Fréchet’s classical isometric embedding argument has evolved to become a major tool in the study of metric spaces. An important example of a Fréchet embedding is Bourgain’s embedding [4]. The authors have recently shown [2] that for every ε > 0 any n-point metric space contains a subset of size at least n1−ε which embeds into `2 with distortion O ( log(2/ε) ε ) . The embedding used in [2] is no...

We consider the problem of learning a measure of distance among vectors in a feature space and propose a hybrid method that simultaneously learns from similarity ratings assigned to pairs of vectors and class labels assigned to individual vectors. Our method is based on a generative model in which class labels can provide information that is not encoded in feature vectors but yet relates to per...

We examine the linear convergence rates of variants of the proximal point method for finding zeros of maximal monotone operators. We begin by showing how metric subregularity is sufficient for linear convergence to a zero of a maximal monotone operator. This result is then generalized to obtain convergence rates for the problem of finding a common zero of multiple monotone operators by consider...

In a robust parameter design (RPD) problem, the experimenter is interested to determine the values of con-trol factors such that responses will be robust or insensitive to variability of the noise factors. Response sur-face methodology (RSM) is one of the effective methods that can be employed for this purpose. Since quality of products or processes is usually evaluated through several quality ...

This paper,  applies the concept  of KM-fuzzy metric spaces and  introduces a novel concept of KM-fuzzy metric  graphs based on KM-fuzzy metric spaces.  This study, investigates the finite KM-fuzzy metric spaces with respect to metrics and KM-fuzzy metrics and constructs KM-fuzzy metric spaces on any given non-empty sets. It tries to  extend   the concept of KM-fuzzy metric spaces to  a larger ...

In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α,β) -metric admits no concurrent vector fields. We also prove that an L-reducible Finsler metric admitting a concurrent vector field reduces to a Landsberg metric.In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α,β) -metric admits no concurrent vector fi...

in this paper, we study a class of finsler metrics which contains the class of p-reducible andgeneral relatively isotropic landsberg metrics, as special cases. we prove that on a compact finsler manifold,this class of metrics is nothing other than randers metrics. finally, we study this class of finsler metrics withscalar flag curvature and find a condition under which these metrics reduce to r...

It is shown that most, but not all, of the four dimensional metrics in the MultiCentre family with integrable geodesic flow may be recognized as belonging to spatially homogeneous Bianchi type A metrics. We show that any diagonal bi-axial Bianchi II metric has an integrable geodesic flow, and that the simplest hyperkähler metric in this family displays a finite dimensional W-algebra for its obs...