Preprint Article Version 1 This version is not peer-reviewed

Specific and Complete Local Integration of Patterns in Bayesian Networks

Version 1 : Received: 21 March 2017 / Approved: 21 March 2017 / Online: 21 March 2017 (16:23:00 CET)

A peer-reviewed article of this Preprint also exists.

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

Journal reference: Entropy 2017, 19, 230
DOI: 10.3390/e19050230

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 i-entities in small example systems as a first sanity check and find that ι-entities largely fulfil simple expectations.

Subject Areas

identity over time; Bayesian networks; multi-information; entity; persistence; integration; emergence; naturalising agency

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