Ziel: Dreidimensionale MRT-Sequenzen erlauben sowohl eine verbesserte räumliche Auflösung bei guten Signalund Kontrasteigenschaften als auch multiplanare Rekonstruktionen. Wir verglichen Cube, eine 3-D-FLAIR-Sequenz, mit einer Standard-2D-FLAIR-Sequenz bei der Bildgebung der multiplen Sklerose (MS). Material und Methoden: Die Untersuchungenwurden an einem 3-Tesla-Scanner in der klinischen Routi...

We describe recent results, obtained in collaborations with C. Borgs, J.T. Chayes, R. van der Hofstad and J. Spencer, which provide a detailed description of the phase transition for random subgraphs of the n-cube. Résumé. Nous présentons des résultats récents qui donnent une description détaillée de la transition de phase des sous-graphes aléatoires du n-cube. Ces résultats sont obtenus en col...

Any set system can be represented as an n -cube vertices set. Restricted sets of n -cube weighted subsets are considered. The problem considered is in simple description of all set of partitioning characteristic vectors. A smaller generating sets are known as “boundary” and ”steepest” sets and finally we prove that the intersection of these two sets is also generating for the partitioning chara...

The h-extra connectivity is an important parameter to measure the reliability and fault tolerance ability of large interconnection networks. The k-ary ncube is an important interconnection network of parallel computing systems. The 1-restricted connectivity of k-ary n-cubes has been obtained by Chen et al. for k ≥ 4 in [6]. Nevertheless, the h-extra connectivity of 3-ary ncubes has not been obt...

PURPOSE Three-dimensional (3 D) MRI sequences allow improved spatial resolution with good signal and contrast properties as well as multiplanar reconstruction. We sought to compare Cube, a 3 D FLAIR sequence, to a standard 2 D FLAIR sequence in multiple sclerosis (MS) imaging. MATERIALS AND METHODS Examinations were performed in the clinical routine on a 3.0 Tesla scanner. 12 patients with de...

For a point set of n elements in the d-dimensional unit cube and a class of test sets we are interested in the largest volume of a test set which does not contain any point. For all natural numbers n, d and under the assumption of a δ -cover with cardinality |Γδ | we prove that there is a point set, such that the largest volume of such a test set without any point is bounded by log |Γδ | n + δ ...

In this paper, we study the problem of constructing subcubes in faulty hypercubes. First a divide-and-conquer technique is used to form the set of disjoint subcubes in the faulty hypercube. The concept of irregular subcubes is then introduced to take advantage of advanced switching techniques, such as wormhole routing, to increase the sizes of the available subcubes. We present a subcube partit...

In this paper we show a lower bound for the generalization of Heilbronn’s triangle problem to d dimensions; namely, we show that there exists a set S of n points in the d-dimensional unit cube so that every d + 1 points of S define a simplex of volume Ω( 1 nd ). We also show a constructive incremental positioning of n points in a unit 3-cube for which every tetrahedron defined by four of these ...

The use of edge-disjoint spanning trees for data broadcasting and scattering problem in networks provides a number of advantages, including the increase of bandwidth and faulttolerance. In this paper, we present an algorithm for constructing n edge-disjoint spanning trees in ann-dimensional locally twisted cube. Since then-dimensional locally twisted cube is regular with the common degree n, th...