Widely used in speech and language processing, Kneser-Ney (KN) smoothing has consistently been shown to be one of the best-performing smoothing methods. However, KN smoothing assumes integer counts, limiting its potential uses—for example, inside Expectation-Maximization. In this paper, we propose a generalization of KN smoothing that operates on fractional counts, or, more precisely, on distri...

In this article, we consider the bipartite graphs K2 × Kn. We first show that the connectedness of N (Kn n+1) = 0. Further, we show that Hom(K2 ×Kn,Km) is homotopic to Sm−2, if 2 6 m < n.

We give a group-theoretic proof of the following fact, proved initially by methods of topological design theory: Up to isomorphism, the number of regular hamiltonian embeddings of Kn,n is 2 or 1, depending on whether n is a multiple of 8 or not. We also show that for each n there is, up to isomorphism, a unique regular triangular embedding of Kn,n,n. This is a preprint of an article accepted fo...

Let Kn,n denote the complete bipartite graph with n vertices in each partite set and Kn,n+I denote Kn,n with a 1-factor added. It is proved in this paper that there exists an m-cycle system of Kn,n + I if and only if n ≡ 1 (mod 2), m ≡ 0 (mod 2), 4 ≤ m ≤ 2n and n(n + 1) ≡ 0 (mod m).

Scheinerman and Wilf [SW94] assert that “an important open problem in the study of graph embeddings is to determine the rectilinear crossing number of the complete graph Kn.” A rectilinear drawing of Kn is an arrangement of n vertices in the plane, every pair of which is connected by an edge that is a line segment. We assume that no three vertices are collinear, and that no three edges intersec...

The selective inhibitor of the multifunctional calcium/calmodulin-dependent kinases (CaMK), KN-93, arrests a variety of cell types in G(1). However, the biochemical nature of this G(1) arrest point and the physiological target of KN-93 in G(1) remain controversial. Here we show that in WI-38 human diploid fibroblasts KN-93 reversibly arrested cells in late G(1) prior to detectable cyclin-depend...