Transfinite thin plate spline interpolation

Duchon's method of thin plate splines defines a polyharmonic interpolant to scattered data values as the minimizer of a certain integral functional. For transfinite interpolation, i.e. interpolation of continuous data prescribed on curves or hypersurfaces, Kounchev has developed the method of polysplines, which are piecewise polyharmonic functions of fixed smoothness across the given hypersurfaces and satisfy some boundary conditions. Recently, Bejancu has introduced boundary conditions of Beppo Levi type to construct a semi-cardinal model for polyspline interpolation to data on an infinite set of parallel hyperplanes. The present paper proves that, for periodic data on a finite set of parallel hyperplanes, the polyspline interpolant satisfying Beppo Levi boundary conditions is in fact a thin plate spline, i.e. it minimizes a Duchon type functional

A Comparison of the Use of Binary Decision Trees and Neural Networks in Top Quark Detection

The use of neural networks for signal vs.~background discrimination in high-energy physics experiment has been investigated and has compared favorably with the efficiency of traditional kinematic cuts. Recent work in top quark identification produced a neural network that, for a given top quark mass, yielded a higher signal to background ratio in Monte Carlo simulation than a corresponding set of conventional cuts. In this article we discuss another pattern-recognition algorithm, the binary decision tree. We have applied a binary decision tree to top quark identification at the Tevatron and found it to be comparable in performance to the neural network. Furthermore, reservations about the "black box" nature of neural network discriminators do not apply to binary decision trees; a binary decision tree may be reduced to a set of kinematic cuts subject to conventional error analysis.Comment: 14pp. Plain TeX + mtexsis.tex (latter available through 'get mtexsis.tex'.) Two postscript files avail. by emai

A vector partition function for the multiplicities of sl_k(C)

We use Gelfand-Tsetlin diagrams to write down the weight multiplicity function for the Lie algebra sl_k(C) (type A_{k-1}) as a single partition function. This allows us to apply known results about partition functions to derive interesting properties of the weight diagrams. We relate this description to that of the Duistermaat-Heckman measure from symplectic geometry, which gives a large-scale limit way to look at multiplicity diagrams. We also provide an explanation for why the weight polynomials in the boundary regions of the weight diagrams exhibit a number of linear factors. Using symplectic geometry, we prove that the partition of the permutahedron into domains of polynomiality of the Duistermaat-Heckman function is the same as that for the weight multiplicity function, and give an elementary proof of this for sl_4(C) (A_3).Comment: 34 pages, 11 figures and diagrams; submitted to Journal of Algebr