Abstract
When modeling complex systems, we usually encounter the following difficulties: partiality, large amount of data, and uncertainty of conclusions. It can be said that none of the known approaches solves these difficulties perfectly, especially in cases where we expect emergences in the complex system. The most common is the physical approach, sometimes reinforced by statistical procedures. The physical approach to modeling leads to a complicated description of phenomena associated with a relatively simple geometry. If we assume emergences in the complex system, the physical approach is not appropriate at all. In this article, we apply the approach of structural invariants, which has the opposite properties: a simple description of phenomena associated with a more complicated geometry (in our case pregeometry). It does not require as much data and the calculations are simple. The price paid for the apparent simplicity is a qualitative interpretation of the results, which carries a special type of uncertainty. Attention is mainly focused (in this article) on the invariant matroid and bases of matroid (M, BM) in combination with the Ramsey graph theory. In addition, this article introduces a calculus that describes the emergent phenomenon using two quantities—the power of the emergent phenomenon and the complexity of the structure that is associated with this phenomenon. The developed method is used in the paper for modeling and detecting emergent situations in cases of water floods, traffic jams, and phase transition in chemistry.
Highlights
Only some substantial issues of our developed method and its application are introduced: e structural invariants are defined by expressions (1) and (2)
Calculating #B and RN(#B, Y) in expression (12), we consider a perfect subgraph with #B nodes in a perfect graph Gp with RN(#B, Y) nodes. is case leads to the calculation of Δf(RN) and to ΔV(B + 1) in normalization procedure
Additive Representation of Drivers. e Possible Appearance of Emergent Situation (PAES) that corresponds to values of symptoms concentrated in the power of the emergent phenomenon (ΔHP(B + 1)) is associated with the result of the normalization procedure ΔV(B + 1)
Summary
In the small overview, some works that could serve as an information as to how we approach the modeling of complex systems is introduced. ese are main sources related to the topic of the article and ordered according to expert fields referred in the article. The introduced approaches include a large number of sources referring methods of artificial intelligence in connection with complex systems, especially with emergence phenomena in creative activities and problemsolving. From this field we quote only one source [29] in which are another references of the research line managed by John Gero. In this article [33], the authors have investigated a large area of resources based on Granger’s concept of causality and the concept of causality in dynamic systems They focus on the analysis of paleontological time series and refer to three approaches: Stochastic differential equations (SDEs). E mathematical background needed for our article is covered in [10, 32, 35,36,37]. e most important knowledge from these sources is a conceptual part of the theory of matroids combined with essential knowledge from Ramsey theory of graph
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