Cyber-physical systems (CPS) interweave computation, communication, and control to facilitate our interaction with the physical world. Drawing inspiration from biological systems, we define new theoretical foundations and master the spatio-temporal complexity of CPS in order to model, analyze, and optimize their operations. From microbial communities to neural connections and social networks, complex interdependent systems display multi-scale spatio-temporal patterns. We propose a new mathematical strategy for constructing compact yet accurate models of CPS that can capture their non-linear, non-Gaussian, and/or fractal structure through a minimum number of parameters while preserving a high degree of modeling fidelity and prediction accuracy. The benefits of this mathematical modeling are tested in the context of a cyber-physical systems approach to brain-machine interface for decoding human intention and describing muscle dynamics.
Harnessing the complexity of biological systems, we also discuss a statistical physics inspired framework for analyzing complex collectives. More precisely, we describe the dynamics of a collective group of agents moving and interacting in a three-dimensional space through a free-energy landscape. Based on the energy landscape, we quantify the missing information, emergence, self-organization, and complexity for a collective motion. Further, we exploit this energy model to describe and analyze the drug-drug interaction networks. We uncover functional drug categories along with the intricate relationships between them. Out of the 1141 drugs from the DrugBank 4.1 database, 85% of our analytical predictions are confirmed against current state of knowledge. This analysis enables us to identify unaccounted interactions and solve the drug-repositioning problem.
Despite significant research, we still face significant challenges concerning the multi-fractal geometry of time-varying complex (weighted) networks, the role of interaction intensity, the embedding of metric spaces and the design of reliable estimation algorithms. To address these issues, we introduce a reliable multi-fractal estimation approach for quantifying the structural complexity and the heterogeneity of complex networks. For the first time, we demonstrate that (i) the weights of complex networks and their underlying metric space play a key role in dictating the existence of multi-fractal scaling and (ii) the multi-fractal scaling can be localized in both space and scales. In addition, we show that the multi-fractal geometric characterization enables the construction of a scaling-based similarity metric and the identification of community structure in human brain connectome. The detected communities are accurately aligned with the brain connectivity patterns. This framework has no constraint on the target network and can be leveraged as a basis for both structural and dynamic analysis of networks in a wide spectrum of applications.