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.

The spectrum of an open vertex model based on the U(q)[SU(2)] algebra at roots of unity

We study the exact solution of an N-state vertex model based on the representation of the U(q)[SU(2)] algebra at roots of unity with diagonal open boundaries. We find that the respective reflection equation provides us one general class of diagonal K-matrices having one free-parameter. We determine the eigenvalues of the double-row transfer matrix and the respective Bethe ansatz equation within the algebraic Bethe ansatz framework. The structure of the Bethe ansatz equation combine a pseudomomenta function depending on a free-parameter with scattering phase-shifts that are fixed by the roots of unity and boundary variables. (C) 2010 Elsevier B.V. All rights reserved.

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.

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.

Iteration of closed geodesics in stationary Lorentzian manifolds

Following the lines of Bott in (Commun Pure Appl Math 9:171-206, 1956), we study the Morse index of the iterates of a closed geodesic in stationary Lorentzian manifolds, or, more generally, of a closed Lorentzian geodesic that admits a timelike periodic Jacobi field. Given one such closed geodesic gamma, we prove the existence of a locally constant integer valued map Lambda(gamma) on the unit circle with the property that the Morse index of the iterated gamma(N) is equal, up to a correction term epsilon(gamma) is an element of {0,1}, to the sum of the values of Lambda(gamma) at the N-th roots of unity. The discontinuities of Lambda(gamma) occur at a finite number of points of the unit circle, that are special eigenvalues of the linearized Poincare map of gamma. We discuss some applications of the theory.

Protein partitioning in poly(ethylene glycol)/sodium polyacrylate aqueous two-phase systems

The partition of hemoglobin, lysozyme and glucose-6-phospate dehydrogenase (G6PDH) in a novel inexpensive aqueous two-phase system (ATPS) composed by poly(ethylene glycol) (PEG) and sodium polyacrylate (NaPA) has been studied. The effect of NaCl and Na2SO4, pH and PEG molecular size on the partitioning has been studied. At high pH (above 9), hemoglobin partitions strongly to the PEG-phase. Although some precipitation of hemoglobin occurs, high recovery values are obtained particularly for lysozyme and G6PDH. The partitioning forces are dominated by the hydrophobic and electrochemical (salt) effects, since the positively charged lysozyme and negatively charged G6PDH partitions to the non-charged PEG and the strongly negatively charged polyacrylate enriched phase, respectively. (c) 2007 Elsevier B.V. All rights reserved.

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.

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.

Adsorption of amyloglucosidase from Aspergillus niger NRRL 3122 using ion exchange resin

Amyloglucosidase enzyme was produced by Aspergillus niger NRRL 3122 from solid-state fermentation, using deffated rice bran as substrate. The effects of process parameters (pH, temperature) in the equilibrium partition coefficient for the system amyloglucosidase - resin DEAE-cellulose were investigated, aiming at obtaining the optimum conditions for a subsequent purification process. The highest partition coefficients were obtained using 0.025M Tris-HCl buffer, pH 8.0 and 25ºC. The conditions that supplied the highest partition coefficient were specified, the isotherm that better described the amyloglucosidase process of adsorption obtained. It was observed that the adsorption could be well described by Langmuir equation and the values of Qm and Kd estimated at 133.0 U mL-1 and 15.4 U mL-1, respectively. From the adjustment of the kinetic curves using the fourth-order Runge-Kutta algorithm, the adsorption (k1) and desorption (k2) constants were obtained through optimization by the least square procedure, and the values calculated were 2.4x10-3 mL U-1 min-1 for k1 and 0.037 min-1 for k2 .

Transpressive dextral shear in the Italva-Itaperuna section, Northern State of Rio de Janeiro, Brazil

Structural analysis carried out on a segment of the Neoproterozoic Ribeira Belt, southeastern Brazil, show that it represents part of the transpressive dextral orogen related to the Central Mantiqueira Province. NNE-trending and steeply dipping regional mylonitic belts form anastomosed geometry, and describe a map-scale, S-C-like structure that is characterized by their deflection towards NE near the Além Paraíba Lineament. Lithological and structural control related to deformation partition were responsible for the formation of felsic mylonitic granulites with S-type granites lenses developed in ductile shear zones, alternated with less deformed intermediate to basic granulites associated with charnockites. The dextral shear sense indicators are consistent with transpressive deformation in the region and are common especially at the border of the main shear zones. The presence of S-type leucogranite may lead to variations of linear and planar relationships, which result in local extension zones. These elements are consistent with oblique continental collision considering the São Francisco Craton as a stable block.

