Related papers: Frozen Gaussian approximation for high frequency w…
This paper concerns the propagation of high frequency wave-beams in highly turbulent atmospheres. Using a paraxial model of wave propagation, we show in the long-distance weak-coupling regime that the wavefields are approximately described…
We provide accurate expressions for the $s$-wave scattering length for a Gaussian potential well in one, two and three spatial dimensions. The Gaussian potential is widely used as a pseudopotential in the theoretical description of…
We consider the singular semiclassical initial value problem for the phase space Schrodinger equation. We approximate semiclassical quantum evolution in phase space by analyzing initial states as superpositions of Gaussian wave packets and…
Accurate propagation of orbital uncertainty is essential for a range of applications within space domain awareness. Adaptive Gaussian mixture-based approaches offer tractable nonlinear uncertainty propagation through splitting mixands to…
This paper introduces a method to approximate Gaussian process regression by representing the problem as a stochastic differential equation and using variational inference to approximate solutions. The approximations are compared with full…
Distributed estimation methods have recently been used to compute the maximum likelihood estimate of the precision matrix for large graphical Gaussian models. Our aim, in this paper, is to give a Bayesian estimate of the precision matrix…
In the article, new asymptotic approximation of the $n$th order is obtained and proposed to be used in calculations of radiation propagation without scattering in optically thick media; the asymptotic approximation is much simpler and more…
Fuzzy Transform (F-transform) has been introduced as an approximation method which encompasses both classical transforms and approximation methods studied in fuzzy modeling and fuzzy control. It has been proved that, under some conditions,…
Recently, Gaussian splatting has emerged as a strong alternative to NeRF, demonstrating impressive 3D modeling capabilities while requiring only a fraction of the training and rendering time. In this paper, we show how the standard Gaussian…
The sparse Beyesian learning (also referred to as Bayesian compressed sensing) algorithm is one of the most popular approaches for sparse signal recovery, and has demonstrated superior performance in a series of experiments. Nevertheless,…
We present an approach for adapting the Gaussian dispersion analysis (GDA) of optical materials to time-domain simulations. Within a GDA model, the imaginary part of a measured dielectric function is presented as a sum of Gaussian…
To alleviate the computational cost associated with on-the-fly ab initio semiclassical calculations of molecular spectra, we propose the single-Hessian thawed Gaussian approximation, in which the Hessian of the potential energy at all…
Gaussian variational approximation is a popular methodology to approximate posterior distributions in Bayesian inference especially in high dimensional and large data settings. To control the computational cost while being able to capture…
In this paper, a Bayesian fusion technique for remotely sensed multi-band images is presented. The observed images are related to the high spectral and high spatial resolution image to be recovered through physical degradations, e.g.,…
Examples with bound information on the regression function and density abound in many real applications. We propose a novel approach for estimating such functions by incorporating the prior knowledge on the bounds. Specially, a Gaussian…
Solutions to the stochastic wave equation on the unit sphere are approximated by spectral methods. Strong, weak, and almost sure convergence rates for the proposed numerical schemes are provided and shown to depend only on the smoothness of…
Gravitational wave detectors will need optimal signal-processing algorithms to extract weak signals from the detector noise. Most algorithms designed to date are based on the unrealistic assumption that the detector noise may be modeled as…
The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation…
At a horizontally homogeneous isothermal atmosphere approximation, we derive an ordinary six-order differential equation describing linear disturbances with consideration for heat conductivity and viscosity of medium. The wave problem may…
We propose a quantum algorithm that simulates the propagation of a light field through a weakly inhomogeneous medium. The wave equation in the paraxial approximation in inhomogeneous material takes the form of the Schr\"odinger equation…