NSF Award
2404617
A wide variety of systems of interest in science, technology, and medicine can be represented as networks, including the Internet, the power grid, transportation networks, social networks, biological and biochemical networks, and the contact networks between individuals over which diseases spread. This project focuses on the mathematical and computational modeling of networked systems and addresses three specific challenges at the forefront of current research. The first concerns the creation of accurate mathematical models of networks that can serve as a foundation for many other calculations, such as simulating realistic network structures when only limited data are available. The second focus is on practical methods for analyzing network structure and behavior using tools of information theory, which will allow us to quantify complexity and similarity between networks and processes on networks. The third focus is on improved methods for network ranking with guaranteed performance or faster performance, or that incorporate additional features such as variable depth of competition or applications to networks with higher-order interactions. Graduate students will be trained as part of the project. <br/><br/>This project will develop new mathematical tools for the modeling of network structure and processes taking place on networks, and the analysis of network data. The first of three research themes focuses on expressive yet solvable new models for network structure. This work will leverage recent developments in message passing methods to show how a large class of random graph models can be implicitly defined to directly mimic the local structure of any observed network. The second theme focuses on information-theoretic approaches for analyzing and understanding networks and network data. This work will develop new unbiased information-theoretic measures, improved approximations for computing measures for large system sizes, and generalizations to new classes of problems. The third theme focuses on new approaches for network ranking problems. One of the oldest of network problems, ranking has played a major role in technological advances in the 21st century, but has historically also been important in many other applications, such as consumer research, competition, and the study of social networks. Work under this theme will develop new mathematics and methods for a range of cases, including improved algorithms for rapid rank inference with provable performance, multimodal ranking and its applications, and new permutation models for ranking on networks with higher-order interactions.<br/><br/>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.
