A method for fitting a surface to line data is introduced. A weighted-mean approach to the problem is described using rational Gaussian (RaG) weights. The Gaussians are stretched along the lines and their widths are selected to reproduce sharp edges and corners in the surface. When the length of the lines becomes zero, the formulation converges to a weighted sum of points. Therefore, traditiona...

We consider the problem of approximating a function f from an Euclidean domain to a manifold M by scattered samples [Formula: see text], where the data sites [Formula: see text] are assumed to be locally close but can otherwise be far apart points scattered throughout the domain. We introduce a natural approximant based on combining the moving least square method and the Karcher mean. We prove ...

We study properties of spherical Bernstein-Bézier splines. Algorithms for practical implementation of the global splines are presented for a homogeneous case as well as a non-homogeneous. Error bounds are derived for the global splines in terms of Sobolev type spherical semi-norms. Multiple star technique is studied for the minimal energy interpolation problem. Numerical summary supporting theo...

We investigate the process of quantum measurements on scattered probes. Before scattering, the probes are independent, but they become entangled afterwards, due to the interaction with the scatterer. The collection of measurement results (the history) is a stochastic process of dependent random variables. We link the asymptotic properties of this process to spectral characteristics of the dynam...

We report on measurements of quantum electrodynamic processes in an intense electromagnetic wave, where nonlinear e ects (both multiphoton and vacuum polarization) are prominent. Nonlinear Compton scattering and electronpositron pair production have been observed in collisions of 46.6 GeV and 49.1 GeV electrons of the Final Focus Test Beam at SLAC with terawatt pulses of 1053 nm and 527 nm wave...

In d-Scattered Set we are given an (edge-weighted) graph and are asked to select at least k vertices, so that the distance between any pair is at least d, thus generalizing Independent Set. We provide upper and lower bounds on the complexity of this problem with respect to various standard graph parameters. In particular, we show the following: • For any d ≥ 2, an O∗(dtw)-time algorithm, where ...