Related papers: Space-filling lattice designs for computer experim…
This paper investigates quasi-Monte Carlo (QMC) integration of Lebesgue integrable functions with respect to a density function over $\mathbb{R}^s$. We extend the construction-free median QMC rule proposed by Goda and L'ecuyer (SIAM J. Sci.…
Given a set of $n$ points in the plane, the Unit Disk Cover (UDC) problem asks to compute the minimum number of unit disks required to cover the points, along with a placement of the disks. The problem is NP-hard and several approximation…
We consider the approximate recovery of multivariate periodic functions from a discrete set of function values taken on a rank-$s$ integration lattice. The main result is the fact that any (non-)linear reconstruction algorithm taking…
Lattice networks are indispensable to study heterogeneous materials such as concrete or rock as well as textiles and woven fabrics. Due to the discrete character of lattices, they quickly become computationally intensive. The QuasiContinuum…
Quasi-set theory was proposed as a mathematical context to investigate collections of indistinguishable objects. After presenting an outline of this theory, we define an algebra that has most of the standard properties of an orthocomplete…
We demonstrate single site addressability in a two-dimensional optical lattice with 600 nm lattice spacing. After loading a Bose-Einstein condensate in the lattice potential we use a focused electron beam to remove atoms from selected…
Quasi-Monte Carlo algorithms are studied for designing discrete approximations of two-stage linear stochastic programs. Their integrands are piecewise linear, but neither smooth nor lie in the function spaces considered for QMC error…
We propose a new class of space-filling designs called rotated sphere packing designs for computer experiments. The approach starts from the asymptotically optimal positioning of identical balls that covers the unit cube. Properly scaled,…
A new type of experiment with joint considerations of quantitative and sequence factors is recently drawing much attention in medical science, bio-engineering, and many other disciplines. The input spaces of such experiments are…
The continuous 1D defects of an isotropic homogeneous material in a flat 3D space are classified by the Volterra process construction method. We employ the same method to classify the continuous 2D defects of a vacuum in a 4D maximally…
We study multivariate numerical integration of smooth functions in weighted Sobolev spaces with dominating mixed smoothness $\alpha\geq 2$ defined over the $s$-dimensional unit cube. We propose a new quasi-Monte Carlo (QMC)-based quadrature…
Importance Sampling (IS), an effective variance reduction strategy in Monte Carlo (MC) simulation, is frequently utilized for Bayesian inference and other statistical challenges. Quasi-Monte Carlo (QMC) replaces the random samples in MC…
Space-filling designs are commonly used in computer experiments to fill the space of inputs so that the input-output relationship can be accurately estimated. However, in certain applications such as inverse design or feature-based…
We give a new completion for the quasi-uniform spaces. We call the whole procedure {\it $\tau$-completion} and the new space {\it $\tau$-complement of the given}. The basic result is that every $T_{_0}$ quasi-uniform space has a…
This paper studies a generalization of hyperinterpolation over the high-dimensional unit cube. Hyperinterpolation of degree \( m \) serves as a discrete approximation of the \( L_2 \)-orthogonal projection of the same degree, using Fourier…
The topological charge density and topological susceptibility are determined by multi-probing approximation using overlap fermions in quenched SU(3) gauge theory. Then we investigate the topological structure of the quenched QCD vacuum, and…
A (q,k,t)-design matrix is an m x n matrix whose pattern of zeros/non-zeros satisfies the following design-like condition: each row has at most q non-zeros, each column has at least k non-zeros and the supports of every two columns…
Using quantum Monte Carlo (QMC) simulations we study the ground-state properties of the one-dimensional fermionic Hubbard model in traps with an underlying lattice. Since due to the confining potential the density is space dependent,…
The goal of this work is to lay the groundwork to construct and characterize a quantum device; which we refer to as a superfluid ring lattice; that could serve as a multi-qubit system in the future. Accordingly, a mathematical framework,…
The Kantorovich-Rubinshtein metric is an $L^1$-like metric on spaces of probability distributions that enjoys several serendipitous properties. It is complete separable if the underlying metric space of points is complete separable, and in…