Publications (3)4.08 Total impact
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ABSTRACT: Parametric and implicit forms are two common representations of geometric objects. It is important to be able to pass back and forth between the two representations, two processes called parameterization and implicitization, respectively. In this paper, we study the parametrization and implicitization of quadrics (quadratic parametric surfaces with two base points) and cubic surfaces (cubic parametric surfaces with six base points) with the help of μ-bases – a newly developed tool which connects the parametric form and the implicit form of a surface. For both cases, we show that the minimal μ-bases are all linear in the parametric variables, and based on this observation, very efficient algorithms are devised to compute the minimal μ-bases either from the parametric equation or the implicit equation. The conversion between the parametric equation and the implicit equation can be easily accomplished from the minimal μ-bases.Computing 04/2012; 79(2):131-142. · 0.70 Impact Factor
Article: An Ang1-Tie2-PI3K axis in neural progenitor cells initiates survival responses against oxygen and glucose deprivation.[show abstract] [hide abstract]
ABSTRACT: Neural progenitor cells (NPCs) have the potential to survive brain ischemia and participate in neurogenesis after stroke. However, it is not clear how survival responses are initiated in NPCs. Using embryonic mouse NPCs and the in vitro oxygen and glucose deprivation (OGD) model, we found that angiopoietin-1 (Ang1) could prevent NPCs from OGD-induced apoptosis, as evidenced by terminal deoxynucleotidyl transferase-mediated dUTP nick end labeling and annexin V labeling. Ang1 significantly elevated tunica intima endothelial kinase 2 (Tie2) autophosphorylation level, suggesting the existence of functional Tie2 receptors on NPCs. NPCs under OGD conditions exhibited reduction of Akt phosphorylation, decrease of the Bcl-2/Bax ratio, activation of caspase-3, cleavage of PARP, and downregulation of beta-catenin and nestin. Ang1 reversed the above changes concomitantly with significant rising of survival rates of NPCs under OGD, but all these effects of Ang1 could be blocked by either soluble extracellular domain of Tie2 Fc fusion protein (sTie2Fc) or the phosphoinositide 3-kinase (PI3K) inhibitor 2-(4-morpholinyl)-8-phenyl-1(4H)-benzopyran-4-one (LY294002). Our findings suggest the existence of an Ang1-Tie2-PI3K signaling axis that is essential in initiation of survival responses in NPCs against cerebral ischemia and hypoxia.Neuroscience 06/2009; 160(2):371-81. · 3.38 Impact Factor
Computing. 01/2007; 79:131-142.