Mathematical modeling assumes that the object’s identity is well known and can be accessed at any time. However, in the previous chapter, we formalized the concept of elastic statesElastic states. Elastic statesElastic states arise from interacting elementsElement (interacting) with identities that depend on their specific context. According to such a concept, causal effects and causal properties can also be elastic. We introduce a complexity measurement providing information about both the inherent autonomy and variability of a system by estimating a persistent entropy in the measured data. With this method, one can determine the degree of causality between systems and visualize the boundary between objective understanding and observability. In addition, this method can be used to automatically extract features from time series data so that machine learning models can be trained.

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System Observability and \({\varvec{\varPhi}}_{{\varvec{S}}}\) Complexity

  • Juan Guillermo Diaz Ochoa

摘要

Mathematical modeling assumes that the object’s identity is well known and can be accessed at any time. However, in the previous chapter, we formalized the concept of elastic statesElastic states. Elastic statesElastic states arise from interacting elementsElement (interacting) with identities that depend on their specific context. According to such a concept, causal effects and causal properties can also be elastic. We introduce a complexity measurement providing information about both the inherent autonomy and variability of a system by estimating a persistent entropy in the measured data. With this method, one can determine the degree of causality between systems and visualize the boundary between objective understanding and observability. In addition, this method can be used to automatically extract features from time series data so that machine learning models can be trained.