Diakonova, Marina (2012) Persistent mutual information. PhD thesis, University of Warwick.

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Abstract

We study Persistent Mutual Information (PMI), the information about the past that persists into the future as a function of the length of an intervening time interval. Particularly relevant is the limit of an infinite intervening interval, which we call Permanently Persistent MI. In the logistic and tent maps PPMI is found to be the logarithm of the global periodicity for both the cases of periodic attractor and multi-band chaos. This leads us to suggest that PPMI can be a good candidate for a measure of strong emergence, by which we mean behaviour that can be forecast only by examining a specific realisation. We develop the phenomenology to interpret PMI in systems where it increases indefinitely with resolution. Among those are area-preserving maps. The scaling factor r for how PMI grows with resolution can be written in terms of the combination of information dimensions of the underlying spaces. We identify r with the extent of causality recoverable at a certain resolution, and compute it numerically for the standard map, where it is found to reflect a variety of map features, such as the number of degrees of freedom, the scaling related to existence of different types of trajectories, or even the apparent peak which we conjecture to be a direct consequence of the stickiness phenomenon. We show that in general only a certain degree of mixing between regular and chaotic orbits can result in the observed values of r. Using the same techniques we also develop a method to compute PMI through local sampling of the joint distribution of past and future. Preliminary results indicate that PMI of the Double Pendulum shows some similar features, and that in area-preserving dynamical systems there might be regimes where the joint distribution is multifractal.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > Q Science (General) Q Science > QC Physics
Library of Congress Subject Headings (LCSH):	System theory, Stochastic processes, Mappings (Mathematics), Double pendulums
Official Date:	September 2012
Dates:	Date Event September 2012 Submitted
Institution:	University of Warwick
Theses Department:	Department of Physics ; Centre for Complexity Science
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Ball, R. C.; MacKay, R. S. (Robert Sinclair)
Extent:	vi, 228 leaves : illustrations.
Language:	eng

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