Related papers: Construction of nested space-filling designs
The paper is devoted to developing subdifferential theory for set-valued mappings taking values in ordered infinite-dimensional spaces. This study is motivated by applications to problems of vector and set optimization with various…
Discussions of software design often refer to using "design spaces" to describe the spectrum of available design alternatives. This supports design thinking in many ways: to capture domain knowledge, to support a wide variety of design…
Various non-trivial spaces are becoming popular for embedding structured data such as graphs, texts, or images. Following spherical and hyperbolic spaces, more general product spaces have been proposed. However, searching for the best…
Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level…
The purpose of this work is two-fold. First, we introduce an efficient homogenization-based approach to perform topology optimization of coated structures with orthotropic infill material. By making use of the relaxed design space, we can…
Given a finite collection of two-dimensional tile types, the field of study concerned with covering the plane with tiles of these types exclusively has a long history, having enjoyed great prominence in the last six to seven decades. Much…
Supersaturated design (SSD) has received much recent interest because of its potential in factor screening experiments. In this paper, we provide equivalent conditions for two columns to be fully aliased and consequently propose methods for…
A supersaturated design is a design whose run size is not large enough for estimating all the main effects. The goodness of multi-level supersaturated designs can be judged by the generalized minimum aberration criterion proposed by Xu and…
We propose a set of compositional design patterns to describe a large variety of systems that combine statistical techniques from machine learning with symbolic techniques from knowledge representation. As in other areas of computer science…
Space-filling designs are important in computer experiments, which are critical for building a cheap surrogate model that adequately approximates an expensive computer code. Many design construction techniques in the existing literature are…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Combining the use of our data structure for characterizing feasible packings with our new classes of…
Distributing spatially located heterogeneous workloads is an important problem in parallel scientific computing. We investigate the problem of partitioning such workloads (represented as a matrix of non-negative integers) into rectangles,…
For paired comparison experiments involving competing options described by two-level attributes several different methods of constructing designs having block paired observations under the main effects model are presented. These designs are…
The two-layer computer simulators are commonly used to mimic multi-physics phenomena or systems. Usually, the outputs of the first-layer simulator (also called the inner simulator) are partial inputs of the second-layer simulator (also…
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…
Minimax designs provide a uniform coverage of a design space $\mathcal{X} \subseteq \mathbb{R}^p$ by minimizing the maximum distance from any point in this space to its nearest design point. Although minimax designs have many useful…
We introduce the concept of nested topological order in a class of exact quantum lattice Hamiltonian models with non-abelian discrete gauge symmetry. The topological order present in the models can be partially destroyed by introducing a…
Inversive geometry can be used to generate exactly self-similar space-filling sphere packings. We present a construction method in two dimensions and generalize it to search for packings in higher dimensions. We newly discover 29…
In this paper we introduce a new type of code, called projective nested cartesian code. It is obtained by the evaluation of homogeneous polynomials of a fixed degree on a certain subset of $\mathbb{P}^n(\mathbb{F}_q)$, and they may be seen…
Modeling folding surfaces with nonzero thickness is of practical interest for mechanical engineering. There are many existing approaches that account for material thickness in folding applications. We propose a new systematic and broadly…