Related papers: Interleaved lattice-based maximin distance designs
We show that the maximum number of unit distances or of diameters in a set of n points in d-dimensional Euclidean space is attained only by specific types of Lenz constructions, for all d >= 4 and n sufficiently large, depending on d. As a…
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,…
Consider the problem of constructing an experimental design, optimal for estimating parameters of a given statistical model with respect to a chosen criterion. To address this problem, the literature usually provides a single solution.…
In this paper, we give a method for constructing linear codes with small hulls by generalizing the method in \cite{LCD-T-matric}. As a result, we obtain many optimal Euclidean LCD codes and Hermitian LCD codes, which improve the previously…
Learning well-separated features in high-dimensional spaces, such as text or image embeddings, is crucial for many machine learning applications. Achieving such separation can be effectively accomplished through the dispersion of…
There exists a large literature of construction of convolutional codes with maximal or near maximal free distance. Much less is known about constructions of convolutional codes having optimal or near optimal column distances. In this paper,…
Gromov-Wasserstein distance has found many applications in machine learning due to its ability to compare measures across metric spaces and its invariance to isometric transformations. However, in certain applications, this invariance…
Enumeration of various types of lattice polygons and in particular polyominoes is of primary importance in many machine learning, pattern recognition, and geometric analysis problems. In this work, we develop a large deviation principle for…
It is proposed that the propagation of light in disordered photonic lattices can be harnessed as a random projection that preserves distances between a set of projected vectors. This mapping is enabled by the complex evolution matrix of a…
In this paper, we considier the limiting distribution of the maximum interpoint Euclidean distance $M_n=\max _{1 \leq i<j \leq n}\left\|\boldsymbol{X}_i-\boldsymbol{X}_j\right\|$, where $\boldsymbol{X}_1, \boldsymbol{X}_2, \ldots,…
An effective way to design structured coherent wave interference patterns that builds on the theory of coherent lattices, is presented. The technique combines prime number factorization in the complex plane with moir\'e theory to provide a…
Generative adversarial nets (GANs) and variational auto-encoders have significantly improved our distribution modeling capabilities, showing promise for dataset augmentation, image-to-image translation and feature learning. However, to…
The minimum distance of a code is an important concept in information theory. Hence, computing the minimum distance of a code with a minimum computational cost is a crucial process to many problems in this area. In this paper, we present…
Let $\mathcal{S}$ be a finite set of integer points in $\mathbb{R}^d$, which we assume has many symmetries, and let $P\in\mathbb{R}^d$ be a fixed point. We calculate the distances from $P$ to the points in $\mathcal{S}$ and compare the…
We develop a new method for constructing "good" designs for computer experiments. The method derives its power from its basic structure that builds large designs using small designs. We specialize the method for the construction of…
Maximum distance separable (MDS) codes are optimal where the minimum distance cannot be improved for a given length and code size. Twisted Reed-Solomon codes over finite fields were introduced in 2017, which are generalization of…
High dimensional integrals are abundant in many fields of research including quantum physics. The aim of this paper is to develop efficient recursive strategies to tackle a class of high dimensional integrals having a special product…
Merge trees are a type of graph-based topological summary that tracks the evolution of connected components in the sublevel sets of scalar functions. They enjoy widespread applications in data analysis and scientific visualization. In this…
Recent results of Grepstad and Lev are used to show that weighted cut-and-project sets with one-dimensional physical space and one-dimensional internal space are bounded distance equivalent to some lattice if the weight function $h$ is…
Many applications of computer vision rely on the alignment of similar but non-identical images. We present a fast algorithm for aligning heterogeneous images based on optimal transport. Our approach combines the speed of fast Fourier…