Related papers: A general formulation for computing spherical heli…
Impact localisation on composite aircraft structures remains a significant challenge due to operational and environmental uncertainties, such as variations in temperature, impact mass, and energy levels. This study proposes a novel Gaussian…
We consider a kernel based harmonic analysis of "boundary," and boundary representations. Our setting is general: certain classes of positive definite kernels. Our theorems extend (and are motivated by) results and notions from classical…
Kernel smoothing is a highly flexible and popular approach for estimation of probability density and intensity functions of continuous spatial data. In this role it also forms an integral part of estimation of functionals such as the…
The degrees of quantum coherence of cosmological perturbations of different spins are computed in the large-scale limit and compared with the standard results holding for a single mode of the electromagnetic field in an optical cavity. The…
The detailed modelling of stellar oscillations is a powerful approach to characterising stars. However, poor treatment of systematics in theoretical models leads to misinterpretations of stars. Here we propose a more principled statistical…
In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape…
In the macroscopic gravity approach to the averaging problem in cosmology, the Einstein field equations on cosmological scales are modified by appropriate gravitational correlation terms. We study the averaging problem within the class of…
In this pedagogically structured article, we describe a generalized harmonic formulation of the Einstein equations in spherical symmetry which is regular at the origin. The generalized harmonic approach has attracted significant attention…
Many three-dimensional spatial fields are anisotropic, with directions of rapid and slow variation that need not align with the coordinate axes. Standard Gaussian process kernels with Automatic Relevance Determination (ARD) capture only…
We study spherically symmetric perturbations determined by alternative theories of gravity to the gravitational field of a central mass in General Relativity. In particular, we focus on perturbations in the form of power laws and calculate…
In the noisy intermediate-scale quantum era, an important goal is the conception of implementable algorithms that exploit the rich dynamics of quantum systems and the high dimensionality of the underlying Hilbert spaces to perform tasks…
We introduce a technique to compute exact anelastic sensitivity kernels in the time domain using parsimonious disk storage. The method is based on a reordering of the time loop of time-domain forward/adjoint wave propagation solvers…
In Paper II [N. G. Phillips and B. L. Hu, previous abstract] we presented the details for the regularization of the noise kernel of a quantum scalar field in optical spacetimes by the modified point separation scheme, and a Gaussian…
We propose a class of spherical wavelet bases for the analysis of geophysical models and forthe tomographic inversion of global seismic data. Its multiresolution character allows for modeling with an effective spatial resolution that varies…
The quantization of gauge fields and gravitation on manifolds with boundary makes it necessary to study boundary conditions which involve both normal and tangential derivatives of the quantized field. The resulting one-loop divergences can…
We demonstrate that an effect other than anharmonicity can severely distort the spectroscopic signatures of quantum mechanical systems. This is done through an analytic calculation of the spectroscopic response of a simple system, a charged…
Quantum kernel methods are a promising branch of quantum machine learning, yet their effectiveness on diverse, high-dimensional, real-world data remains unverified. Current research has largely been limited to low-dimensional or synthetic…
In this paper, we compare two optimization algorithms using full Hessian and approximation Hessian to obtain numerical spherical designs through their variational characterization. Based on the obtained spherical design point sets, we…
In this article, we consider flat and curved Riemannian symmetric spaces in the complex case and we study their basic integral kernels, in potential and spherical analysis: heat, Newton, Poisson kernels and spherical functions, i.e. the…
Spherical harmonics provide a smooth, orthogonal, and symmetry-adapted basis to expand functions on a sphere, and they are used routinely in physical and theoretical chemistry as well as in different fields of science and technology, from…