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We propose to trace the dynamical motion of a shearing hot spot near the SgrA* source through a dynamical image reconstruction algorithm, StarWarps. Such a hot spot may form as the exhaust of magnetic reconnection in a current sheet near…

In dynamical systems theory, a fixed point of the dynamics is called nonhyperbolic if the linearization of the system around the fixed point has at least one eigenvalue with zero real part. The center manifold existence theorem guarantees…

In this paper, we present an adaptive step-size homotopy tracking method for computing bifurcation points of nonlinear systems. There are four components in this new method: 1) an adaptive tracking technique is developed near bifurcation…

In large-scale applications, such as machine learning, it is desirable to design non-convex optimization algorithms with a high degree of parallelization. In this work, we study the adaptive complexity of finding a stationary point, which…

Construction sites are challenging environments for autonomous systems due to their unstructured nature and the presence of dynamic actors, such as workers and machinery. This work presents a comprehensive panoptic scene understanding…

Many complex flows such as those arising from ocean plastics in geophysics or moving cells in biology are characterized by sparse and noisy trajectory datasets. We introduce techniques for identifying Lagrangian Coherent Structures (LCSs)…

This is a survey on the local structure about a fixed point of discrete finite-dimensional holomorphic dynamical systems, discussing in particular the existence of local topological conjugacies to normal forms, and the structure of local…

We present an novel algorithm for tracking massless solid particles in a divergence-free velocity field that is only available at discrete points in space and time such as those arising from a direct numerical simulation of Navier-Stokes.…

Robust bipedal locomotion in exoskeletons requires the ability to dynamically react to changes in the environment in real time. This paper introduces the hybrid data-driven predictive control (HDDPC) framework, an extension of the…

We present a scalable and efficient iterative solver for high-order hybridized discontinuous Galerkin (HDG) discretizations of hyperbolic partial differential equations. It is an interplay between domain decomposition methods and HDG…

We extend the recently developed discrete geometric singular perturbation theory to the non-normally hyperbolic regime. Our primary tool is the Takens embedding theorem, which provides a means of approximating the dynamics of particular…

Non-Hermitian systems with parity-time ($\mathcal{PT}$) symmetry and anti-$\mathcal{PT}$ symmetry give rise to exceptional points (EPs) with intriguing properties related to, e.g., chiral transport and enhanced sensitivity, due to the…

We introduce a non-parametric hierarchical Bayesian approach for open-ended 3D object categorization, named the Local Hierarchical Dirichlet Process (Local-HDP). This method allows an agent to learn independent topics for each category…

In this paper we apply the method of Lagrangian descriptors to explore the geometrical structures in phase space that govern the dynamics of dissipative systems. We demonstrate through many classical examples taken from the nonlinear…

Understanding the topological structure of phase space for dynamical systems in higher dimensions is critical for numerous applications, including the computation of chemical reaction rates and transport of objects in the solar system. Many…

Lagrangian coherent structures (LCSs) are material surfaces that shape finite-time tracer patterns in flows with arbitrary time dependence. Depending on their deformation properties, elliptic and hyperbolic LCSs have been identified from…

Nonequilibrium statistical models of point vortex systems are constructed using an optimal closure method, and these models are employed to approximate the relaxation toward equilibrium of systems governed by the two-dimensional Euler…

This paper introduces a novel Differential Dynamic Programming (DDP) algorithm for solving discrete-time finite-horizon optimal control problems with inequality constraints. Two variants, namely Feasible- and Infeasible-IPDDP algorithms,…

An algorithm for detecting unstable periodic orbits in chaotic systems [Phys. Rev. E, 60 (1999), pp. 6172-6175] which combines the set of stabilising transformations proposed by Schmelcher and Diakonos [Phys. Rev. Lett., 78 (1997), pp.…

We propose a new algorithm for real-time detection and tracking of elliptic patterns suitable for real-world robotics applications. The method fits ellipses to each contour in the image frame and rejects ellipses that do not yield a good…