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.

Effect of solvent hydration and temperature in the deacidification process of sunflower oil using ethanol

This work presents liquid-liquid experimental data for systems composed of sunflower seed oil, ethanol and water from 10 to 60 degrees C. The influence of process variables (temperature (T) and water concentration in the solvent (W)) on both the solvent content present in the raffinate (S(RP)) and extract (S(EP)) phases and the partition of free fatty acids (k(2)) was evaluated using the response surface methodology, where flash calculations were performed for each trial using the UNIQUAC equation. Water content in the solvent was the most important factor on the responses of S(EP) and k(2). Additionally, statistical analysis showed that the S(RP) was predominantly affected by temperature factor for low water content in the solvent. (c) 2009 Elsevier Ltd. All rights reserved.

Electrification of precipitating systems over the Amazon: Physical processes of thunderstorm development

This study investigated the physical processes involved in the development of thunderstorms over southwestern Amazon by hypothesizing causalities for the observed cloud-to-ground lightning variability and the local environmental characteristics. Southwestern Amazon experiences every year a large variety of environmental factors, such as the gradual increase in atmospheric moisture, extremely high pollution due to biomass burning, and intense deforestation, which directly affects cloud development by differential surface energy partition. In the end of the dry period it was observed higher percentages of positive cloud-to-ground (+CG) lightning due to a relative increase in +CG dominated thunderstorms (positive thunderstorms). Positive (negative) thunderstorms initiated preferentially over deforested (forest) areas with higher (lower) cloud base heights, shallower (deeper) warm cloud depths, and higher (lower) convective potential available energy. These features characterized the positive (negative) thunderstorms as deeper (relatively shallower) clouds, stronger (relatively weaker) updrafts with enhanced (decreased) mixed and cold vertically integrated liquid. No significant difference between thunderstorms (negative and positive) and nonthunderstorms were observed in terms of atmospheric pollution, once the atmosphere was overwhelmed by pollution leading to an updraft-limited regime. However, in the wet season both negative and positive thunderstorms occurred during periods of relatively higher aerosol concentration and differentiated size distributions, suggesting an aerosol-limited regime where cloud electrification could be dependent on the aerosol concentration to suppress the warm and enhance the ice phase. The suggested causalities are consistent with the invoked hypotheses, but they are not observed facts; they are just hypotheses based on plausible physical mechanisms.

Nested diets: a novel pattern of individual-level resource use

Many generalist populations may actually be composed of relatively specialist individuals. This `individual specialization` may have important ecological and evolutionary implications. Although this phenomenon has been documented in more than one hundred taxa, it is still unclear how individuals within a population actually partition resources. Here we applied several methods based on network theory to investigate the intrapopulation patterns of resource use in the gracile mouse opossum Gracilinanus microtarsus. We found evidence of significant individual specialization in this species and that the diets of specialists are nested within the diets of generalists. This novel pattern is consistent with a recently proposed model of optimal foraging and implies strong asymmetry in the interactions among individuals of a population.

Diet and food selection by small mammals in an old-growth Atlantic forest of south-eastern Brazil

Here we describe the stomach contents of nine small mammal species (seven rodents and two didelphid marsupials) co-occurring in an old-growth Atlantic forest area. For four terrestrial rodents, we also compared the importance of arthropods in the diet and the selection of arthropod groups by comparing consumption with availability. Small mammals and arthropods were sampled in a 36-ha grid containing 25 sampling stations spaced every 150 m, and 47 stomach contents were analysed. While plant matter was the predominant item in the stomach contents of two rodents (Oligoryzomys nigripes and Rhipidomys mastacalis), four species presented arthropods as the main food item (the rodents Brucepattersonius soricinus and Oxymycterus dasytrichus, and the marsupials Monodelphis n. sp. and Marmosops incanus) and three consumed more plant matter than arthropods, but had significant amounts of both items (the rodents Delomys sublineatus, Euryoryzomys russatus and Thaptomys nigrita). Our results suggest that differences in diet, coupled with differences in habit and microhabitat preferences, are important factors allowing resource partition among species of the diverse group of co-occurring terrestrial small mammals in Atlantic forest areas. Moreover, arthropods were not preyed opportunistically by any of the four terrestrial rodents, since consumption was not proportional to availability. Rather, selection or rejection of arthropod groups seems to be determined by aspects other than availability, such as nutritional value, easiness of capture and handling or palatability.

