The field of dynamical systems is being transformed by the mathematical tools and
algorithms emerging from modern computing and data science. First-principles derivations …

Koopman operators linearize nonlinear dynamical systems, making their spectral
information of crucial interest. Numerous algorithms have been developed to approximate …

One of the main challenges in molecular dynamics is overcoming the 'timescale barrier': in
many realistic molecular systems, biologically important rare transitions occur on timescales …

Every day, hundreds of thousands of people undergo general anesthesia. One hypothesis is
that anesthesia disrupts dynamic stability—the ability of the brain to balance excitability with …

This article presents a novel approach to analyzing quasiperiodically driven dynamical
systems. It presents a holistic data-driven framework for reconstructing such a system and …

Many physical processes display complex high-dimensional time-varying behavior, from
global weather patterns to brain activity. An outstanding challenge is to express high …

While spectral clustering algorithms for undirected graphs are well established and have
been successfully applied to unsupervised machine learning problems ranging from image …

The Koopman operator provides a linear perspective on non-linear dynamics by focusing on
the evolution of observables in an invariant subspace. Observables of interest are typically …

Koopman operator theory has gained interest as a framework for transforming nonlinear
dynamics on the state space into linear dynamics on abstract function spaces, which …

Objective. Deep brain stimulation is a treatment for medically refractory essential tremor. To
improve the therapy, closed-loop approaches are designed to deliver stimulation according …