相关论文: Rigorous numerics for fast-slow systems with one-d…

Quantum dynamics is of fundamental interest and has implications in quantum information processing. The four-point out-of-time-ordered correlator (OTOC) is traditionally used to quantify quantum information scrambling under many-body…

In this work we study the existence of mechanisms of transition to global chaos in a closed Friedmann-Robertson-Walker universe with a massive conformally coupled scalar field. We propose a complexification of the radius of the universe so…

Given copies of a quantum state $\rho$, a shadow tomography protocol aims to learn all expectation values from a fixed set of observables, to within a given precision $\epsilon$. We say that a shadow tomography protocol is triply efficient…

A bound-violation designates a case that the turn-around radius of a bound object exceeds the upper limit put by the spherical collapse model based on the standard $\Lambda$CDM paradigm. Given that the turn-around radius of a bound object…

Persistent homology is a popular tool in Topological Data Analysis. It provides numerical characteristics of data sets which reflect global geometric properties. In order to be useful in practice, for example for feature generation in…

Building models that comply with the invariances inherent to different domains, such as invariance under translation or rotation, is a key aspect of applying machine learning to real world problems like molecular property prediction,…

The presence of silicate material in known rings in the Solar System raises the possibility of ring systems existing even within the snow line -- where most transiting exoplanets are found. Previous studies have shown that the detection of…

This paper proposes a computationally efficient framework, based on interval analysis, for rigorous verification of nonlinear continuous-time dynamical systems with neural network controllers. Given a neural network, we use an existing…

In this work, we present a symplectic integration scheme to numerically compute space debris motion. Such an integrator is particularly suitable to obtain reliable trajectories of objects lying on high orbits, especially geostationary ones.…

We study the dynamics of a pair of parametrically-driven coupled nonlinear mechanical resonators of the kind that is typically encountered in applications involving microelectromechanical and nanoelectromechanical systems (MEMS & NEMS). We…

We present a computational method for studying transverse homoclinic orbits for periodic solutions of delay differential equations, a phenomenon that we refer to as the \emph{Poincar\'{e} scenario}. The strategy is geometric in nature, and…

Efficient fidelity estimation of multiqubit quantum states is crucial to many applications in quantum information processing. However, to estimate the infidelity $\epsilon$ with multiplicative precision, conventional estimation protocols…

Snapshot matrices of hyperbolic equations have a slow singular value decay, resulting in inefficient reduced-order models. We develop on the idea of inducing a faster singular value decay by computing snapshots on a transformed spatial…

We present a fast and efficient hybrid algorithm for selecting exoplanetary candidates from wide-field transit surveys. Our method is based on the widely-used SysRem and Box Least-Squares (BLS) algorithms. Patterns of systematic error that…

The goal of the paper is to develop a systematic approach to the study of (perhaps degenerate) singularities of integrable systems and their structural stability. As the main tool, we use "hidden" system-preserving torus actions near…

We consider periodic homogenization of boundary value problems for quasilinear second-order ODE systems in divergence form of the type $a(x,x/\varepsilon,u(x),u'(x))'= f(x,x/\varepsilon,u(x),u'(x))$ for $x \in [0,1]$. For small…

Following Part~I, we consider a class of reversible systems and study bifurcations of homoclinic orbits to hyperbolic saddle equilibria. Here we concentrate on the case in which homoclinic orbits are symmetric, so that only one control…

This paper extends a recently proposed robust computational framework for constructing the boundary representation (brep) of the volume swept by a given smooth solid moving along a one parameter family $h$ of rigid motions. Our extension…

The co-varying physical couplings (CPC) framework states that physical parameters like the speed of light in vacuum $c$, the Newtonian constant $G$, and the cosmological constant $\Lambda$ could indeed vary with the spacetime coordinates…

By varying a parameter of a one-dimensional piecewise smooth map, stable periodic orbits are observed. In this paper, complete analytic characterization of these stable periodic orbits is obtained. An interesting relationship between the…