SEASONAL MICROHABITAT SELECTION BY TERRESTRIAL RODENTS IN AN OLD-GROWTH ATLANTIC FOREST

We tested the hypothesis that microhabitat variables, abundance of terrestrial rodents, and microhabitat selection patterns of terrestrial rodents vary between the cool-dry and warm-wet season in the Atlantic forest of Brazil. We selected variables associated with ecological factors potentially important to terrestrial rodents (physical structure of litter and woody debris, and arthropod availability) and established 25 small, independent sampling units covering 36 ha of a homogenous, mature Atlantic forest patch. Litter humidity and height, amount of small woody debris, arthropod availability, and terrestrial rodent abundance increased, whereas the quantity of large woody debris decreased in the warm-wet season. Greater spatial segregation among terrestrial rodents also was observed in this season, especially between morphologically similar species. The distribution of 3 of the 4 most common terrestrial rodents was influenced by microhabitat variables in at least I of the seasons, and these species also differed in their pattern of microhabitat selection between seasons. In general, the amount of small woody debris and litter humidity were more important for the microscale distribution of terrestrial rodents in the cool-dry season, whereas in the mild warm-wet season species distributions were associated with food availability or were not clearly influenced by the measured variables. The patterns of microhabitat selection by 3 common terrestrial rodents, which were associated with features that characterize old-growth forest, may be responsible for their vulnerability to forest fragmentation.

Generalized external indexes for comparing data partitions with overlapping categories

There is a family of well-known external clustering validity indexes to measure the degree of compatibility or similarity between two hard partitions of a given data set, including partitions with different numbers of categories. A unified, fully equivalent set-theoretic formulation for an important class of such indexes was derived and extended to the fuzzy domain in a previous work by the author [Campello, R.J.G.B., 2007. A fuzzy extension of the Rand index and other related indexes for clustering and classification assessment. Pattern Recognition Lett., 28, 833-841]. However, the proposed fuzzy set-theoretic formulation is not valid as a general approach for comparing two fuzzy partitions of data. Instead, it is an approach for comparing a fuzzy partition against a hard referential partition of the data into mutually disjoint categories. In this paper, generalized external indexes for comparing two data partitions with overlapping categories are introduced. These indexes can be used as general measures for comparing two partitions of the same data set into overlapping categories. An important issue that is seldom touched in the literature is also addressed in the paper, namely, how to compare two partitions of different subsamples of data. A number of pedagogical examples and three simulation experiments are presented and analyzed in details. A review of recent related work compiled from the literature is also provided. (c) 2010 Elsevier B.V. All rights reserved.

Quality indices for (practical) clustering evaluation

Clustering quality or validation indices allow the evaluation of the quality of clustering in order to support the selection of a specific partition or clustering structure in its natural unsupervised environment, where the real solution is unknown or not available. In this paper, we investigate the use of quality indices mostly based on the concepts of clusters` compactness and separation, for the evaluation of clustering results (partitions in particular). This work intends to offer a general perspective regarding the appropriate use of quality indices for the purpose of clustering evaluation. After presenting some commonly used indices, as well as indices recently proposed in the literature, key issues regarding the practical use of quality indices are addressed. A general methodological approach is presented which considers the identification of appropriate indices thresholds. This general approach is compared with the simple use of quality indices for evaluating a clustering solution.

HIERARCHICAL DECOMPOSITION OF MULTICLASS PROBLEMS

Several popular Machine Learning techniques are originally designed for the solution of two-class problems. However, several classification problems have more than two classes. One approach to deal with multiclass problems using binary classifiers is to decompose the multiclass problem into multiple binary sub-problems disposed in a binary tree. This approach requires a binary partition of the classes for each node of the tree, which defines the tree structure. This paper presents two algorithms to determine the tree structure taking into account information collected from the used dataset. This approach allows the tree structure to be determined automatically for any multiclass dataset.

