Data-enabled Science

Abstract Dimension reduction techniques for dynamical systems on networks are considered to promote our understanding of the original high-dimensional dynamics. One strategy of dimension reduction is to derive a low-dimensional dynamical system whose behavior approximates the observables of the original dynamical system that are weighted linear summations of the state variables at the different nodes.

Summary: Groundbreaking study at the University at Buffalo uses brain stimulation to assess how large-scale patterns of brain activity could vary between cognitive systems and across people. Our research at the University at Buffalo explores brain activity and its association with cognitive systems. Each cognitive system consists of a network of brain regions that are linked to different functions.

Abstract Interevent times in temporal contact data from humans and animals typically obey heavy-tailed distributions, which impacts contagion and other dynamical processes on networks. We theoretically show that distributions of interevent times heavier-tailed than exponential distributions are a consequence of the most basic metapopulation model used in epidemiology and ecology, in which individuals move from one patch to another according to the simple random walk.