Related papers: Interleaved lattice-based maximin distance designs
Experimental designs that spread out points apart from each other on projections are important for computer experiments when not necessarily all factors have substantial influence on the response. We provide a theoretical framework to…
Computer experiments are pivotal for modeling complex real-world systems. Maximizing information extraction and ensuring accurate surrogate modeling necessitates space-filling designs, where design points extensively cover the input domain.…
An $m$-distance set is a collection of points such that the distances between any two points have $m$ possible values. We use two different methods to construct large $m$-distance sets on the triangular lattices. One is to use the first m…
In this work we study the interleaving distance between merge trees from a combinatorial point of view. We use a particular type of matching between trees to obtain a novel formulation of the distance. With such formulation, we tackle the…
Computer simulations serve as powerful tools for scientists and engineers to gain insights into complex systems. Less costly than physical experiments, computer experiments sometimes involve large number of trials. Conventional design…
This paper studies the lattice agreement problem and proposes a stronger form, $\varepsilon$-bounded lattice agreement, that enforces an additional tightness constraint on the outputs. To formalize the concept, we define a quasi-metric on…
Lattice structures have great potential for several application fields ranging from medical and tissue engineering to aeronautical one. Their development is further speeded up by the continuing advances in additive manufacturing…
Sequential Latin hypercube designs have recently received great attention for computer experiments. Much of the work has been restricted to invariant spaces. The related systematic construction methods are inflexible while algorithmic…
Merge trees are fundamental structures in topological data analysis. Interleaving distance is a widely accepted metric for comparing merge trees, with applications in visualization and scientific computing. While a greedy algorithm exists…
Inspired by natural cellular materials such as trabecular bone, lattice structures have been developed as a new type of lightweight material. In this paper we present a novel method to design lattice structures that conform with both the…
A higher dimensional lattice space can be decomposed into a number of four-dimensional lattices called as layers. The higher dimensional gauge theory on the lattice can be interpreted as four-dimensional gauge theories on the multi-layer…
The notion of multidimensional quadrilateral lattice is introduced. It is shown that such a lattice is characterized by a system of integrable discrete nonlinear equations. Different useful formulations of the system are given. The…
Alternative novel measures of the distance between any two partitions of a n-set are proposed and compared, together with a main existing one, namely 'partition-distance' D(.,.). The comparison achieves by checking their restriction to…
We study multivariate integration over the $s$-dimensional unit cube in a weighted space of infinitely differentiable functions. It is known from a recent result by Suzuki that there exists a good quasi-Monte Carlo (QMC) rule which achieves…
This work investigates linear precoding over non-singular linear channels with additive white Gaussian noise, with lattice-type inputs. The aim is to maximize the minimum distance of the received lattice points, where the precoder is…
We obtain lower bound for the maximum distance between any three distinct points in an affine lattice which are close to a helix with small curvature and torsion.
We present a unified deterministic approach for experimental design problems using the method of interlacing polynomials. Our framework recovers the best-known approximation guarantees for the well-studied D/A/E-design problems with simple…
New types of designs called nested space-filling designs have been proposed for conducting multiple computer experiments with different levels of accuracy. In this article, we develop several approaches to constructing such designs. The…
The possibility of creating different geometries with the help of an extra synthetic dimension in optical lattices is studied. Additional linear potential and Raman assisted tunnelings are used to engineer well controlled tunnelings between…
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,…