In the past 15 years a study of “noncommutative projective geometry” has flourished. By using and generalizing techniques of commutative projective geometry, one can study certain noncommutative graded rings and obtain results for which no purely algebraic proof is known. For instance, noncommutative graded domains of quadratic growth, or “noncommutative curves,” have now been classified by geo...

We present new constructions for (n, w, λ) optical orthogonal codes (OOC) using techniques from finite projective geometry. In one case codewords correspond to (q − 1)-arcs contained in Baer subspaces (and, in general, kth-root subspaces) of a projective space. In the other construction, we use sublines isomorphic to PG(1, q) lying in a projective plane isomorphic to PG(1, qk), k > 1. Our const...

In many applications it is desirable to cluster high dimensional data along various subspaces, which we refer to as projective clustering. We propose a new objective function for projective clustering, taking into account the inherent trade-off between the dimension of a subspace and the induced clustering error. We then present an extension of the -means clustering algorithm for projective clu...

A new technique for the Geometry of Numbers is exhibited. This technique provides sharp estimates on the number of bounded height rational rational points in subsets of projective space whose “projective cone” is semi–algebraic. This technique improves existing techniques as the one introduced by H. Davenport in [15]. As main outcome, we conclude that systems of rational polynomial equations of...

We formalize weighted dependency parsing as searching for maximum spanning trees (MSTs) in directed graphs. Using this representation, the parsing algorithm of Eisner (1996) is sufficient for searching over all projective trees inO(n3) time. More surprisingly, the representation is extended naturally to non-projective parsing using Chu-Liu-Edmonds (Chu and Liu, 1965; Edmonds, 1967) MST algorith...

In their paper “Quantum cohomology of projective bundles over IP” (Trans. Am. Math. Soc. (1998) 350:9 3615-3638) Z. Qin and Y. Ruan introduce interesting techniques for the computation of the quantum ring of Fano manifolds which are projectivized bundles over projective spaces; in particular, in the case of splitting bundles they prove under some restrictions the conjecture of Batyrev about the...

We formalize weighted dependency parsing as searching for maximum spanning trees (MSTs) in directed graphs. Using this representation, the parsing algorithm of Eisner (1996) is sufficient for searching over all projective trees in O(n3) time. More surprisingly, the representation is extended naturally to non-projective parsing using Chu-Liu-Edmonds (Chu and Liu, 1965; Edmonds, 1967) MST algorit...

This paper integrates the object relations concept of projective identification and the systemic concept of marital dances to develop a more powerful model for working with more difficult and distressed couples. This integrated model explains how some couples use the defenses of splitting and projective identification to externalize and transpose internal conflicts into interpersonal conflicts ...

In this paper we establish the Cayley expansion theory on factored and shortest expansions of typical Cayley expressions in twoand three-dimensional projective geometry. We set up a group of Cayley factorization formulae based on the classification of Cayley expansions. We continue to establish three powerful simplification techniques in bracket computation. On top of the Cayley expansions and ...

We look at some techniques for constructing permutation arrays using projections in finite projective spaces and the geometry of arcs in the finite projective plane. We say a permutation array PA(n, d) has length n and minimum distance d when it consists of a collection of permutations on n symbols that pairwise agree in at most n − d coordinate positions. Such arrays can also be viewed as non-...