Related papers: A heuristic approach for designing cyclic group co…
This short contribution presents a method for generating $N$-point spherical configurations with low mesh ratios. The method extends Caspar-Klug icosahedral point-grids to non-icosahedral nets through the use of planar barycentric…
This paper explores hierarchical clustering in the case where pairs of points have dissimilarity scores (e.g. distances) as a part of the input. The recently introduced objective for points with dissimilarity scores results in every tree…
Higher-order correlation functions are firmly established as a fundamental tool for the statistical analysis of clustering in modern galaxy surveys. It was demonstrated that they greatly enrich the information content extracted by two-point…
This article presents an efficient algorithm to generate a discrete uniform distribution on a set of $p$ elements using a biased random source for $p$ prime. The algorithm generalizes Von Neumann's method and improves computational…
Let $p$ be a prime number. In this paper, we discuss the structures of cyclic codes over the ring $ \mathbb{F}_p[u, v] / \langle u^k, v^2, uv-vu\rangle$. We find a unique set of generators for these codes. We also study the rank and the…
Hierarchical clustering is a powerful tool for exploratory data analysis, organizing data into a tree of clusterings from which a partition can be chosen. This paper generalizes these ideas by proving that, for any reasonable hierarchy, one…
We have developed a general Bayesian algorithm for determining the coordinates of points in a three-dimensional space. The algorithm takes as input a set of probabilistic constraints on the coordinates of the points, and an a priori…
In this paper, we study the problem of finding the Euclidean distance to a convex cone generated by a set of discrete points in $\mathbb{R}^n_+$. In particular, we are interested in problems where the discrete points are the set of feasible…
This paper concentrates on the homogeneous (conformal) model of Euclidean space (Horosphere) with subspaces that intuitively correspond to Euclidean geometric objects in three dimensions. Mathematical details of the construction and…
Stratified sampling is a fast and simple method to generate point sets with uniform distribution in hypercubes. However, for the most common paraxial stratfication it has the prominent drawback that the number of sampled points in n…
We introduce group surface codes, which are a natural generalization of the $\mathbb{Z}_2$ surface code, and equivalent to quantum double models of finite groups with specific boundary conditions. We show that group surface codes can be…
We give the parameters of any evaluation code on a smooth quadric surface. For hyperbolic quadrics the approach uses elementary results on product codes and the parameters of codes on elliptic quadrics are obtained by detecting a BCH…
We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our…
The aim of this paper is twofold. First, we introduce "resource constraints" as a general concept that covers many practical restrictions on experimental design. Second, for computing efficient exact designs of experiments under any…
Cutting plane methods, particularly outer approximation, are a well-established approach for solving nonlinear discrete optimization problems without relaxing the integrality of decision variables. While powerful in theory, their…
Clustering is a powerful tool in data analysis, but it is often difficult to find a grouping that aligns with a user's needs. To address this, several methods incorporate constraints obtained from users into clustering algorithms, but…
A new methodology is proposed for generating realizations of a random vector with values in a finite-dimensional Euclidean space that are statistically consistent with a data set of observations of this vector. The probability distribution…
We develop a novel clustering method for distributional data, where each data point is regarded as a probability distribution on the real line. For distributional data, it has been challenging to develop a clustering method that utilizes…
Getting a labeling of vertices close to the structure of the graph has been proved to be of interest in many applications e.g., to follow smooth signals indexed by the vertices of the network. This question can be related to a graph…
I provide methods of constructing elliptic and hyperelliptic curves over global fields with interesting rational points over the given fields or over large field extensions. I also provide a elliptic curves defined over any given number…