Short proofs are given to various characterizations of the (circum-)Euclidean squared distance matrices. Linear preserver problems related to these matrices are discussed.

In this paper we present an implementation of a perceptual completion model performed in the three dimensional space of position and orientation of level lines of an image. We show that the space is equipped with a natural subriemannian metric. This model allows to perform disocclusion representing both the occluding and occluded objects simultaneously in the space. The completion is accomplish...

Motivated by the problem of cluster identification, we consider two multivariate normally distributed points. We seek to find the distribution of the squared Euclidean distance between these two point. Consequently, we find the corresponding distribution in the general case. We then reduce this distribution for special cases based on the mean and covariance.

Article history: Received 13 October 2007 Received in revised form 12 June 2008 Accepted 31 July 2008

The design a novel location aided routing protocol with the concept of baseline and distance minimization is presented in this paper. The protocol has been implemented successfully for a vehicular adhoc network and Manhattan model is utilized. The vehicular movement used a new concept of communication using minimization of distance from base line. The base line was drawn from source to destinat...

We introduce the notion of weak convexity in metric spaces, a generalization ordinary commonly used machine learning. It is shown that weakly convex sets can be characterized by closure operator and have unique decomposition into set pairwise disjoint connected blocks. give two generic efficient algorithms, an extensional intensional one for learning concepts study their formal properties. Our ...

We solve two related extremal-geometric questions in the n?dimensional space R?n equipped with maximum metric. First, we prove that size of a right-equidistant sequence points equals 2n+1?1. A is if each at same distance from all succeeding points. Second, number pairwise odd distances 2n. also obtain partial results for both n-dimensional R1n Manhattan distance.

In this paper, we derive some local a priori estimates for Ricci flow. This gives rise to some strong uniqueness theorems. As a corollary, let g(t) be a smooth complete solution to the Ricci flow on R, with the canonical Euclidean metric E as initial data, then g(t) is trivial, i.e. g(t) ≡ E.

In this paper we introduce metric-based means for the space of positive-definite matrices. The mean associated with the Euclidean metric of the ambient space is the usual arithmetic mean. The mean associated with the Riemannian metric corresponds to the geometric mean. We discuss some invariance properties of the Riemannian mean and we use differential geometric tools to give a characterization...