Emergence and complex systems: The contribution of dynamic graph theory

Abstract

International audienceEmergence and complex systems have been the topic of many papers and are still disputed concepts in many fields. This lack of consensus hinders the use of these concepts in practice, particularly in modelling. All definitions of emergence imply the existence of a hierarchical system: a system that can be observed, 15 measured and analysed at both macroscopic and microscopic levels. We argue that such systems are well described by mathematical graphs and, using graph theory, we propose an ontology (i.e. a set of consistent, formal concept definitions) of dynamic hierarchical systems capable of displaying emergence. Using graph theory enables formal definitions of system macro-state, micro-state and dynamic structural changes. From these definitions, we identify four major families of emergence that match existing definitions from the 20 literature. All but one depend on the relation between the observer and the system, and remind us that a major feature of most supposedly complex systems is our inability to describe them in full. The fourth definition is related to causality, in particular, to the ability of the system itself to create sources of change, independent from other external or internal sources. Feedback loops play a key role in this process. We propose that their presence is a necessary condition for a hierarchical system to be qualified as complex

Emergence Aiming Innovation for Sustainability

“…Most definitions of emergence share the assumption that emergence arises only in hierarchical systems made up of interacting components, which is why they can be described at macroscopic and microscopic levels [39]. In this hierarchical view, a component at a higher level may be represented by a complete system at a lower level.…”

“…Level theories often use the concept of emergence as a designation for the relationship between new or unpredictable properties at the top level [30]. The impossibility of explaining the macrostate from the microstates, that is, the lack of a link between the microstate and the macrostate, is called a strong emergency; conversely, a weak emergency is defined by the existence of an irreducible link between macro and microstates [39]. The importance of choosing the scale, is tied to it determining the causal model, because each scale corresponds to a particular causal model of the represented system [41]: "causal models are those that represent the influence of subparts of a system on other subparts, or over the system as a whole".…”

Development of methods for structural and logical model unification of metaknowledge for ontologies evolution managing of intelligent systems

“…It follows from the stated principles that structural models of all levels of knowledge representation can be considered as signal (pulse) linear digraphs [26]. The latter model inference as a conducting system of logic chains [27].…”

Topological Structures Influencing Kinetic Control in Small, Catalytically Closed, RNA Recombinase Systems Emerging from the Spontaneous Self-Organization of Heterogeneous Fragments of the Azoarcus Ribozyme

“…that are characteristic of these types of systems. While a precise definition of emergent complexity continues to be disputed throughout many disciplines, virtually every working definition discussed in the literature implies the existence of the sorts of hierarchical, self-organizational structures, required to produce these motifs [27].…”

“…properties at various levels of interaction-can be well described by mathematical graphs [27]. The branch of discrete mathematics concerned with the structures and properties of graphs is known as graph theory.…”