we give an algorithm, called t*, for finding the k shortest simplepaths connecting a certain pair of nodes, s and t, in a acyclic digraph.first the nodes of the graph are labeled according to the topologicalordering. then for node i an ordered list of simple s − i paths iscreated. the length of the list is at most k and it is created by usingtournament trees. we prove the correctness of t* and ...

The collection of k-closed subsets of X forms a topology, which contains the original topology of X (i.e. closed subsets are always k-closed). Notation 1.2. Let kX denote the space whose underlying set is that of X, but equipped with the topology of k-closed subsets of X. Because the k-topology contains the original topology on X, the identity function id : kX → X is continuous. Definition 1.3....

We establish the existence of non-constant closed geodesics on moduli spaces of SU(2) monopoles of arbitrary charge. More generally, we show that the moduli space of strongly centred monopoles of charge k, k 2, contains a totally geodesic submanifold which can be identiied with the moduli space of strongly centred 2-monopoles for even k's and with the moduli space of centred 2-monopoles for odd...

Does K-Means reasonably divides the data into k groups is an important question that arises when one works on Image Segmentation? Which color space one should choose and how to ascertain that the k we determine is valid? The purpose of this study was to explore the answers to aforementioned questions. We perform K-Means on a number of 2-cluster, 3cluster and k-cluster color images (k>3) in RGB ...