Scaffolding of Complex Systems Data
Complex systems, in many different scientific sectors, show coarse-grain properties at different levels of magnification. Discrete data sequences generated by such systems call for the relevant tools for their classification and analysis. We show that dis
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Abstract Complex systems, in many different scientific sectors, show coarse-grain properties at different levels of magnification. Discrete data sequences generated by such systems call for the relevant tools for their classification and analysis. We show that discrete time scale-dependent random walks on the graph models of relational databases can be generated by a variety of equivalence relations imposed between walks (e.g., composite functions, inheritance, property relations, ancestor– descendant relations, data queries, address allocation and assignment polices). The Green function of diffusion process induced by the random walks allows to define scale-dependent geometry. Geometric relations on databases can guide the data interpretation. In particular, first passage times in a urban spatial network help to evaluate the tax assessment value of land. We also discuss a classification scheme of growth laws which includes human aging, tumor (and/or tissue) growth, logistic and generalized logistic growth, and the aging of technical devices. The proposed classification permits to evaluate the aging/failure of combined new bio-technical “manufactured products,” where part of the system evolves in time according to biological-mortality laws and part according to technical device behaviors. Moreover it suggests a direct relation between the mortality leveling-off for humans and technical devices and the observed small cure probability for large tumors.
1 Introduction There is an impressive number of experimental verifications, in many different scientific sectors, that coarse-grain properties of systems, with simple laws with respect to fundamental microscopic algorithms, emerge at different levels of magnification
P. Blanchard () • D. Volchenkov Faculty of Physics, Bielefeld University, Universitaetsstr. 25, 33615 Bielefeld, Germany e-mail: [email protected]; [email protected] V. Afraimovich et al. (eds.), Nonlinear Dynamics and Complexity, Nonlinear Systems and Complexity 8, DOI 10.1007/978-3-319-02353-3__7, © Springer International Publishing Switzerland 2014
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providing important tools for explaining and predicting new phenomena. Discrete data sequences obtained from observations of complex systems consisting of many interacting elementary parts are ubiquitous in the real world. The most of such systems are often considered computationally irreducible [52, 53] which means that the only way to decide about their evolution is to let them evolve in time. By capturing how the individual data units in the observed data sequences are related to each other, we can convert it into a relational database subjected to further investigations. In our work, we, first, propose a method of feature extraction for relational databases by introducing different equivalence relations on the set of walks over its graph model (Sect. 2) following [49], and, second, describe the generalization of the classification scheme of growth and aging of complex systems
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