ABSTRACT.A maximal vector of a set ~s one which is not less than any other vector m all components We derive a recurrence relation for computing the average number of maxunal vectors m a set of n vectors m d-space under the assumpUon that all (nl) a relative ordermgs are equally probable. Solving the recurrence shows that the average number of maxmaa is O((ln n) a-~) for fixed d We use this result to construct an algorithm for finding all the maxima that have expected running tmae hnear m n (for sets of vectors drawn under our assumptions) We then use the result to find an upper bound on the expected number of convex hull points m a random point set KE~ WORDS AND eHRASES maxtma of a set of vectors, average number of maxtma, expected-tsme algorithms, analysts of algorithms, convex hulls, dynamtc programming CR CATEGORIES" 5 25, 5.39, 5.42
The hallmark of rheumatoid arthritis (RA) is the progressive destruction of articular joints, characterized by invasive synovial hyperplasia and pathological neovascularization. Here we report that PPI-2458, a member of the fumagillin class of irreversible methionine aminopeptidase-2 (MetAP-2) inhibitors, potently inhibits the proliferation of human fibroblast-like synoviocytes (HFLS-RA), derived from RA patients, with a growth inhibitory concentration 50 (GI 50) of 0.04 nM and a maximum inhibition of >95% at 1 nM. Human umbilical vein endothelial cells (HUVEC) are similarly inhibited in proliferation by PPI-2458 (GI 50, 0.2 nM). We developed a method to measure the level of MetAP-2 enzyme inhibition after exposure to PPI-2458 and demonstrate that growth inhibition of PPI-2458-sensitive HFLS-RA and HUVEC is linked to MetAP-2 enzyme inhibition, in a dose-dependent fashion. The secretion of several inflammatory mediators such as IL-6 and vascular endothelial growth factor from activated HFLS-RA was not inhibited by PPI-2458. The CNS toxicity profile of PPI-2458, determined by the incidence of seizures, is significantly improved over that of the parental compound TNP-470. In the rat model of peptidoglycan-polysaccharide-induced arthritis, PPI-2458 significantly attenuated paw swelling when therapeutically administered after the onset of chronic disease. We suggest that the mechanism of PPI-2458 action, highly selective and potent antiproliferative activity on HFLS-RA and HUVEC in vitro, a significantly improved CNS toxicity profile, and marked attenuation of chronic disease in the rat peptidoglycan-polysaccharide arthritis model in vivo, positions this compound as a drug for the treatment of RA.
495The complexity of the Discrete Fourier Transform (OFT) is studied with respect to a new model of computation appropriate to VLSI technology. This model focuses on two key parameters, the amount of silicon area and time required to implement a OFT on a single chip. Lower bounds on area (A) and time (T) are related to the number of points (N) in the OFT: AT2 > N2/16. This inequality holds for any chip design based on any algorithm, and is nearly tight when T • e
Abstract.We examine the problem of routing wires of a VLSI chip, where the pins to be connected are arranged in a regular rectangular array. We obtain tight bounds for the worst-case "channel-width" needed to route an n x n array, and develop provably good heuristics for the general case. Single-turn routings are proved to be near-optimal in the worst-case.A central result of our paper is a "rounding algorithm" for obtaining integral approximations to solutions of linear equations. Given a matrix A and a real vector x, then we can find an integral i such that for all i, li~-x,l
The dependence of cell growth on methionine aminopeptidase (MetAP) function in bacteria and yeast is firmly established. Here we report experimental evidence that the control of cell proliferation in mammalian cells is directly linked and strictly dependent on the activity of both MetAP-1 and MetAP-2. The targeted downregulation of either methionine aminopeptidase MetAP-1 or MetAP-2 protein expression by small interfering RNA (siRNA) significantly inhibited the proliferation of human umbilical vein endothelial cells (HUVEC) (70%-80%), while A549 human lung carcinoma cell proliferation was less inhibited (20%-30%). The cellular levels of MetAP-2 enzyme were measured after MetAP-2 siRNA treatment and found to decrease over time from 4 to 96 h, while rapid and complete depletion of MetAP-2 enzyme activity was observed after 4 h treatment with two pharmacological inhibitors of MetAP-2, PPI-2458 and fumagillin. When HUVEC and A549 cells were treated simultaneously with MetAP-2 siRNA and PPI-2458, or fumagillin, which irreversibly inhibit MetAP-2 enzyme activity, no additive effect on maximum growth inhibition was observed. This strongly suggests that MetAP-2 is the single critical cellular enzyme affected by either MetAP-2 targeting approach. Most strikingly, despite their significantly different sensitivity to growth inhibition after targeting of either MetAP-1 or MetAP-2, HUVEC, and A549 cells, which were made functionally deficient in both MetAP-1 and MetAP-2 were completely or almost completely inhibited in their growth, respectively. This closely resembled the observed growth inhibition in genetically double-deficient map1map2 yeast strains. These results suggest that MetAP-1 and MetAP-2 have essential functions in the control of mammalian cell proliferation and that MetAP-dependent growth control is evolutionarily highly conserved.
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