This paper describes the application of a framework for text analysis to the problem of distinguishing unusual or non-standard usage of words in large corpora. The need to identify such novel uses, and augment machine-readable dictionaries is a constant battle for professional lexicographers that need to update their resources in order to keep up with the development of the dynamic and evolving...

The anchored hyperplane location problem is to locate a hyperplane passing through some given points P ⊆ IR and minimizing either the sum of weighted distances (median problem), or the maximum weighted distance (center problem) to some other points Q ⊆ IR. This problem of computational geometry is analyzed by using nonlinear programming techniques. If the distances are measured by a norm, it wi...

R. Thomas (with a remark of B. Totaro) proved that the Hodge conjecture is essentially equivalent to the existence of a hyperplane section, called a generalized Thomas hyperplane section, such that the restriction to it of a given primitive Hodge class does not vanish. We study the relations between the vanishing cycles in the cohomology of a general fiber, and show that each relation between t...

Abstract Two notions of riffle shuffling on finite Coxeter groups are given: one using Solomon’s descent algebra and another using random walk on chambers of hyperplane arrangements. These definitions coincide for types A,B,H3, and rank two groups. Both notions satisfy a convolution property and have the same simple eigenvalues. The hyperplane definition is especially natural and satisfies a po...

Various methods have been proposed for defining an environmental contour, based on different concepts of exceedance probability. In the inverse first-order reliability method (IFORM) and direct sampling (DS) method, contours are defined in terms exceedances within a region bounded by hyperplane either standard normal space or original parameter space, corresponding to marginal probabilities und...

A classical result of Arnold and Brieskorn [Bk], [Bk2] states that the complement of the discriminant of the versal unfolding of a simple hypersurface singularity is a K(π, 1). Deligne [Dg] showed this result could be placed in the general framework by proving that the complement of an arrangement of reflecting hyperplanes for a Coxeter group is again a K(π, 1) (and more generally for simplicia...