Related papers: Modified Rayleigh Conjecture for static problems
Radar uncertainty principle indicates that there is an inherent invariance in the product of the time-delay and Doppler-shift measurement accuracy and resolution which can be tuned by the waveform at transmitter. In this paper, based on the…
We study the energy critical wave equation in 3 dimensions around a single soliton. We obtain energy boundedness (modulo unstable modes) for the linearised problem. We use this to construct scattering solutions in a neighbourhood of…
This paper studies the continuous-time reinforcement learning (RL) for optimal switching problems across multiple regimes. We consider a type of exploratory formulation under entropy regularization where the agent randomizes both the timing…
Detection of scattered light can determine the susceptibility of dielectrics. Such imaging normally holds Rayleigh's limit: details finer than the wavelength of the incident light cannot be determined from the far-field zone. We show that…
Sample-based Bayesian inference provides a route to uncertainty quantification in the geosciences, and inverse problems in general, though is very computationally demanding in the naive form that requires simulating an accurate computer…
The problem of substructure characteristic modes is developed using a scattering matrix-based formulation, generalizing subregion characteristic mode decomposition to arbitrary computational tools. It is shown that the modes of the…
The correction to Maxwell-Boltzmann's velocity distribution law is obtained in the framework of the modified special relativity theory. The detection of velocity and velocity rate distributions for thermal molecules or atoms or other…
Semi-analytic expressions for the static limit of the T-matrix for electromagnetic scattering are derived for a circular torus, expressed in bases of both toroidal and spherical harmonics. The scattering problem for an arbitrary static…
Time Resolved Correlation (TRC) is a recently introduced light scattering technique that allows to detect and quantify dynamic heterogeneities. The technique is based on the analysis of the temporal evolution of the speckle pattern…
We derive a Cram\'er-Rao lower bound for the variance of Floquet multiplier estimates that have been constructed from stable limit cycles perturbed by noise. To do so, we consider perturbed periodic orbits in the plane. We use a periodic…
In the context of nonparametric Bayesian estimation a Markov chain Monte Carlo algorithm is devised and implemented to sample from the posterior distribution of the drift function of a continuously or discretely observed one-dimensional…
The transition-matrix ($T$-matrix) approach provides a general formalism to study scattering problems in various areas of physics, including acoustics (scalar fields) and electromagnetics (vector fields), and is related to the theory of the…
This review article provides an overview of random matrix theory (RMT) with a focus on its growing impact on the formulation and inference of statistical models and methodologies. Emphasizing applications within high-dimensional statistics,…
We prove the existence of a unique unstable strong solution in the sense of $L^1$-norm for an abstract Rayleigh--Taylor (RT) problem arising from stratified viscous fluids in Lagrangian coordinates based on a bootstrap instability method.…
A machine-learning strategy for investigating the stability of fluid flow problems is proposed herein. The goal is to provide a simple yet robust methodology to find a nonlinear mapping from the parametric space to an indicator representing…
The Misspecification-Resistant Information Criterion (MRIC) proposed in [H.-L. Hsu, C.-K. Ing, H. Tong: On model selection from a finite family of possibly misspecified time series models. The Annals of Statistics. 47 (2), 1061--1087…
Markov chain Monte Carlo(MCMC) is a popular approach to sample from high dimensional distributions, and the asymptotic variance is a commonly used criterion to evaluate the performance. While most popular MCMC algorithms are reversible,…
We introduce a Monte-Carlo algorithm for the simulation of charged particles moving in the continuum. Electrostatic interactions are not instantaneous as in conventional approaches, but are mediated by a constrained, diffusing electric…
This paper addresses the inverse scattering problem for Maxwell's equations. We first show that a bianisotropic scatterer can be uniquely determined from multi-static far-field data through the factorization analysis of the far-field…
We present a novel numerical method for solving the anisotropic diffusion equation in magnetic fields confined to a periodic box which is accurate and provably stable. We derive energy estimates of the solution of the continuous initial…