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In this paper we present an efficient algorithm to test if two given paths are homotopic; that is, whether they wind around obstacles in the plane in the same way. For simple paths specified by <i>n</i> line segments with obstacles described by <i>n</i> points, our algorithm runs in <i>O</i>(<i>n</i> log <i>n</i>) time, which we show is tight. For(More)
We show how to greatly accelerate algorithms that compute Delaunay triangulations of huge, well-distributed point sets in 2D and 3D by exploiting the natural spatial coherence in a stream of points. We achieve large performance gains by introducing <i>spatial finalization</i> into point streams: we partition space into regions, and augment a stream of input(More)
It is difficult to generate raster Digital Elevation Models (DEMs) from terrain mass point data sets too large to fit into memory, such as those obtained by LIDAR. We describe prototype tools for streaming DEM generation that use memory and disk I/O very efficiently. From 500 million bare-earth LIDAR double precision points (11.2 GB) our tool can, in just(More)
Fibroblast growth factor 1 (FGF1) has been recently characterized as a potent insulin sensitizer that regulates adipose tissue remodeling, but the physiological role of FGF1 remains unclear. This study measured serum FGF1 levels for the first time in patients with newly diagnosed type 2 diabetes mellitus (T2DM), and further explored the correlations between(More)
For centuries, artists have used traditional media and tools to express their thoughts and feelings creatively. More recently there has been a growing interest in non-photorealistic rendering and in recreating these media faithfully on a computer. Some of the most popular materials used in painting are acrylics and oils, and a key feature of these paints is(More)
A long-standing problem in spline theory has been to generalize classic B-splines to the multivariate setting, and its full solution will have broad impact. We initiate a study of triangulations that generalize the duals of higher order Voronoi diagrams, and show that these can serve as a foundation for a family of multivariate splines that generalize the(More)
M. Word and coauthors from the Richardsons' 3D Protein Structure laboratory at Duke University propose <i>dot scores</i> to measure interatomic interactions in molecular structures. Their program REDUCE uses these scores in a brute-force search to solve instances of the <i>NP</i>-hard problem of finding the optimal placement of hydrogen atoms in molecular(More)
The neurohypophysial hormone, oxytocin, is involved in the regulation of energy metabolism. Adiponectin (APN) is an adipose tissue-specific serum protein that inversely associates with metabolic syndrome (MetS). High-molecular-weight adiponectin (HMW APN) is considered the active form. In the present study, we aimed to determine the relationships of(More)
The Delaunay diagram in d dimensions is the dual of the Voronoi diagram of a set of input sites. If we assume no degeneracies in the input, i.e. no d + 2 sites are co-spherical, then the diagram is a triangulation. Because this assumption is common, and can be enforced by symbolic perturbation, we often forget that Delaunay diagrams need not be(More)