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A semi-analytical technique for the solution of problems of wave scattering from multiple spheres is developed. This technique extensively uses the theory for the translation and rotation of Helmholtz multipoles that ...

In a number of problems in computational physics, a finite sum of kernel functions centered at N particle locations located in a box in three dimensions must be extended by imposing periodic boundary conditions on box ...

Fast algorithms for Debye summation, which arises in computations performed in crystallography, small/wide-angle X-ray scattering (SAXS/WAXS) and small-angle neutron scattering (SANS), were recently presented in Gumerov ...

The fast Gauss transform proposed by Greengard and Strain reduces the computational complexity of the evaluation of the sum of $N$ Gaussians at $M$ points in $d$ dimensions from $O(MN)$ to $O(M+N)$. However, the ...

The Pascal matrix arises in a number of applications. We present a few ways to decompose the Pascal matrices of size $n \times n$ into products of matrices with structure. Based on these decompositions, we propose ...

We present an overview of the Fast Multipole Method, explain the use of optimal data structures and present complexity results for the algorithm. We explain how octree structures and bit interleaving can be simply used to ...

An object tracking algorithm that uses a novel simple symmetric similarity function between spatially-smoothed kernel-density estimates of the model and target distributions is proposed and tested. The similarity ...

We develop exact expressions for translations and rotations of local and multipole fundamental solutions of the Helmholtz equation in spherical coordinates. These expressions are based on recurrence relations that ...

The Keck Laboratory for the Analysis of Vision Motion is a state-of-the art multi-perspective imaging laboratory recently established at the University of Maryland. In this paper, we describe the design and architecture ...

We develop a computational method based on a scalar potential representation, which efficiently reduces the solution of Maxwell’s equations to the solution of two scalar Helmholtz equations. One of the key contributions ...