Balanced Hodge Laplacians optimize consensus dynamics over simplicial complexes.

Despite the vast literature on network dynamics, we still lack basic insights into dynamics on higher-order structures (e.g., edges, triangles, and more generally, k-dimensional "simplices") and how they are influenced through higher-order interactions.

Machine learning for the New York City power grid.

Power companies can benefit from the use of knowledge discovery methods and statistical machine learning for preventive maintenance. We introduce a general process for transforming historical electrical grid data into models that aim to predict the risk of failures for components and systems. These models can be used directly by power companies to assist with prioritization of maintenance and repair work.