Summary

Proceedings of the 2013 International Symposium on Nonlinear Theory and its Applications

2013

Session Number:B1L-A

Session:

Number:182

Information-theoretical applications of ordinal patterns

J.M. Amigó,  T. Aschenbrenner,  W. Bunk,  R. Monetti,  

pp.182-185

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.2.182

PDF download (352.1KB)

The symbolization of time series by means of ordinal patterns (i.e., permutations) have a number of advantages. One of them is that ordinal patterns are algebraic objects that, therefore, can be further operated with. The transcript of two ordinal patterns, which is the product of one of them by the inverse of the other, is a realization of this possibility. Transcripts have been already used to characterize the synchronization of coupled nonlinear oscillators and, more generally, to quantify the complexity of coupled time series. In this paper we use transcripts to reduce the dimensionality of the permutation conditional mutual information.

[1] J.M. Amigó, R. Monetti, T. Aschenbrenner, and W. Bunk, “Transcripts: An algebraic approach to coupled time series,” Chaos 22, 013105, 2012.

[2] C. Bandt, and B. Pompe, “Permutation entropy: A natural complexity measure for time series,” Physical Review Letters 88, 174102, 2002.

[3] T.M. Cover, J.A. Thomas, Elements of Information Theory (2nd edition), John Wiley, Hoboken, 2006.

[4] R. Monetti, W. Bunk, T. Aschenbrenner, and F. Jamitzky, “Characterizing synchronization in time series using information measures extracted from symbolic representations,” Physical Review E 79, 046207, 2009.

[5] R. Monetti, J.M. Amigó, Aschenbrenner, and W. Bunk, “Permutation complexity of interacting dynamical systems, European Physical Journal Special Topics 222 (to appear)

[6] R. Monetti, W. Bunk, T. Aschenbrenner, S. Springer, and J.M. Amigó, “Information direc- tionality in coupled time series using transcripts”, arXiv 1304.7613v1.

[7] M. Staniek, K. Lehnertz, Symbolic transfer entropy, Phys. Rev. Lett. 100 (2008) 158101.