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Geometric properties are critical for the function of molecules consisting of atoms which are usually modeled as a set of spheres in 3D. We propose "Molecular Geometry" which is a theoretical framework of computational understanding of the geometry of molecules in the claim that most, hopefully all, molecular structure problems can be effectively and efficiently facilitated by the "geometrization"...
Voronoi diagrams are powerful for solving spatial problems among particles with different sizes. In particular, the Voronoi diagram of spheres, also called the additively-weighted Voronoi diagram, has proven its powerful capability for solving molecular biology/material science problems in an unified framework. Beta-complex is a generalization of (weighted) alpha-complex and they share similarities...
Biological integration of implant to surrounding tissue is important process as it determines its clinical success and attraction of bone cells. Also, in order to reduce the problems of implant-related infections, many kinds of the surface treatment on titanium have been proposed. The formations of TiO2 nanotubes on the titanium have been widely studied to improve the biocompatibility of the surface,...
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