DMS-EPSRC: The Dynamics and Structure of Multiway Networks

Cornell University, Ithaca NY

Investigators

Abstract

Network science is a widespread mathematical framework for interacting systems and connected data. Much of the power of network science comes from breaking down complex connectivity into basic structure: nodes that model entities and edges that connect two nodes at a time. For example, social relationships can be modeled as networks where individuals are nodes and edges correspond to friendship, family, or work relationships. Transportation systems, the Internet, and gene regulation can similarly be modeled by networks. This awarded project centers on the mathematical development of multiway networks, which model interactions between more than two entities at a time. The research will involve the development and theoretical analysis of new types of dynamical systems on multiway networks, including diffusions, random walks, and consensus formation to understand processes involving the spread of information or disease. The dynamics will be studied on empirical data and new mathematical models developed in the project, which will in turn lead to new algorithms for data science and machine learning. Much of the funding of this award goes to support a graduate student working on the topics of the award. Graphs or networks are a broadly used mathematical model for complex systems and relational data. The research in this award will advance the understanding of dynamics and structure of multiway networks, which go beyond graphs by directly modeling multiway interactions. The methodology is based on hypergraph and simplicial complex models of multiway networks, and studying random walks, diffusions, and consensus in the context of these models. The research is organized around four directions. The first is the development of random network models and the collection of empirical data for motivating and evaluating new dynamical systems. The second involves the theory and analysis of dynamics on hypergraphs. The third is based on new types of dynamics for simplicial complexes and how these differ from similar dynamics on hypergraphs. The fourth is the development of new data science and machine learning algorithms for multiway networks based on these dynamics, such as clustering and semi-supervised learning. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.