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Article

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
Entropy 2017, 19(5), 230; https://doi.org/10.3390/e19050230
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))
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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MDPI and ACS Style

Biehl, M.; Ikegami, T.; Polani, D. Specific and Complete Local Integration of Patterns in Bayesian Networks. Entropy 2017, 19, 230. https://doi.org/10.3390/e19050230

AMA Style

Biehl M, Ikegami T, Polani D. Specific and Complete Local Integration of Patterns in Bayesian Networks. Entropy. 2017; 19(5):230. https://doi.org/10.3390/e19050230

Chicago/Turabian Style

Biehl, Martin, Takashi Ikegami, and Daniel Polani. 2017. "Specific and Complete Local Integration of Patterns in Bayesian Networks" Entropy 19, no. 5: 230. https://doi.org/10.3390/e19050230

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