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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Algorithmica 8 (1992), S. 177-194 
    ISSN: 1432-0541
    Keywords: Matching ; Computational geometry ; Bottleneck optimization problem ; Relative neighborhood graph
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Given a set of pointsV in the plane, the Euclidean bottleneck matching problem is to match each point with some other point such that the longest Euclidean distance between matched points, resulting from this matching, is minimized. To solve this problem, we definek-relative neighborhood graphs, (kRNG) which are derived from Toussaint's relative neighborhood graphs (RNG). Two points are calledk-relative neighbors if and only if there are less thank points ofV which are closer to both of the two points than the two points are to each other. AkRNG is an undirected graph (V,E r k ) whereE r k is the set of pairs of points ofV which arek-relative neighbors. We prove that there exists an optimal solution of the Euclidean bottleneck matching problem which is a subset ofE r 17 . We also prove that ¦E r k ¦ 〈 18kn wheren is the number of points in setV. Our algorithm would construct a 17RNG first. This takesO(n 2) time. We then use Gabow and Tarjan's bottleneck maximum cardinality matching algorithm for general graphs whose time-complexity isO((n logn)0.5 m), wherem is the number of edges in the graph, to solve the bottleneck maximum cardinality matching problem in the 17RNG. This takesO(n 1.5 log0.5 n) time. The total time-complexity of our algorithm for the Euclidean bottleneck matching problem isO(n 2 +n 1.5 log0.5 n).
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1432-0428
    Keywords: Atherosclerosis ; cell death ; cell mitosis ; endothelium ; Evans blue-albumin ; permeability ; streptozotocin diabetes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary Hypertension, cigarette smoking and diabetes mellitus are well-known risk factors for atherosclerosis and coronary heart disease. Repeated endothelial cell injury and increased lipid entry have been suggested as initiating events in atherogenesis. Our previous studies have demonstrated that the frequency of endothelial cell death and associated endothelial permeability were significantly increased in the aorta of spontaneously hypertensive rats and chronic oral nicotine-treated rats. In the present investigation, we examined the hypothesis that diabetes also increases the frequency of arterial endothelial cell death and hence transendothelial macromolecular transport, which may have some implications in increasing lipid entry and thus accelerating atherogenesis. Diabetes was induced in 15 male Sprague-Dawley rats by intraperitoneal injection of 60 mg streptozotocin per kg body weight. The duration of diabetes was 6 weeks. A group of 15 age-matched rats, injected only with the buffer and maintained over the same time period, served. as the controls. In en face preparations of the thoracic aorta, IgG-containing dead endothelial cells were identified by an indirect immunoperoxidase method, and endothelial leakage to Evans blue-albumin complexes was quantified by fluorescence microscopy. Diabetic rats, compared to control rats, had significantly higher values for the frequency of endothelial cell death (0.77±0.10% vs 0.38±0.04%;p〈0.005 by two-tailed, unpaired Student'st-test) and the number density of Evans blue-albumin leaky foci (4.33±0.48/mm2 vs 2.99±0.38/mm2;p〈0.05 by two-tailed, unpairedt-test) in the aorta. It is concluded that, similar to the situations in hypertension and nicotine consumption, the observed increase in the frequency of endothelial cell death and macromolecular permeability to large molecules in the aorta in streptozotocin-induced diabetic rats suggest that these changes may contribute to accelerated atherogenesis in diabetes.
    Type of Medium: Electronic Resource
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