Unraveling Hidden Major Factors by Breaking Heterogeneity into Homogeneous Parts within Many-System Problems.

For a large ensemble of complex systems, a Many-System Problem (MSP) studies how heterogeneity constrains and hides structural mechanisms, and how to uncover and reveal hidden major factors from homogeneous parts. All member systems in an MSP share common governing principles of dynamics, but differ in idiosyncratic characteristics. A typical dynamic is found underlying response features with respect to covariate features of quantitative or qualitative data types. Neither all-system-as-one-whole nor individual system-specific functional structures are assumed in such response-vs-covariate (Re-Co) dynamics. We developed a computational protocol for identifying various collections of major factors of various orders underlying Re-Co dynamics. We first demonstrate the immanent effects of heterogeneity among member systems, which constrain compositions of major factors and even hide essential ones. Secondly, we show that fuller collections of major factors are discovered by breaking heterogeneity into many homogeneous parts. This process further realizes Anderson's "More is Different" phenomenon. We employ the categorical nature of all features and develop a Categorical Exploratory Data Analysis (CEDA)-based major factor selection protocol. Information theoretical measurements-conditional mutual information and entropy-are heavily used in two selection criteria: C1-confirmable and C2-irreplaceable. All conditional entropies are evaluated through contingency tables with algorithmically computed reliability against the finite sample phenomenon. We study one artificially designed MSP and then two real collectives of Major League Baseball (MLB) pitching dynamics with 62 slider pitchers and 199 fastball pitchers, respectively. Finally, our MSP data analyzing techniques are applied to resolve a scientific issue related to the Rosenberg Self-Esteem Scale.