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72
Cellpaths in mono and bichromatic line arrangements in the plane∗
, 2014
"... We prove that the dual graph of any arrangement of n lines in general position always contains a path of length at least n2/4. Further, we show that in every arrangement of n red and blue lines — in general position and not all of the same color — there is a simple path through at least n cells wher ..."
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We prove that the dual graph of any arrangement of n lines in general position always contains a path of length at least n2/4. Further, we show that in every arrangement of n red and blue lines — in general position and not all of the same color — there is a simple path through at least n cells
Colored Ray Configurations
"... We study the cyclic sequences induced at infinity by pairwisedisjoint colored rays with apices on a given balanced bichromatic point set, where the color of a ray is inherited from the color of its apex. We derive a lower bound on the number of color sequences that can be realized from any fixed p ..."
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We study the cyclic sequences induced at infinity by pairwisedisjoint colored rays with apices on a given balanced bichromatic point set, where the color of a ray is inherited from the color of its apex. We derive a lower bound on the number of color sequences that can be realized from any fixed
Invited Speakers
"... This volume contains the proceedings of the 25th Canadian Conference on Computational Geometry (CCCG’13), held in ..."
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This volume contains the proceedings of the 25th Canadian Conference on Computational Geometry (CCCG’13), held in
TwoDimensionalCentrifugationfor DeskTopClinicalChemistry
"... We have developed a new system for clinical chemistry analysis, the VisionTMSystem, in which centrifugal force is usedto separate whole blood, measure reagent and plasma volumes,and completeall steps requiredfora spectrophotometricanalysis.The system is based on use of a multichambered plastictest ..."
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bered plastictest pack containingliquidreagents,whichcan be centrifugedat 500 x g in two planes, oriented at right angles to each other. Alternating centrifugal fields allows liquid reagents and plasma to flow into highly precise measunngand mixingchambers. A uniqueflash lamp and diode array spectrometer provide
3symmetric and 3decomposable geometric drawings of K_n
, 2008
"... Even the most superficial glance at the vast majority of crossingminimal geometric drawings of Kn reveals two hardtomiss features. First, all such drawings appear to be 3fold symmetric (or simply 3symmetric). And second, they all are 3decomposable, that is, there is a triangle T enclosing the ..."
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Cited by 4 (3 self)
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Even the most superficial glance at the vast majority of crossingminimal geometric drawings of Kn reveals two hardtomiss features. First, all such drawings appear to be 3fold symmetric (or simply 3symmetric). And second, they all are 3decomposable, that is, there is a triangle T enclosing the drawing, and a balanced partition A, B, C of the underlying set of points P, such that the orthogonal projections of P onto the sides of T show A between B and C on one side, B between A and C on another side, and C between A and B on the third side. In fact, we conjecture that all optimal drawings are 3decomposable, and that there are 3symmetric optimal constructions for all n multiple of 3. In this paper, we show that any 3decomposable geometric drawing of Kn has at least 0.380029 () n 3 4 + Θ(n³) crossings. On the other hand, we produce 3symmetric and 3decomposable drawings that improve the general upper bound for the rectilinear crossing number of Kn to 0.380488 () n 3 4 +Θ(n³). We also give explicit 3symmetric and 3decomposable constructions for n < 100 that are at least as good as those previously known.
Interactive Exploration in Virtual Environments
, 2003
"... This thesis describes the technological, application and scientific issues involved in the design of environments for the purpose of interactive exploration in virtual environments. ..."
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Cited by 7 (0 self)
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This thesis describes the technological, application and scientific issues involved in the design of environments for the purpose of interactive exploration in virtual environments.
Finding Data Broadness Via Generalized Nearest
"... Abstract. A data object is broad if it is one of the kNearest Neighbors (kNN) of many data objects. We introduce a new database primitive called Generalized Nearest Neighbor (GNN) to express data broadness. We also develop three strategies to answer GNN queries efficiently for large datasets of mu ..."
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Abstract. A data object is broad if it is one of the kNearest Neighbors (kNN) of many data objects. We introduce a new database primitive called Generalized Nearest Neighbor (GNN) to express data broadness. We also develop three strategies to answer GNN queries efficiently for large datasets of multidimensional objects. The R*Tree based search algorithm generates candidate pages and ranks them based on their distances. Our first algorithm, Fetch All (FA), fetches as many candidate pages as possible. Our second algorithm, Fetch One (FO), fetches one candidate page at a time. Our third algorithm, Fetch Dynamic (FD), dynamically decides on the number of pages that needs to be fetched. We also propose three optimizations, Column Filter, Row Filter and Adaptive Filter, to eliminate pages from each dataset. Column Filter prunes the pages that are guaranteed to be nonbroad. Row Filter prunes the pages whose removal do not change the broadness of any data point. Adaptive Filter prunes the search space dynamically along each dimension to eliminate unpromising objects. Our experiments show that FA is the fastest when the buffer size is large and FO is the fastest when the buffer size is small. FD is always either fastest or very close to the faster of FA and FO. FD is significantly faster than the existing methods adapted to the GNN problem. 1
Results 1  10
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72