Fiedler trees for multiscale surface analysis

In this work we introduce a new hierarchical surface decomposition method for multiscale analysis of surface meshes. In contrast to other multiresolution methods, our approach relies on spectral properties of the surface to build a binary hierarchical decomposition. Namely, we utilize the first nontrivial eigenfunction of the Laplace-Beltrami operator to recursively decompose the surface. For this reason we coin our surface decomposition the Fiedler tree. Using the Fiedler tree ensures a number of attractive properties, including: mesh-independent decomposition, well-formed and nearly equi-areal surface patches, and noise robustness. We show how the evenly distributed patches can be exploited for generating multiresolution high quality uniform meshes. Additionally, our decomposition permits a natural means for carrying out wavelet methods, resulting in an intuitive method for producing feature-sensitive meshes at multiple scales. Published by Elsevier Ltd.

The degree of polydispersity in micellar dispersions: A sum rule approach

Statistical properties of a two-dimensional ideal dispersion of polydisperse micelles are derived by analyzing the convergence properties of a sum rule set by mass conservation. Internal micellar degrees of freedom are accounted for by a microscopic model describing small displacements of the constituting amphiphiles with respect to their equilibrium positions. The transfer matrix (TM) method is employed to compute internal micelle partition function. We show that the conditions under which the sum rule is saturated by the largest eigenvalue of the TM determine the value of amphiphile concentration above which the dispersion becomes highly polydisperse and micelle sizes approach a Schultz distribution. (C) 2011 Elsevier B.V. All rights reserved.

Classical simulation of deposition of thiophene oligomers on TiO(2)-anatase: Relevance of long-range electrostatic interactions

We performed classical molecular dynamics simulations of the vapor-deposition of alpha-T4 oligomers on the TiO(2)-anatase (101) surface, comparing different sets of charges associated with the atoms of the model. The potential energy surfaces for alpha-T4 and TiO(2) were described by re-parametrizations of the Universal force field with charges given by the charge equilibration (QEq) scheme, or with fixed charges obtained by an ab initio method using the Hirshfeld partition. The two sets of charges lead to completely different results for the interface formation, and for the characteristics of the organic film, with a clearly defined alpha-T4 contact layer in the QEq case, and a more homogeneous molecular distribution when using Hirshfeld charges. The main reason for the discrepancy was found to be the incorrect charge assignment given by QEq to the sulfur and alpha-carbon atoms in thiophenes, and highlight the relevance of long-range interactions in the organization of molecular films. (C) 2009 Elsevier B.V. All rights reserved.

EXPERIMENTAL AND THEORETICAL STUDY OF SHYNTESIS OF N-ALKYL-NITROIMIDAZOLES.

In this work we realized and experimental and theoretical study of the N-alkylation of nitroimidazoles. The N-alkyl-2-methyl-nitroimidazoles correspond to biologically active molecules, obtained by reaction of 2-methyl-5-nitroimidazole and different alkyl halides. This reaction showed the formation of a mixture of isomeric products in different proportions, denominated like N-alkyl-2-methyl-4-nitroimidazole and N-alkyl-2-methyl-5-nitroimidazole, respectively. The reaction suggestes the formation of a tautomeric equilibrium, which generates two nucleophilic sites susceptible to electrophilic attack by the alkyl halide. The local nucleophilic reactivity of the nitroimidazole nng is determined using local reactivity indices such as the Fukui function and the electrostatic potential, besides the electronic localization function (ELF). The Fukui function was integrated for each atom using partition schemes based on analysis of Mulliken charges and natural bond orbital (NBO). Finally the reaction profiles were assessed. The results show a minor difference in the local reactivity. Nevertheless a significant difference in energy barriers is observed explaining the formation of an isomeric product over another. These results agree quite well with the experimental data.