Design and fabrication of microcavity-array superhydrophobic surfaces

We have modeled, fabricated, and characterized superhydrophobic surfaces with a morphology formed of periodic microstructures which are cavities. This surface morphology is the inverse of that generally reported in the literature when the surface is formed of pillars or protrusions, and has the advantage that when immersed in water the confined air inside the cavities tends to expel the invading water. This differs from the case of a surface morphology formed of pillars or protrusions, for which water can penetrate irreversibly among the microstructures, necessitating complete drying of the surface in order to again recover its superhydrophobic character. We have developed a theoretical model that allows calculation of the microcavity dimensions needed to obtain superhydrophobic surfaces composed of patterns of such microcavities, and that provides estimates of the advancing and receding contact angle as a function of microcavity parameters. The model predicts that the cavity aspect ratio (depth-to-diameter ratio) can be much less than unity, indicating that the microcavities do not need to be deep in order to obtain a surface with enhanced superhydrophobic character. Specific microcavity patterns have been fabricated in polydimethylsiloxane and characterized by scanning electron microscopy, atomic force microscopy, and contact angle measurements. The measured advancing and receding contact angles are in good agreement with the predictions of the model. (C) 2010 American Institute of Physics. [doi:10.1063/1.3466979]

Design and fabrication of superhydrophobic surfaces formed of microcavities

We have developed a theoretical model for superhydrophobic surfaces that are formed from an extended array of microcavities, and have fabricated specific microcavity patterns to form superhydrophobic surfaces of the kind modeled. The model shows that the cavity aspect ratio can be significantly less than unity, indicating that the microcavities do not need to be deep in order to enhance the superhydrophobic character of the surface. We have fabricated surfaces of this kind and measured advancing contact angle as high as 153 degrees, in agreement with predictions of the model.

Exploitation of a single interface flow system for on-line aqueous biphasic extraction

The exploitation of aqueous biphasic extraction is proposed for the first time in flow analysis This extraction strategy stands out for being environmentally attractive since it is based in the utilization of two immiscible phases that are intrinsically aqueous The organic solvents of the traditional liquid-liquid extractions ale no longer used, being replaced by non-toxic, non-flammable and non-volatile ones. A single interface flow analysis (SIFA) system was implemented to carry out the extraction process due to its favourable operational characteristics that include the high automation level and simplicity of operation, the establishment of a dynamic interface where the mass transfer occurred between the two immiscible aqueous phases, and the versatile control over the extraction process namely the extraction time The application selected to demonstrate the feasibility of SIFA to perform this aqueous biphasic extraction was the pre-concentration of lead. After extraction, lead reacted with 8-hydroxyquinoline-5-sulfonic acid and the resulting product was determined by a fluorimetric detector included in the flow manifold. Therefore, the SIFA single interface was used both as extraction (enrichment) and reaction interface. (C) 2010 Elsevier B.V All rights reserved.

Solution Polymerization of N-vinylcaprolactam in 1,4-dioxane. Kinetic Dependence on Temperature, Monomer, and Initiator Concentrations

The kinetics of the solution free radical polymerization of N-vinylcaprolactam, in 1,4-dioxane and under various polymerization conditions was studied. Azobisisobutyronitrile and 3-mercaptopropionic acid were used as initiator and as chain transfer agent (CTA), respectively. The influence of monomer and initiator concentrations and polymerization temperature on the rate of polymerizations (R(p)) was investigated. In general, high conversions were obtained. The order with respect to initiator was consistent with the classical kinetic rate equation, while the order with respect to the monomer was greater than unity. The overall activation energy of 53.6 kJ mol(-1) was obtained in the temperature range 60-80 degrees C. The decreasing of the absolute molecular weights when increasing the CIA concentration was confirmed by GPC/SEC/LALS analyses. It was confirmed by UV-visible analyses the effect of molecular weights on the lower critical solution temperature of the polymers. It was also verified that the addition of the CTA influenced the kinetic of the polymerizations. (C) 2010 Wiley Periodicals, Inc. J Appl Polym Sci 118: 229-240, 2010