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Entropy 2017, 19(5), 230; doi:10.3390/e19050230

Specific and Complete Local Integration of Patterns in Bayesian Networks

1
Araya Incorporation, 2F Mori 15 Building, 2-8-10 Toranomon, Minato-ku, Tokyo 105-0001, Japan
2
School of Computer Science, University of Hertfordshire, Hatfield AL10 9AB, UK
3
Department of General Systems Studies, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan
*
Author to whom correspondence should be addressed.
Academic Editor: Mikhail Prokopenko
Received: 19 March 2017 / Revised: 11 May 2017 / Accepted: 12 May 2017 / Published: 18 May 2017
(This article belongs to the Special Issue Complexity, Criticality and Computation (C³))

Abstract

We present a first formal analysis of specific and complete local integration. Complete local integration was previously proposed as a criterion for detecting entities or wholes in distributed dynamical systems. Such entities in turn were conceived to form the basis of a theory of emergence of agents within dynamical systems. Here, we give a more thorough account of the underlying formal measures. The main contribution is the disintegration theorem which reveals a special role of completely locally integrated patterns (what we call ι-entities) within the trajectories they occur in. Apart from proving this theorem we introduce the disintegration hierarchy and its refinement-free version as a way to structure the patterns in a trajectory. Furthermore, we construct the least upper bound and provide a candidate for the greatest lower bound of specific local integration. Finally, we calculate the ι -entities in small example systems as a first sanity check and find that ι -entities largely fulfil simple expectations. View Full-Text
Keywords: identity over time; Bayesian networks; multi-information; entity; persistence; integration; emergence; naturalising agency identity over time; Bayesian networks; multi-information; entity; persistence; integration; emergence; naturalising agency
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Biehl, M.; Ikegami, T.; Polani, D. Specific and Complete Local Integration of Patterns in Bayesian Networks. Entropy 2017, 19, 230.

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