The study of connectivity parameters forms an integral part the research conducted in establishing fault tolerance networks. A number variations on classical notion have been proposed and studied. In particular, super-connectivity asks for minimum vertices that need to be deleted from a graph order disconnect without creating isolated vertices. this work, we determine value two closely related ...

We use stable Kneser hypergraphs to construct ideals in N which are not nonatomic yet have the Nikodým property.

We present power low rank ensembles (PLRE), a flexible framework for n-gram language modeling where ensembles of low rank matrices and tensors are used to obtain smoothed probability estimates of words in context. Our method can be understood as a generalization of ngram modeling to non-integer n, and includes standard techniques such as absolute discounting and Kneser-Ney smoothing as special ...

1. A new approach to the chromatic number of the square of Kneser graph K(2k + 1, k), submitted. Füredi in early 2000 proposed to determine the chromatic number χ of the square of the Kneser graph K(n, k). The problem is interesting when 2k + 1 ≤ n ≤ 3k − 2. The problem has turned out to be surprisingly difficult, and is still open even in the first case n = 2k + 1. It is believed to be χ = 2k ...

The Kneser graph K(n, k) has as vertices all the k-subsets of a fixed n-set and has as edges the pairs [A, B] of vertices such that A and B are disjoint. It is known that these graphs are Hamiltonian if ( n&1 k&1) ( n&k k ) for n 2k+1. We determine asymptotically for fixed k the minimum value n=e(k) for which this inequality holds. In addition we give an asymptotic formula for the solution of k...

Frequency counts from very large corpora, such as the Web 1T dataset, have recently become available for language modeling. Omission of low frequency n-gram counts is a practical necessity for datasets of this size. Naive implementations of standard smoothing methods do not realize the full potential of such large datasets with missing counts. In this paper I present a new smoothing algorithm t...