Twofold adaptive partition of unity implicits

Partition of Unity Implicits (PUI) has been recently introduced for surface reconstruction from point clouds. In this work, we propose a PUI method that employs a set of well-observed solutions in order to produce geometrically pleasant results without requiring time consuming or mathematically overloaded computations. One feature of our technique is the use of multivariate orthogonal polynomials in the least-squares approximation, which allows the recursive refinement of the local fittings in terms of the degree of the polynomial. However, since the use of high-order approximations based only on the number of available points is not reliable, we introduce the concept of coverage domain. In addition, the method relies on the use of an algebraically defined triangulation to handle two important tasks in PUI: the spatial decomposition and an adaptive polygonization. As the spatial subdivision is based on tetrahedra, the generated mesh may present poorly-shaped triangles that are improved in this work by means a specific vertex displacement technique. Furthermore, we also address sharp features and raw data treatment. A further contribution is based on the PUI locality property that leads to an intuitive scheme for improving or repairing the surface by means of editing local functions.

Sparse partition universal graphs for graphs of bounded degree

In 1983, Chvatal, Trotter and the two senior authors proved that for any Delta there exists a constant B such that, for any n, any 2-colouring of the edges of the complete graph K(N) with N >= Bn vertices yields a monochromatic copy of any graph H that has n vertices and maximum degree Delta. We prove that the complete graph may be replaced by a sparser graph G that has N vertices and O(N(2-1/Delta)log(1/Delta)N) edges, with N = [B`n] for some constant B` that depends only on Delta. Consequently, the so-called size-Ramsey number of any H with n vertices and maximum degree Delta is O(n(2-1/Delta)log(1/Delta)n) Our approach is based on random graphs; in fact, we show that the classical Erdos-Renyi random graph with the numerical parameters above satisfies a stronger partition property with high probability, namely, that any 2-colouring of its edges contains a monochromatic universal graph for the class of graphs on n vertices and maximum degree Delta. The main tool in our proof is the regularity method, adapted to a suitable sparse setting. The novel ingredient developed here is an embedding strategy that allows one to embed bounded degree graphs of linear order in certain pseudorandom graphs. Crucial to our proof is the fact that regularity is typically inherited at a scale that is much finer than the scale at which it is assumed. (C) 2011 Elsevier Inc. All rights reserved.

A New Approach to the Prediction of Partition Coefficients in Water/Organic Interfaces

In the present work, a new approach for the determination of the partition coefficient in different interfaces based on the density function theory is proposed. Our results for log P(ow) considering a n-octanol/water interface for a large super cell for acetone -0.30 (-0.24) and methane 0.95 (0.78) are comparable with the experimental data given in parenthesis. We believe that these differences are mainly related to the absence of van der Walls interactions and the limited number of molecules considered in the super cell. The numerical deviations are smaller than that observed for interpolation based tools. As the proposed model is parameter free, it is not limited to the n-octanol/water interface.

Microwave-assisted digestion procedures for biological samples with diluted nitric acid: Identification of reaction products

Microwave-assisted sample preparation using diluted nitric acid solutions is an alternative procedure for digesting organic samples. The efficiency of this procedure depends on the chemical properties of the samples and in this work it was evaluated by the determination of crude protein amount. fat and original carbon. Soybeans grains, bovine blood. bovine muscle and bovine viscera were digested in a cavity-microwave oven using oxidant mixtures in different acid concentrations. The digestion efficiency was evaluated based on the determination of residual carbon content and element recoveries using inductively coupled plasma optical emission spectrometry (ICP OES). In order to determine the main residual organic compounds, the digests were characterized by nuclear magnetic resonance (1 H NMR). Subsequently, studies concerning separation of nitrobenzoic acid isomers were performed by ion pair reversed phase liquid chromatography using a C18 stationary phase, water:acetonitrile:methanol (75:20:5, v/v/v) +0.05% (v/v) TFA as mobile phase and ultraviolet detection at 254 nm. Sample preparation based on diluted acids proved to be feasible and a recommendable alternative for organic sample digestion, reducing both the reagent volumes and the variability of the residues as a result of the process of decomposition. It was shown that biological matt-ices containing amino acids, proteins and lipids in their composition produced nitrobenzoic acid isomers and other organic compounds after cleavage of chemical bonds. (C) 2009 Elsevier B.V. All rights reserved.