Conceptual framework to enable early warning of relevant phenomena “Emerging phenomena and big data”

Graphs are commonly used to represent natural and man-made dynamic systems such as food webs, economic and social networks, gene regulation, and the internet. We describe a conceptual framework to enable early warning of relevant phenomena that is based on an artificial time-based, evolving network graph that can give rise to one or more recognizable structures. We propose to quantify the dynamics using the method of delays through Takens´ Theorem to produce another graph we call the Phase Graph. The Phase Graph enables us to quantify changes of the system that form a topology in phase space. Our proposed method is unique because it is based on dynamic system analysis that incorporates Takens´ Theorem, Graph Theory, and Franzosi-Pettini (F-P) theorem about topology and phase transitions. The F-P Theorem states that the necessary condition for phase transition is a change in the topology. By detecting a change in the topology that we represent as a set of M-order Phase Graphs, we conclude a corresponding change in the phase of the system. The onset of this phase change enables early warning of emerging relevant phenomena.