Related papers: Optimal Designs for Spherical Harmonic Regression
The subject of this work is two treatment groups random coefficient regression models, in which observational units receive some group-specific treatments. We provide A- and D-optimality criteria for the estimation of the fixed parameter…
We construct spherical wavelets based on approximate identities that are directional, i.e. not rotation-invariant, and have an adaptive angular selectivity. The problem of how to find a proper representation of distinct kinds of details of…
The interference model has been widely used and studied in block experiments where the treatment for a particular plot has effects on its neighbor plots. In this paper, we study optimal circular designs for the proportional interference…
P. Baird and the second author studied harmonic morphisms from a three-dimensional simply-connected space form to a surface and obtained a complete local and global classification of them. In this paper, we obtain a description of all…
A sphere is a fundamental geometric object widely used in (computer aided) geometric design. It possesses rational parameterizations but no parametric polynomial parameterization exists. The present study provides an approach to the optimal…
Based on the concept of the cloak generating function, we propose a numerical method to compute the invisibility performance of various quadratic spherical cloaks and obtain optimal invisibility results. A non-ideal discrete model is used…
This paper traces the strong relations between experimental design and control, such as the use of optimal inputs to obtain precise parameter estimation in dynamical systems and the introduction of suitably designed perturbations in…
This work presents a novel framework for spherical mesh parameterization. An efficient angle-preserving spherical parameterization algorithm is introduced, which is based on dynamic Yamabe flow and the conformal welding method with solid…
This study is devoted to a detailed numerical testing of the analytical results obtained recently for the $M_t$-scaling of the parameters of the Bose-Einstein correlation functions. Numerical testing of analytical results for the spectrum…
A common problem in Phase II clinical trials is the comparison of dose response curves corresponding to different treatment groups. If the effect of the dose level is described by parametric regression models and the treatments differ in…
We study random spherical harmonics at shrinking scales. We compare the mass assigned to a small spherical cap with its area, and find the smallest possible scale at which, with high probability, the discrepancy between them is small…
Order parameters based on spherical harmonics and Fourier coefficients already play a significant role in condensed matter research in the context of systems of spherical or point particles. Here, we extend these types of order parameter to…
In clinical trials, the response of a given subject often depends on the selected treatment as well as on some covariates. We study optimal approximate designs of experiments in the models with treatment and covariate effects. We allow for…
The spherical-radial decomposition (SRD) is an efficient method for estimating probabilistic functions and their gradients defined over finite-dimensional elliptical distributions. In this work, we generalize the SRD to infinite stochastic…
Spherical harmonics (SH) have been extensively used as a basis for analyzing the morphology of particles in granular mechanics. The use of SH is facilitated by mapping the particle coordinates onto a unit sphere, in practice often a…
We define spherical Heron triangles (spherical triangles with "rational" side-lengths and angles) and parametrize them via rational points of certain families of elliptic curves. We show that the congruent number problem has infinitely many…
During the last few years several new results on packing problems were obtained using a blend of tools from semidefinite optimization, polynomial optimization, and harmonic analysis. We survey some of these results and the techniques…
We provide a systematic treatment of $D$-optimal design for binary regression and quantal response models in toxicology studies. For the two-parameter case, we provide an analytical equation (WC equation) for computing the $D$-optimal…
The well-known spatial integration schemes in molecular electronic structure theory, immune to cusps and point singularities of some kind at atomic positions, use a set of weighting functions to split the integrand into a sum of…
We propose novel optimal designs for longitudinal data for the common situation where the resources for longitudinal data collection are limited, by determining the optimal locations in time where measurements should be taken. As for all…