Feedforward control of sound and vibration using a neural network-based control system is considered, with the aim being to derive an architecture/algorithm combination which is capable of supplanting the commonly used finite impulse response filter/filtered-x least mean square (LMS) linear arrangement for certain nonlinear problems. An adaptive algorithm is derived which enables stable adaptat...

We construct a formal connection on the Aomoto complex of an arrangement of hyperplanes, and use it to study the Gauss-Manin connection for the moduli space of the arrangement in the cohomology of a complex rank one local system. We prove that the eigenvalues of the Gauss-Manin connection are integral linear combinations of the weights which define the local system.

If an algebraic torus T acts on a complex projective algebraic variety X then the affine scheme Spec H∗ T (X;C) associated to the equivariant cohomology is often an arrangement of linear subspaces of the vector space H 2 (X;C). In many situations the ordinary cohomology ring of X can be described in terms of this arrangement.

We prove a conjecture of Bayer and Brandt J. Alg. Combin. 6 (1997), 229{246] about the \largest" intersection lattice of a discriminantal arrangement based on an essential arrangement of n linear hyperplanes in R k. An important ingredient in the proof is Crapo's characterization of the matroid of circuits of the connguration of n generic points in R k .

For each element X of codimension two of the intersection lattice of a hyperplane arrangement we define a differential logarithmic 1-forms tax with poles along the arrangement. Then we describe the class of arrangements for which forms wX generate the whole module of the logarithmic 1-forms with poles along the arrangement. The description is done in terms of linear relations among the function...

In this paper we study a version of the Multidimensional Arrangement Problem (MAP) that embeds a graph into a multidimensional array minimizing the aggregated (Manhattan) distance of the embedded edges. This problem includes the minimum Linear Arrangement Problem (minLA) as a special case, among others. We propose JAM, a tabu-based two-stage simulated annealing heuristic for this problem. Our a...

We present a new algorithm to compute the Legendre–Fenchel conjugate of convex piecewise linear-quadratic (PLQ) bivariate functions. The algorithm stores a function using a (primal) planar arrangement. It then computes the (dual) arrangement associated with the conjugate by looping through vertices, edges, and faces in the primal arrangement and building associated dual vertices, edges, and fac...

In combinatorial problems it is sometimes possible to define a G-equivariant mapping from a space X of configurations of a system to a Euclidean space Rm for which a coincidence of the image of this mapping with an arrangement A of linear subspaces insures a desired set of linear conditions on a configuration. BorsukUlam type theorems give conditions under which no G-equivariant mapping of X to...