We show that half-integral polytopes obtained as the convex hull of a random set of half-integral points of the 0/1 cube have rank as high as Ω(log n/ log log n) with positive probability — even if the size of the set relative to the total number of half-integral points of the cube tends to 0. The high rank is due to certain obstructions. We determine the exact threshold number, when these obst...

Since Å xi for binary variables, aiiÅ 0 could be assumed without any loss of generality. 2 x i It is well known that finding the minimum of f is an NP-hard problem (Garey and Johnson 1979); it contains, as special cases, the vertex cover, maximum cut, signed-graph balancing and MAX-2SAT problems. Moreover, for the general minimization problem there exists a constant c ú 0 such that the existenc...

We study the standard retrieval task of ranking a fixed set of documents given a previously unseen query and pose it as the half-transductive ranking problem. The task is partly transductive as the document set is fixed. Existing transductive approaches are natural non-linear methods for this set, but have no direct out-ofsample extension. Functional approaches, on the other hand, can be applie...

Since its introduction by de Groot and colleagues in the early 1980s [1], the concept of half metallic ferromagnetism has attracted great interest. Idealized, half-metals have only one spin channel for conduction: the spin-polarized band structure exhibits metallic behavior for one spin channel, while the other spin band structure exhibits a gap at the Fermi level. Due to the gap for one spin d...

This article investigates the effects of different degrees of contextual granularity on language model performance. It presents a new language model that combines clustering and halfcontextualization, a novel representation of contexts. Half-contextualization is based on the halfcontext hypothesis that states that the distributional characteristics of a word or bigram are best represented by tr...

M y half-told lie is the claim that Melissa chose me as her research advisor. But with only a modest effort, you could paw through the thousands of emails on my server and find the one in which I recruited her to pursue a project on civilizing the Internet. Yet as it is only half a lie, the half-truth is the fact that she appeared on my doorstep unannounced two years ago and asked how she might...

The Half-Plane Half-Comb walk is a random on the plane, when we have square lattice upper half-plane and comb structure lower half-plane, i.e., horizontal lines below x-axis are removed. We prove that probability this returns to origin in 2N steps asymptotically equal $$2/(\pi N).$$ 2 / ( ? N ) . As consequence, strong laws limit distribution for local time.