The Internet, social networks, and genetic networks are examples of large-scale systems composed by a large number of units coupled through a complex network of interactions. This proposal aims to improve our understanding of the relationship between the structure of a network and the performance of networked dynamical processes, such as the spread of diseases in human contact networks, the propagation of information in online social networks, and coordination protocols in robotic networks. From an engineering perspective, a central focus of this work will be the development of efficient strategies to design secure and efficient critical networked infrastructures. In particular, those factors that make a network efficient and/or resilient with respect to a particular dynamical process will be explored. For example, the following questions will be studied: What structural factors make a communication network efficient in the coordination of a group of robotic agents? What network properties are useful while containing the spread of a disease in a human contact network? Since networks are ubiquitous across science and engineering, developing efficient tools for network analysis and design is of great relevance to many scientific disciplines. The proposed research program will be complemented with a comprehensive educational agenda spanning K-12, undergraduate, and graduate level education at the University of Pennsylvania. At the level of K-12 education, the PI will teach a three-week intense course about Engineering Complex Networks to encourage high-school students to further pursue an education in STEM-related fields. This project would also support and train doctorate students in the field of complex networks; as well as undergraduate students working on short-term projects, with an emphasis on increasing retention rates of under-represented minorities in engineering.
During the last decade, Network Science has matured into an established research field, providing a plethora of tools for modeling and analyzing complex systems. In particular, the field of spectral graph theory has been instrumental in the development of a wide array of powerful network analysis techniques, such as spectral graph partitioning, community detection, and ranking techniques (including Google PageRank). Furthermore, spectral-graph properties are directly related to the dynamical behavior of many networked processes, such as synchronization of oscillators, multi-agent coordination, and viral spreading processes. The goal of this project is to develop a novel computational framework based on recent results from algebraic graph theory and real algebraic geometry to infer global spectral properties of dynamical relevance from local structural information. Theoretical advancements in this proposal will go hand-in-hand with the development of scalable algorithms for spectral analysis of massive networked systems. Furthermore, an important part of this proposal will be focused on developing efficient strategies to design secure and efficient networked dynamical systems. Examples of particular design problems that will be considered are the design of efficient topologies to facilitate in-network coordination in multi-agent robotic systems, as well as the design of network interventions to contain viral processes in human contact networks. During the course of this proposal, the PI will address a number of fundamental open theoretical problems, as well as explore the application of newly developed techniques to a diverse array of network control problems in collaborations with domain-specific experts.
