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Quantifying emergence in terms of persistent mutual information

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Ball, Robin, Diakonova, Marina and MacKay, R. S. (Robert Sinclair). (2010) Quantifying emergence in terms of persistent mutual information. Advances in Complex Systems, Vol.13 (No.3). pp. 327-338. ISSN 0219-5259

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Official URL: http://dx.doi.org/10.1142/S021952591000258X

Abstract

We define Persistent Mutual Information (PMI) as the Mutual (Shannon) Information between the past history of a system and its evolution significantly later in the future. This quantifies how much past observations enable long-term prediction, which we propose as the primary signature of (Strong) Emergent Behavior. The key feature of our definition of PMI is the omission of an interval of "present" time, so that the mutual information between close times is excluded: this renders PMI robust to superposed noise or chaotic behavior or graininess of data, distinguishing it from a range of established Complexity Measures. For the logistic map, we compare predicted with measured long-time PMI data. We show that measured PMI data captures not just the period doubling cascade but also the associated cascade of banded chaos, without confusion by the overlayer of chaotic decoration. We find that the standard map has apparently infinite PMI, but with well-defined fractal scaling which we can interpret in terms of the relative information codimension. Whilst our main focus is in terms of PMI over time, we can also apply the idea to PMI across space in spatially-extended systems as a generalization of the notion of ordered phases.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Divisions:	Faculty of Science > Mathematics Faculty of Science > Physics
Library of Congress Subject Headings (LCSH):	Dynamics, Mathematical physics, Self-Organizing Systems
Journal or Publication Title:	Advances in Complex Systems
Publisher:	World Scientific Publishing
ISSN:	0219-5259
Official Date:	June 2010
Volume:	Vol.13
Number:	No.3
Number of Pages:	12
Page Range:	pp. 327-338
Identification Number:	10.1142/S021952591000258X
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access
Funder:	Engineering and Physical Sciences Research Council (EPSRC), University of Warwick. Complexity Science Doctoral Training Centre
Grant number:	EP/E501311/1
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URI:	http://wrap.warwick.ac.uk/id/eprint/5588