11 papers
Stability of localized solutions to lattice dynamical systems
Bocheng Ruan, Jack M. Hughes, Jason J. Bramburger
Localized patterns are spatially confined structures that arise in lattice dynamical systems and play an important role in physics, biology, and materials science. While their exis…
Learning graphons from data: Random walks, transfer operators, and spectral clustering
Stefan Klus, Jason J. Bramburger
Many signals evolve in time as a stochastic process, randomly switching between states over discretely sampled time points. Here we make an explicit link between the underlying sto…
Weighted Birkhoff Averages Accelerate Data-Driven Methods
Maria Bou-Sakr-El-Tayar, Jason J. Bramburger, Matthew J. Colbrook
Many data-driven algorithms in dynamical systems rely on ergodic averages that converge painfully slowly. One simple idea changes this: taper the ends. Weighted Birkhoff averages c…
Reconstruction of frequency-localized functions from pointwise samples via least squares and deep learning
A. Martina Neuman, Andres Felipe Lerma Pineda, Jason J. Bramburger +1
Recovering frequency-localized functions from pointwise data is a fundamental task in signal processing. We examine this problem from an approximation-theoretic perspective, focusi…
Bounding Escape Rates and Approximating Quasi-Stationary Distributions of Brownian Dynamics
Jason J. Bramburger
Throughout physics Brownian dynamics are used to describe the behaviour of molecular systems. When the Brownian particle is confined to a bounded domain, a particularly important q…
Data-Driven Stabilisation of Unstable Periodic Orbits of the Three-Body Problem
Owen M. Brook, Jason J. Bramburger, Davide Amato +1
Many different models of the physical world exhibit chaotic dynamics, from fluid flows and chemical reactions to celestial mechanics. The study of the three-body problem (3BP) and…