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Various lines of evidence suggest that the striatum is implicated in cognitive flexibility. The neuropsychological evidence has, for the most part, been based on research with patients with Parkinson's disease, which is accompanied by chemical disruption of both the striatum and the prefrontal cortex. The present study examined this issue by testing… (More)

Sequences of points with a low discrepancy are the basic building blocks of quasi-Monte Carlo methods. Traditionally these points are generated in a unit cube. Not much theory exists on generating low-discrepancy point sets on other domains, for example a simplex. We introduce a variation and a star discrepancy for the simplex and derive a Koksma-Hlawka… (More)

Lattice rules are a family of equal-weight cubature formulas for approximating high-dimensional integrals. By now it is well established that good generating vectors for lattice rules having n points can be constructed component-by-component for integrands belonging to certain weighted function spaces, and that they can achieve the optimal rate of… (More)

The classical Theorem of Bézout yields an upper bound for the number of finite solutions to a given polynomial system, but is very often too large to be useful for the construction of a start system, for the solution of a polynomial system by means of homotopy continuation. The BKK bound gives a much lower upper bound for the number of solutions, but… (More)

CUBPACK aims to offer a collection of re-usable code for automatic <i>n</i>-dimensional (<i>n</i> ≥ 1) numerical integration of functions over a collection of regions, i.e., quadrature and cubature. The current version allows this region to consist of a union of <i>n</i>-simplices and <i>n</i>-parellellepids. The framework of CUBPACK is described as… (More)

A globally adaptive algorithm for numerical cubature of a vector of functions over a collection of <i>n</i>-dimensional simplices is described. The algorithm is based on a subdivision strategy that chooses for subdivision at each stage the subregion (of the input simplices) with the largest estimated error. This subregion is divided into two, three or four… (More)

We reformulate the original component-by-component algorithm for rank-1 lattices in a matrix-vector notation so as to highlight its structural properties. For function spaces similar to a weighted Korobov space, we derive a technique which has construction cost O(sn log(n)), in contrast with the original algorithm which has construction cost O(sn 2). Herein… (More)

About 13 years ago we started collecting published cubature formulas for the approximation of multivariate integrals over some standard regions. In this paper we describe how we make this information available to a larger audience via the World Wide Web. About three decades ago, Arthur H. Stroud published his encyclopedic work on multiple numerical… (More)