Let A be a real arrangement of hyperplanes. Let B = B(q) be Varchenko’s quantum bilinear form of A, introduced [15], specialized so that all hyperplanes have weight q . B(q) is nonsingular for all complex q except certain roots of unity. Here, we examine the kernel of B at roots of unity in relation to the topology of the hyperplane singularity. We use Varchenko’s work [16] to relate B(q) to a ...

We prove a new, tight upper bound on the number of incidences between points and hyperplanes in Euclidean d-space. Given n points, of which k are colored red, there are Od(m 2/3 k 2/3 n +kn+m) incidences between the k red points and m hyperplanes spanned by all n points provided that m = Ω(n). For the monochromatic case k = n, this was proved by Agarwal and Aronov [1]. We use this incidence bou...

A method is described for finding decision boundaries, approximated by piecewise linear segments, for classifying patterns in R(N),N>/=2, using an elitist model of genetic algorithms. It involves generation and placement of a set of hyperplanes (represented by strings) in the feature space that yields minimum misclassification. A scheme for the automatic deletion of redundant hyperplanes is als...

In this paper we present some theoretical results on two forms of multi-point crossover: n-point crossover and uniform crossover. This analysis extends the work from De long's thesis, which dealt with dis~ption of n-point crossover on 2nd order hyperplanes. We present various extensions to this theory, including 1) an analysis of the disruption of n-point crossover on kth order hyperplanes: 2) ...

Rahilly [10] described a construction that relates any Hadamard design H on 4m−1 points with a line spread to an affine design having the same parameters as the classical design of points and hyperplanes in AG(m, 4). Here it is proved that the affine design is the classical design of points and hyperplanes in AG(m, 4) if, and only if, H is the classical design of points and hyperplanes in PG(2m...