Every directed acyclic graph (DAG) over a finite non-empty set of variables (= nodes) N induces an independence model overN , which is a list of conditional independence statements over N . The inclusion problem is how to characterize (in graphical terms) whether all independence statements in the model induced by a DAG K are in the model induced by a second DAG L. Meek [8] conjectured that thi...

Many data mining algorithms make use of the well-known Inclusion-Exclusion principle. As a consequence, using this principle efficiently is crucial for the success of all these algorithms. Especially in the context of condensed representations, such as NDI, and in computing interesting measures, a quick inclusion-exclusion algorithm can be crucial for the performance. In this paper, we give an ...

Given integers t , k, and v such that 0 t k v, let Wtk(v) be the inclusion matrix of t-subsets vs. k-subsets of a v-set. We modify slightly the concept of standard tableau to study the notion of rank of a finite set of positive integers which was introduced by Frankl. Utilizing this, a decomposition of the poset 2[v] into symmetric skipless chains is given. Based on this decomposition, we const...

The Inclusion-Exclusion formula expresses the size of a union of a family of sets in terms of the sizes of intersections of all subfamilies. This paper considers approximating the size of the union when intersection sizes are known for only some of the subfamilies, or when these quantities are given to within some error, or both. In particular, we consider the case when all k-wise intersections...

microalloyed s355n steel plates are extensively used in bridge and high-rise building structures. one ofthe factors affecting the mechanical properties is the size and morphology of inclusions. in this research,microalloyed s355n steel plates with different sizes of inclusions were examined. one contained longmanganese sulfide inclusions (li material) and the other had short ones (si material)....

Financial inclusion is a tool for connecting every individual of the society to formal financial system. Many backward unprivileged individuals are out coverage services. an attempt help who have not access services participate in management and avail like banking ,insurance, overdraft etc,. process ensuring timely needed weaker sections. Government India has announced various schemes purpose p...

We prove local and global invertibility of Sobolev solutions of certain differential inclusions which prevent the differential matrix from having negative eigenvalues. Our results are new even for quasiregular mappings in two dimensions.