Related papers: Optimal Designs for Spherical Harmonic Regression
A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…
In this paper some new properties and computational tools for finding KL-optimum designs are provided. KL-optimality is a general criterion useful to select the best experimental conditions to discriminate between statistical models. A…
Linear regression models are among the models most used in practice, although the practitioners are often not sure whether their assumed linear regression model is at least approximately true. In such situations, only designs for which the…
The connection between spherical harmonics and symmetric tensors is explored. For each spherical harmonic, a corresponding traceless symmetric tensor is constructed. These tensors are then extended to include nonzero traces, providing an…
Delsarte-Goethals-Seidel showed that if $X$ is a spherical $t$-design with degree $s$ satisfying $t\geq 2s-2$, $X$ carries the structure of an association scheme. Also Bannai-Bannai showed that the same conclusion holds if $X$ is an…
We study the optimal design problem under second-order least squares estimation which is known to outperform ordinary least squares estimation when the error distribution is asymmetric. First, a general approximate theory is developed,…
Sliced Latin hypercube designs (SLHDs) are widely used in computer experiments with both quantitative and qualitative factors and in batches. Optimal SLHDs achieve better space-filling property on the whole experimental region. However,…
Spherically symmetric solutions of generic gravitational models are optimally, and legitimately, obtained by expressing the action in terms of the two surviving metric components. This shortcut is not to be overdone, however: a one-function…
We survey many of the important properties of spherically symmetric spacetimes as follows. We present several different ways of describing a spherically symmetric spacetime and the resulting metrics. We then focus our discussion on an…
The problem of resolving spherical harmonic components from numerical data defined on a rectangular grid has many applications, particularly for the problem of gravitational radiation extraction. A novel method due to Misner improves on…
In 3D single particle imaging with X-ray free-electron lasers, particle orientation is not recorded during measurement but is instead recovered as a necessary step in the reconstruction of a 3D image from the diffraction data. Here we use…
This paper describes an optimisation methodology that has been specifically developed for engineering design problems. The methodology is based on a Tabu search (TS) algorithm that has been shown to find high quality solutions with a…
In statistics, experimental designs are methods for making efficient experiments. E-optimal designs are the multisets of experimental conditions which minimize the maximum axis of the confidence ellipsoid of estimators. The aim of this…
Among the major difficulties that one may encounter when estimating parameters in a nonlinear regression model are the nonuniqueness of the estimator, its instability with respect to small perturbations of the observations and the presence…
We consider optimal non-sequential designs for a large class of (linear and nonlinear) regression models involving polynomials and rational functions with heteroscedastic noise also given by a polynomial or rational weight function. The…
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…
Utilizing spherical harmonic (SH) domain has been established as the default method of obtaining continuity over space in head-related transfer functions (HRTFs). This paper concerns different variants of extending this solution by…
Spherical spin glasses are canonical models for smooth random functions in high dimensions. In this review, we survey several interrelated lines of research on their geometric structure. We begin with results concerning critical points and…
We investigate several antipodal spherical designs on whether we can choose half of the points, one from each antipodal pair, such that they are balanced at the origin. In particular, root systems of type A, D and E, minimal points of Leech…
This paper presents a general approach to designing the isotropic spherical media with complex spatial structure that provide different types of imaging for different light rays. It is based on equivalence of the spherical medium and the…