Let x1, · · · ,xn be points randomly chosen from a set G ⊂ R and f(x) be a function. The Euclidean random matrix is given by Mn = (f(∥xi − xj∥))n×n where ∥ · ∥ is the Euclidean distance. When N is fixed and n → ∞ we prove that μ̂(Mn), the empirical distribution of the eigenvalues of Mn, converges to δ0 for a big class of functions of f(x). Assuming both N and n go to infinity proportionally, we ...

The Euclidean distance matrix (EDM) completion problem and the positive semidefinite (PSD) matrix completion problem are considered in this paper. Approaches to determine the location of a point in a linear manifold are studied, which are based on a referential coordinate set and a distance vector whose components indicate the distances from the point to other points in the set. For a given ref...

 This paper present unequal-sized facilities layout solutions generated by a genetic search program named LADEGA (Layout Design using a Genetic Algorithm). The generalized quadratic assignment problem requiring pre-determined distance and material flow matrices as the input data and the continuous plane model employing a dynamic distance measure and a material flow matrix are discussed. Computa...

On page 42, Table 1 should be numbered Table 3, and Table 2 should be numbered Table 4. On page 43, Table 6 should be numbered Table 1 and ordered in first position among the seven tables, Table 7 should be numbered Table 2 and ordered in second position among the seven tables, Table 3 should be numbered Table 5, Table 4 should be numbered Table 6, and Table 5 should be numbered Table 7. The Ta...

Recent work by J. Prades and myself on K ! is described. The rst part describes our method to connect in a systematic fashion the short-distance evolution with long-distance matrix-element calculations taking the scheme dependence of the short-distance evolution into account correctly. In the second part I show the results we obtain for the I = 1=2 rule in the chiral limit.

Let x1, · · · ,xn be points randomly chosen from a set G ⊂ R and f(x) be a function. A special Euclidean random matrix is given by Mn = (f(∥xi − xj∥))n×n. When p is fixed and n → ∞ we prove that μ̂(Mn), the empirical distribution of the eigenvalues of Mn, converges to δ0 for a big class of functions of f(x). Assuming both p and n go to infinity with n/p → y ∈ (0,∞), we obtain the explicit limit ...

A computer code and algorithm are developed for the computer perception of molecular symmetry. The code generates and uses the Euclidian distance matrices of molecular structures to generate the permutationinversion group of the molecule. The permutation-inversion group is constructed as the automorphism group of the Euclidian distance matrix. Applications to several molecular structures and fu...

This paper presents a new implementation of the co-VAT algorithm. We assume we have an m× n matrix D, where the elements of D are pair-wise dissimilarities betweenm row objectsOr and n column objectsOc. The union of these disjoint sets are (N = m + n) objects O. Clustering tendency assessment is the process by which a data set is analyzed to determine the number(s) of clusters present. In 2007,...

Given a pairwise dissimilarity matrix D of a set of n objects, visual methods (such as VAT) for cluster tendency assessment generally represent D as an n × n image I(D̃) where the objects are reordered to reveal hidden cluster structure as dark blocks along the diagonal of the image. A major limitation of such methods is the inability to highlight cluster structure in I(D̃) when D contains highly...

We present an efficient algorithm to find a realization of a (full) n × n squared Euclidean distance matrix in the smallest possible dimension. Most existing algorithms work in a given dimension: most of these can be transformed to an algorithm to find the minimum dimension, but gain a logarithmic factor of n in their worstcase running time. Our algorithm performs cubically in n (and linearly w...