In [Rao, SoCG 1999], it is shown that every n-point Euclidean metric with polynomial spread admits a Euclidean embedding with k-dimensional distortion bounded by O( √ log n log k), a result which is tight for constant values of k. We show that this holds without any assumption on the spread, and give an improved bound of O( √ log n(log k)). Our main result is an upper bound of O( √ log n log lo...

For a domain Ω ⊂ C, the Kerzman-Stein operator is the skewhermitian part of the Cauchy operator acting on L(bΩ), which is defined with respect to Euclidean measure. In this paper we compute the spectrum of the Kerzman-Stein operator for three domains whose boundaries consist of two circular arcs: a strip, a wedge, and an annulus. We also treat the case of a domain bounded by two logarithmic spi...

In this paper, block distance matrices are introduced. Suppose F is a square block matrix in which each block is a symmetric matrix of some given order. If F is positive semidefinite, the block distance matrix D is defined as a matrix whose (i, j)-block is given by Dij = Fii+Fjj−2Fij . When each block in F is 1 × 1 (i.e., a real number), D is a usual Euclidean distance matrix. Many interesting ...

This paper focuses on two main issues; first one is the impact of combination of multi-sensor images on the supervised learning classification accuracy using segment Fusion (SF). The second issue attempts to undertake the study of supervised machine learning classification technique of remote sensing images by using four classifiers like Parallelepiped (Pp), Mahalanobis Distance (MD), MaximumLi...

In this paper, we investigate the veracity of a basic premise, “that network distance is Euclidean”, assumed in a class of recently proposed techniques that embed Internet hosts in a Euclidean space for the purpose of estimating the delay or “distance” between them. Using the classical scaling method on a number of network distance measurement datasets, we observe “non-Euclidean-ness” in the ne...