Analysis of Multivariate High-Dimensional Complex Systems and Applications

Abstract

Complex systems are those having interactions among system states, where states are each considered as input or output variables. These interactions can produce diverse phenomena, such as hysteresis, chaos, positive and negative feedback, higher-order behavior, and so on. In this dissertation, we consider complex systems having both inputs and outputs and examine these using high dimensional model representation and dynamical systems theory. We define high dimensional model representation for systems having multiple inputs and multiple outputs (V-HDMR). This representation can be interpreted as a communication system having direct and indirect communication channels. When sparse, data requirements for reconstruction are dramatically reduced using compressive sensing. These principles can be exploited in learning or control applications. Equipped with analysis tools, we examine the regulatory network of the epithelial mesenchymal transition (EMT), a key biological process related to cellular detachment events occurring during metastasis. In particular, we define and characterize mathematical models of EMT and generate biological hypotheses. We test and confirm these hypotheses with extensive in vitro and in vivo experimentation. These results reveal EMT to possess a sensitive bistable toggle switch and pronounced hysteresis.