Related papers: Constructions of Large m-Distance Sets on Triangul…
Multidimensional record patterns are random sets of lattice points defined by means of a recursive stochastic construction. The patterns thus generated owe their richness to the fact that the construction is not based on a total order,…
It is widely believed that point sets in the plane which determine few distinct distances must have some special structure. In particular, such sets are believed to be similar to a lattice. This note considers two different ways to quantify…
The {\em bottleneck distance} is a natural measure of the distance between two finite point sets of equal cardinality, defined as the minimum over all bijections between the point sets of the maximum distance between any pair of points put…
A time series is a sequence of data items; typical examples are videos, stock ticker data, or streams of temperature measurements. Quite some research has been devoted to comparing and indexing simple time series, i.e., time series where…
Erd\H{o}s and Fishburn studied the maximum number of points in the plane that span $k$ distances and classified these configurations, as an inverse problem of the Erd\H{o}s distinct distances problem. We consider the analogous problem for…
We consider two or more simple symmetric walks on some graphs, e.g. the real line, the plane or the two dimensional comb lattice, and investigate the properties of the distance among the walkers.
Maximum distance separable (MDS) are constructed to required specifications. The codes are explicitly given over finite fields with efficient encoding and decoding algorithms. Series of such codes over finite fields with ratio of distance…
We consider the problem of determining the number of distinct distances between two point sets in $\mathbb{R}^2$ where one point set $\mathcal{P}_1$ of size $m$ lies on a real algebraic curve of fixed degree $r$, and the other point set…
Multidimensional Scaling (MDS) is a classic technique that seeks vectorial representations for data points, given the pairwise distances between them. However, in recent years, data are usually collected from diverse sources or have…
Most Machine Learning (ML) methods, from clustering to classification, rely on a distance function to describe relationships between datapoints. For complex datasets it is hard to avoid making some arbitrary choices when defining a distance…
In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We…
We propose simple schemes that can perfectly identify projective measurement apparatus secretly chosen from a finite set. Entanglements are used in these schemes both to make possible the perfect identification and to improve the efficiency…
Distance plays a fundamental role in measuring similarity between objects. Various visualization techniques and learning tasks in statistics and machine learning such as shape matching, classification, dimension reduction and clustering…
The linear extension diameter of a finite poset P is the maximum distance between a pair of linear extensions of P, where the distance between two linear extensions is the number of pairs of elements of P appearing in different orders in…
This paper is an investigation of a procedure for constructing lattices by means of taking the sum of a pair of isometric lattices. We present various general results pertaining to this construction and discuss several examples of it…
It has been known that the distribution of the random distances between two uniformly distributed points within a convex polygon can be obtained based on its chord length distribution (CLD). In this report, we first verify the existing…
Let $E \subset {\Bbb F}_q^d$, the $d$-dimensional vector space over a finite field with $q$ elements. Construct a graph, called the distance graph of $E$, by letting the vertices be the elements of $E$ and connect a pair of vertices…
Constant dimension codes, with a prescribed minimum distance, have found recently an application in network coding. All the codewords in such a code are subspaces of $\F_q^n$ with a given dimension. A computer search for large constant…
Basic properties of the center of distances of a set are investigated. Computation of the center for achievement sets is particularly aimed at. A new sufficient condition for the center of distances of the set of subsums of a fast…
We show that large subsets of vector spaces over finite fields determine certain point configurations with prescribed distance structure. More specifically, we consider the complete graph with vertices as the points of $A \subseteq…