Carcinoma extension to adjacent organs is an important prognostic factor in papillary thyroid carcinoma (PTC). However, the biological behavior of PTC with carcinoma extension varies according to the degree of extension. In this study, we investigated whether and how subdivision of PTC extension accurately reflects patients' prognosis, using a series of 5508 patients with PTC without distant ...

We derive necessary and sufficient conditions for tangent plane and C-continuity of stationary subdivision schemes near extraordinary vertices. Our criteria generalize most previously known conditions. We introduce a new approach to analysis of subdivision surfaces based on the idea of the universal surface. Any subdivision surface can be locally represented as a projection of the universal sur...

Given a non-planar graph G with a subdivision of K5 as a subgraph, we can either transform the K5-subdivision into a K3,3-subdivision if it is possible, or else we obtain a partition of the vertices of G\K5 into equivalence classes. As a result, we can reduce a projective planarity or toroidality algorithm to a small constant number of simple planarity checks [6] or to a K3,3-subdivision in the...

The ability to control boundary behaviors is critical for the subdivision surface to become a useful representation in computer aided geometric design. Previous methods achieve boundary control by extending the boundary vertices of the control mesh, or by applying different subdivision rules to the boundary edges and vertices. This paper presents an open uniform quadratic subdivision scheme der...

We show that for every graph $G$ and $H$ obtained by subdividing each edge of at least $\Omega(\log |V(G)|)$ times, is nonrepetitively 3-colorable. In fact, we \pi'(G))$ subdivisions per are enough, where $\pi'(G)$ the nonrepetitive chromatic index $G$. This answers a question Wood improves similar result Pezarski Zmarz stated existence one 3-colorable subdivision with linear number vertices ed...

Abstract Subdivision schemes (SSs) have been the heart of computer-aided geometric design almost from its origin, and several unifications SSs established. are commonly used in computer graphics, ways were discovered to connect smooth curves/surfaces generated by applied geometry. To construct link between nonstationary geometry, this paper, we unify interpolating subdivision scheme (INSS) with...