Simplicial Dynamics

Higher-order organization of multivariate time series

Time series analysis has proven to be a powerful method to characterize several phenomena in biology, neuroscience and economics, and to understand some of their underlying dynamical features. Several methods have been proposed for the analysis of …

Connecting Hodge and Sakaguchi-Kuramoto: a mathematical framework for coupled oscillators on simplicial complexes

We formulate a general Kuramoto model on weighted simplicial complexes where phases oscillators are supported on simplices of any order k. Crucially, we introduce linear and non-linear frustration terms that are independent of the orientation of the …