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Dense Set (dense + set)

Distribution by Scientific Domains
Mathematics and Statistics60%

Selected Abstracts

Hierarchical Structure Recovery of Point-Sampled Surfaces

COMPUTER GRAPHICS FORUM, Issue 6 2010
Marco Attene
I.3 COMPUTER GRAPHICS; I.3.5 Computational Geometry and Object Modeling,Object hierarchies Abstract We focus on the class of ,regular' models defined by Várady et al. for reverse engineering purposes. Given a 3D surface,,represented through a dense set of points, we present a novel algorithm that converts,,to a hierarchical representation,. In,, the surface is encoded through patches of various shape and size, which form a hierarchical atlas. If,,belongs to the class of regular models, then,,captures the most significant features of,,at all the levels of detail. In this case, we show that,,can be exploited to interactively select regions of interest on,,and intuitively re-design the model. Furthermore,,,intrinsically encodes a hierarchy of useful ,segmentations' of,. We present a simple though efficient approach to extract and optimize such segmentations, and we show how they can be used to approximate the input point sets through idealized manifold meshes. [source]

Existence of a genetic risk factor on chromosome 5q in Italian Coeliac Disease families

ANNALS OF HUMAN GENETICS, Issue 1 2001
L. GRECO
Coeliac disease (CD) is a malabsorptive disorder of the small intestine resulting from ingestion of gluten. The HLA risk factors involved in CD are well known but do not explain the whole genetic susceptibility. Several regions of potential linkage on chromosomes 3q, 5q, 10q, 11q, 15q and 19q have already been reported in the literature. These six regions were analyzed with the Maximum Lod Score method on a dense set of markers. A new sample of 89 Italian sibpairs was available for study. There was no evidence for linkage for any of the regions tested, except for chromosome 5q. For this region, our data, as well as a sample of 93 sibpairs from our first genome screen (Greco et al. 1998), are compatible with the presence of a risk factor for CD with a moderate effect. [source]

Three circles theorems for Schrödinger operators on cylindrical ends and geometric applications

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 11 2008
Tobias H. Colding
We show that for a Schrödinger operator with bounded potential on a manifold with cylindrical ends, the space of solutions that grows at most exponentially at infinity is finite dimensional and, for a dense set of potentials (or, equivalently, for a surface for a fixed potential and a dense set of metrics), the constant function 0 is the only solution that vanishes at infinity. Clearly, for general potentials there can be many solutions that vanish at infinity. One of the key ingredients in these results is a three circles inequality (or log convexity inequality) for the Sobolev norm of a solution u to a Schrödinger equation on a product N × [0, T], where N is a closed manifold with a certain spectral gap. Examples of such N's are all (round) spheres ,,n for n , 1 and all Zoll surfaces. Finally, we discuss some examples arising in geometry of such manifolds and Schrödinger operators.© 2007 Wiley Periodicals, Inc. [source]

Hamiltonian cycles and paths with a prescribed set of edges in hypercubes and dense sets

JOURNAL OF GRAPH THEORY, Issue 2 2006
Rostislav Caha
Abstract This paper studies techniques of finding hamiltonian paths and cycles in hypercubes and dense sets of hypercubes. This problem is, in general, easily solvable but here the problem was modified by the requirement that a set of edges has to be used in such path or cycle. The main result of this paper says that for a given n, any sufficiently large hypercube contains a hamiltonian path or cycle with prescribed n edges just when the family of the edges satisfies certain natural necessary conditions. Analogous results are presented for dense sets. © 2005 Wiley Periodicals, Inc. J Graph Theory [source]