We prove that the filling order is quadratic for a large class of solvable groups and asymptotically quadratic for all Q-rank one lattices in semisimple groups of R-rank at least 3. As a byproduct of auxiliary results we give a shorter proof of the theorem on the nondistorsion of horospheres providing also an estimate of a nondistorsion

This paper proposes a new method to rank the cases classified by a decision tree. The method applies a posteriori without modification of the tree and doesn’t use additional training cases. It consists in computing the distance of the cases to the decision boundary induced by the decision tree, and to rank them according to this geometric score. When the data are numeric it is very easy to impl...

Many NP-hard graph problems can be efficiently solved on graphs of bounded tree-width. Several articles have recently shown that the so-called rank-width parameter also allows efficient solution of most of these NP-hard problems, while being less restrictive than tree-width. On the other hand however, there exist problems of practical importance which remain hard on graphs of bounded rank-width...

We consider linear codes over some fixed finite field extension Fqm/Fq, where Fq is an arbitrary finite field. In [1], Gabidulin introduced rank metric codes, by endowing linear codes over Fqm with a rank weight over Fq and studied their basic properties in analogy with linear codes and the classical Hamming distance. Inspired by the characterization of the security in wiretap II codes in terms...

In this paper, a new approach to rank fuzzy numbers based on sign distance is proposed. Our proposed method is extension of sign distance method and to decrease the set of equivalence callas of fuzzy numbers. Illustrative examples are included to show the advantage of the proposed method.

In analogy with the Singleton defect for classical codes, we propose a definition of rank defect for Delsarte rank-metric codes. We characterize codes whose rank defect and dual rank defect are both zero, and prove that the rank distribution of such codes is determined by their parameters. This extends a result by Delsarte on the rank distribution of MRD codes. In the general case of codes of p...