Well-Centered Triangulation

Meshes composed of well-centered simplices have nice orthogonal dual meshes (the dual Voronoi diagram). This is useful for certain numerical algorithms that prefer such primal-dual mesh pairs. We prove that well-centered meshes also have optimality properties and relationships to Delaunay and minmax angle triangulations. We present an iterative algorithm that seeks to transform a given triangulation in two or three dimensions into a well-centered one by minimizing a cost function and moving the interior vertices while keeping the mesh connectivity and boundary vertices fixed. The cost function is a direct result of a new characterization of well-centeredness in arbitrary dimensions that we present. Ours is the first optimization-based heuristic for well-centeredness, and the first one that applies in both two and three dimensions. We show the results of applying our algorithm to small and large two-dimensional meshes, some with a complex boundary, and obtain a well-centered tetrahedralization of the cube. We also show numerical evidence that our algorithm preserves gradation and that it improves the maximum and minimum angles of acute triangulations created by the best known previous method.Comment: Content has been added to experimental results section. Significant edits in introduction and in summary of current and previous results. Minor edits elsewher

An Investigation of the Influence of Hope on the Relationship between Racial Discrimination and Depressive Symptoms Among African American College Students

The relationship between perceived racial discrimination, hope, and depressive symptoms among African American college students was investigated. The first supported hypotheses were that racial discrimination, hope, and hope\u27s two components, agency and pathways, would each significantly affect depressive symptoms. Hope and pathways, but not agency, were each found to moderate the relationship between racial discrimination and depressive symptoms and the moderation models were found to explain as much or more variance the models examining direct effects. Also, the interaction of pathways and racial discrimination explained more variance than any of the other models. These results suggest that hope and pathways influence the relationship between racial discrimination and depressive symptoms. Implications for understanding how hope can influence the experience of discrimination for African American college students are discussed

Historical review of research on protein kinase C in learning and memory

1. In 1977, the discovery of a new type of kinase was reported, which turned out to be a receptor for phorbol esters. Thereafter, several mechanisms regulating PKC activity and various PKC subtypes have been discovered. 2. A role for PKC in synaptic plasticity and information storage has been postulated in the mid-1980s. An important role for PKC has since been suggested in several learning and memory models, in which persistent changes in the activation of PKC outlasting the initial stimulating event are thought to be crucial. 3. A vast number of experiments have further substantiated a role of PKC in learning and memory using molecular genetic, behavioral, pharmacological, electrophysiological or immunocytochemical approaches in the late 1980s and the 1990s. PKC research of the past decade or so of has shown some exciting aspects of the putative role of PKC in synaptic plasticity and information storage. 4. The authors have provided highlights (Table 1) on research on PKC

Delaunay Hodge Star

We define signed dual volumes at all dimensions for circumcentric dual meshes. We show that for pairwise Delaunay triangulations with mild boundary assumptions these signed dual volumes are positive. This allows the use of such Delaunay meshes for Discrete Exterior Calculus (DEC) because the discrete Hodge star operator can now be correctly defined for such meshes. This operator is crucial for DEC and is a diagonal matrix with the ratio of primal and dual volumes along the diagonal. A correct definition requires that all entries be positive. DEC is a framework for numerically solving differential equations on meshes and for geometry processing tasks and has had considerable impact in computer graphics and scientific computing. Our result allows the use of DEC with a much larger class of meshes than was previously considered possible.Comment: Corrected error in Figure 1 (columns 3 and 4) and Figure 6 and a formula error in Section 2. All mathematical statements (theorems and lemmas) are unchanged. The previous arXiv version v3 (minus the Appendix) appeared in the journal Computer-Aided Desig

Triangulation of Simple 3D Shapes with Well-Centered Tetrahedra

A completely well-centered tetrahedral mesh is a triangulation of a three dimensional domain in which every tetrahedron and every triangle contains its circumcenter in its interior. Such meshes have applications in scientific computing and other fields. We show how to triangulate simple domains using completely well-centered tetrahedra. The domains we consider here are space, infinite slab, infinite rectangular prism, cube and regular tetrahedron. We also demonstrate single tetrahedra with various combinations of the properties of dihedral acuteness, 2-well-centeredness and 3-well-centeredness.Comment: Accepted at the conference "17th International Meshing Roundtable", Pittsburgh, Pennsylvania, October 12-15, 2008. Will appear in proceedings of the conference, published by Springer. For this version, we fixed some typo