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Title: Persistent mutual information
Author: Diakonova, Marina
ISNI:       0000 0004 2748 6135
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2012
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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 inde finitely 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 re ect 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.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Q Science (General) ; QC Physics