Since its popularization in the 1970s, Fiedler vector of a graph has become standard tool for clustering vertices graph. Recently, Mendel and Noar, Dumitriu Radcliffe, Radcliffe Williamson have introduced geometric generalizations vector. Motivated by questions stemming from their work, we provide structural characterizations when finite metric space can be isometrically embedded Hilbert space.

introduction: appropriate definition of the distance measure between diffusion tensors has a deep impact on diffusion tensor image (dti) segmentation results. the geodesic metric is the best distance measure since it yields high-quality segmentation results. however, the important problem with the geodesic metric is a high computational cost of the algorithms based on it. the main goal of this ...

Can humans recover metric structure from motion sequences or, as has been claimed by Todd and Bressan [(1990) Perception & Psychophysics, 48, 419-430], are they limited to recovering only relief structure? Two experiments were carried out to investigate this question. In a metric-structure task, the angular thresholds for discriminating two rotating bi-planar structures were approximately 91 de...

The present study aimed to examine the influence of musical expertise on the metric and semantic aspects of speech processing. In two attentional conditions (metric and semantic tasks), musicians listened to short sentences ending in trisyllabic words that were semantically and/or metrically congruous or incongruous. Both ERPs and behavioral data were analyzed and the results were compared to p...

In some scientific fields, a scaling is able to modify the topology of an observed object. Our goal in the present work is to introduce a new formalism adapted to the mathematical representation of this kind of phenomenon. To this end, we introduce a new metric structure the galactic spaces which depends on an ordered field extension of R. Moreover, some natural transformations of the category ...

In this work, we prove that metric spaces with uniform normal structure have a kind of intersection property, which is equivalent to reflexivity in Banach spaces.

A large body of results on the characteristics of human spatial vision suggests that space perception is distorted. Recent studies indicate that the geometry of visual space is best understood as Affine. If this is the case, it has far reaching implications on how 3D visualizations can be successfully employed. For instance, all attempts to build visualizations systems where users are expected ...