, pp. 121-130.
19. Helvik, T.; Lindgren, K.; Nordahl, M.G. Continuity of Information Transport in Surjective Cellular Automata. Commun. Math. Phys. 2007, 272, 53-74.
20. Shalizi, C.R.; Haslinger, R.; Rouquier, J.B.; Klinkner, K.L.; Moore, C. Automatic filters for the detection of coherent structure in spatiotemporal systems. Phys. Rev. E 2006, 73, 036104.
21. Langton, C.G. Computation at the edge of chaos: phase transitions and emergent computation. Physica D 1990, 42, 12-37.
22. Mitchell, M.; Crutchfield, J.P.; Hraber, P.T. Evolving Cellular Automata to Perform Computations: Mechanisms and Impediments. Physica D 1994, 75, 361-391.
23. Crutchfield, J.P.; Feldman, D.P. Regularities unseen, randomness observed: Levels of entropy convergence. Chaos 2003, 13, 25-54.
24. Prokopenko, M.; Gerasimov, V.; Tanev, I. Evolving Spatiotemporal Coordination in a Modular Robotic System. In Ninth International Conference on the Simulation of Adaptive Behavior (SAB'06); Nolfi, S., Baldassarre, G., Calabretta, R., Hallam, J., Marocco, D., Meyer, J.A., Parisi, D., Eds.; Springer Verlag: Rome, Italy, 2006; Volume 4095, Lecture Notes in Artificial Intelligence, pp. 548-559.
25. Prokopenko, M.; Lizier, J.T.; Obst, O.;Wang, X.R. Relating Fisher information to order parameters. Phys. Rev. E 2011, 84, 041116+.
26. Mahoney, J.R.; Ellison, C.J.; James, R.G.; Crutchfield, J.P. How hidden are hidden processes? A primer on crypticity and entropy convergence. Chaos 2011, 21, 037112+.
27. Crutchfield, J.P.; Ellison, C.J.; Mahoney, J.R. Time's Barbed Arrow: Irreversibility, Crypticity, and Stored Information. Phys. Rev. Lett. 2009, 103, 094101.
28. Grassberger, P. Toward a quantitative theory of self-generated complexity. Int. J. Theor. Phys. 1986, 25, 907-938.
29. Bialek, W.; Nemenman, I.; Tishby, N. Complexity through nonextensivity. Physica A 2001, 302, 89-99.
30. Crutchfield, J.P.; Young, K. Inferring statistical complexity. Phys. Rev. Lett. 1989, 63, 105.
31. Shalizi, C.R. Causal Architecture, Complexity and Self-Organization in Time Series and Cellular Automata. PhD thesis, University of Wisconsin-Madison, 2001.
32. Lizier, J.T.; Prokopenko, M. Differentiating information transfer and causal effect. Eur. Phys. J. B 2010, 73, 605-615.
33. Shalizi, C.R.; Shalizi, K.L.; Haslinger, R. Quantifying Self-Organization with Optimal Predictors. Phys. Rev. Lett. 2004, 93, 118701.
34. Williams, P.L.; Beer, R.D. Nonnegative Decomposition of Multivariate Information 2010. arXiv:1004.2515.
35. Takens, F. Detecting strange attractors in turbulence. In Dynamical Systems and Turbulence, Warwick 1980; Rand, D.; Young, L.S., Eds.; Springer: Berlin/Heidelberg, Germany, 1981; Vol. 898, Lecture Notes in Mathematics, chapter 21, pp. 366-381.
36. Lizier, J.T. JIDT: An information-theoretic toolkit for studying the dynamics of complex systems. Available online: https://code.google.com/p/information-dynamics-toolkit/ (accessed on 15 November 2012).