Related papers: Average shadowing revisited
We study a special type of shadowing (DSP) of chain transitive continuous self-maps of compact Hausdorff spaces. We prove some basic properties of DSP. As application of DSP, we obtain sufficient conditions for a statistical variant of…
Consider a panel data setting where repeated observations on individuals are available. Often it is reasonable to assume that there exist groups of individuals that share similar effects of observed characteristics, but the grouping is…
In this computational paper, we perform sensitivity analysis of long-time (or ensemble) averages in the chaotic regime using the shadowing algorithm. We introduce automatic differentiation to eliminate the tangent/adjoint equation solvers…
Recently there has been substantial interest in spectral methods for learning dynamical systems. These methods are popular since they often offer a good tradeoff between computational and statistical efficiency. Unfortunately, they can be…
We discuss whether classical examples of dynamical systems satisfying the shadowing property also satisfy the shadowing property for the induced map on the hyperspace of continua, obtaining both positive and negative results. We prove that…
We use Lyapunov type functions to give new conditions under which a homeomorphism of a compact metric space has the shadowing property. These conditions are applied to establish the topological stability of some homeomorphisms with…
Efficiently learning expectation values of unknown quantum states via classical shadows has become an important primitive in both theoretical and experimental aspects of quantum computation. Typically, classical shadow protocols involve…
This paper studies topological definitions of chain recurrence and shadowing for continuous endomorphisms of topological groups generalizing the relevant concepts for metric spaces. It is proved that in this case the sets of chain recurrent…
We study the collective behaviour of an ensemble of coupled motile elements whose interactions depend on time and are alternatively attractive or repulsive. The evolution of interactions is driven by individual internal variables with…
We revisit the classic stability problem of the buckling of an inextensible, axially compressed beam on a nonlinear elastic foundation with a semi-analytical approach to understand how spatially localized deformation solutions emerge in…
This paper presents a novel method of foreground segmentation that distinguishes moving objects from their moving cast shadows in monocular image sequences. The models of background, edge information, and shadow are set up and adaptively…
Recent image protection mechanisms such as Glaze and Nightshade introduce imperceptible, adversarially designed perturbations intended to disrupt downstream text-to-image generative models. While their empirical effectiveness is known, the…
Identifying and suppressing unknown disturbances to dynamical systems is a problem with applications in many different fields. Here we present a model-free method to identify and suppress an unknown disturbance to an unknown system based…
Domain generalization aims to learn an invariant model that can generalize well to the unseen target domain. In this paper, we propose to tackle the problem of domain generalization by delivering an effective framework named Variational…
We present a perturbative technique for modeling the scattering of light by a nonlinear material. This approach eliminates the need for an iterative algorithm to solve the fully coupled nonlinear problem. We demonstrate its effectiveness in…
We present a generalization of the coupled dipole method to the scattering of light by arbitrary periodic structures. This new formulation of the coupled dipole method relies on the same direct-space discretization scheme that is widely…
We study expansivity and the shadowing property for finitely generated group actions on metric spaces. We consider the projecting and lifting problems for actions having these properties. We prove that every expansive action with the…
A tiling is a cover of R^d by tiles such as polygons that overlap only on their borders. A patch is a configuration consisting of finitely many tiles that appears in tilings. From a tiling, we can construct a dynamical system which encodes…
We present a differentiable framework to adaptively compute 4D illumination conditions with respect to an object, for efficient, high-quality simultaneous acquisition of its shape and reflectance, with a unified spatial-angular structured…
Dynamic substructuring (DS) methods encompass a range of techniques to decompose large structural systems into multiple coupled subsystems. This decomposition has the principle benefit of reducing computational time for dynamic simulation…