Preconditioning 2D integer data for fast convex hull computations

In order to accelerate computing the convex hull on a set of n points, a heuristic procedure is often applied to reduce the number of points to a set of s points, s ? n, which also contains the same hull. We present an algorithm to precondition 2D data with integer coordinates bounded by a box of size p × q before building a 2D convex hull, with three distinct advantages. First, we prove that under the condition min(p, q) ? n the algorithm executes in time within O(n); second, no explicit sorting of data is required; and third, the reduced set of s points forms a simple polygonal chain and thus can be directly pipelined into an O(n) time convex hull algorithm. This paper empirically evaluates and quantifies the speed up gained by preconditioning a set of points by a method based on the proposed algorithm before using common convex hull algorithms to build the final hull. A speedup factor of at least four is consistently found from experiments on various datasets when the condition min(p, q) ? n holds; the smaller the ratio min(p, q)/n is in the dataset, the greater the speedup factor achieved

Manipulation of antioxidant pathways in neonatal murine brain

To assess the role of brain antioxidant capacity in the pathogenesis of neonatal hypoxic-ischemic brain injury, we measured the activity of glutathione peroxidase (GPX) in both human-superoxide dismutase-1 (hSOD1) and human-GPX1 overexpressing transgenic (Tg) mice after neonatal hypoxia-ischemia (HI). We have previously shown that mice that overexpress the hSOD1 gene are more injured than their wild-type (WT) littermates after HI, and that H(2)O(2) accumulates in HI hSOD1-Tg hippocampus. We hypothesized that lower GPX activity is responsible for the accumulation of H(2)O(2). Therefore, increasing the activity of this enzyme through gene manipulation should be protective. We show that brains of hGPX1-Tg mice, in contrast to those of hSOD-Tg, have less injury after HI than WT littermates: hGPX1-Tg, median injury score = 8 (range, 0-24) versus WT, median injury score = 17 (range, 2-24), p < 0.01. GPX activity in hSOD1-Tg mice, 2 h and 24 h after HI, showed a delayed and bilateral decline in the cortex 24 h after HI (36.0 +/- 1.2 U/mg in naive hSOD1-Tg versus 29.1 +/- 1.7 U/mg in HI cortex and 29.2 +/- 2.0 for hypoxic cortex, p < 0.006). On the other hand, GPX activity in hGPX1-Tg after HI showed a significant increase by 24 h in the cortex ipsilateral to the injury (48.5 +/- 5.2 U/mg, compared with 37.2 +/- 1.5 U/mg in naive hGPX1-Tg cortex, p < 0.008). These findings support the hypothesis that the immature brain has limited GPX activity and is more susceptible to oxidative damage and may explain the paradoxical effect seen in ischemic neonatal brain when SOD1 is overexpressed