Learning kernels for support vector machines with polynomial powers of sigmoid

In the pattern recognition research field, Support Vector Machines (SVM) have been an effectiveness tool for classification purposes, being successively employed in many applications. The SVM input data is transformed into a high dimensional space using some kernel functions where linear separation is more likely. However, there are some computational drawbacks associated to SVM. One of them is the computational burden required to find out the more adequate parameters for the kernel mapping considering each non-linearly separable input data space, which reflects the performance of SVM. This paper introduces the Polynomial Powers of Sigmoid for SVM kernel mapping, and it shows their advantages over well-known kernel functions using real and synthetic datasets.

Cooperative effects of H+ and H- hydrido carbonyl ruthenium derivatives; role of homogeneous and heterogeneous protonic and lewis acids in catalytic hydrocarbonylation reactions

The role played by H+ hydrido iodocarbonyl and H- hydrido carbonyl ruthenium catalysts in the different catalytic steps of hydroformylation and hydroesterification of olefins, and in the homologation of alcohols has been investigated. The H- hydrido carbonyl species are mainly involved in the activation of olefins and in the hydrogenation of the acyl intermediates to aldehydes and alcohols, whereas the H+ hydrido iodocarbonyl derivatives are involved in the activation of alcohols and other oxygenated substrates, and in their carbonylation to esters. The cooperation between the two species, possible under particular reaction conditions, results in an improvement of the selectivity towards homologation (carbonylation plus hydrogenation) products. Heterogeneous Lewis acid promoters, easily recyclable from the reaction mixture, have also been successfully used in the hydrocarbonylation of alcohols, resulting in an increase of the carbonylation and homologation products. A reaction pathway in agreement with the experimental results is discussed. © 1989.

In Patients With Acute Myocardial Infarction, the Impact of Hyperglycemia as a Risk Factor for Mortality Is Not Homogeneous Across Age-Groups

OBJECTIVE To assess the impact of hyperglycemia in different age-groups of patients with acute myocardial infarction (AM I). RESEARCH DESIGN AND METHODS A total of 2,027 patients with AMI were categorized into one of five age-groups: <50 years (n = 301), >= 50 and <60 (n = 477),>= 60 and <70 (n = 545), >= 70 and <80 (n = 495), and years (n = 209). Hyperglycemia was defined as initial glucose >= 115 mg/dL. RESULTS The adjusted odds ratios for hyperglycemia predicting hospital mortality in groups 1-5 were, respectively, 7.57 (P = 0.004), 3.21 (P 0.046), 3.50 (P = 0.003), 3.20 (P < 0.001.), and 2.16 (P = 0.021). The adjusted P values for correlation between glucose level (as a continuous variable) and mortality were 0.007, <0.001, 0.043, <0.001, and 0.064. The areas under the ROC curves (AUCs) were 0.785, 0.709, 0.657, 0.648, and 0.613. The AUC in group 1 was significantly higher than those in groups 3-5. CONCLUSIONS The impact of hyperglycemia as a risk factor for hospital mortality in AMI is more pronounced in younger patients.

First report on the kinetics of the uncatalyzed esterification of cellulose under homogeneous reaction conditions: a rationale for the effect of carboxylic acid anhydride chain-length on the degree of biopolymer substitution

The kinetics of the homogeneous acylation of microcrystalline cellulose, MCC, with carboxylic acid anhydrides with different acyl chain-length (Nc; ethanoic to hexanoic) in LiCl/N,N-dimethylacetamide have been studied by conductivity measurements from 65 to 85 A degrees C. We have employed cyclohexylmethanol, CHM, and trans-1,2-cyclohexanediol, CHD, as model compounds for the hydroxyl groups of the anhydroglucose unit of cellulose. The ratios of rate constants of acylation of primary (CHM; Prim-OH) and secondary (CHD; Sec-OH) groups have been employed, after correction, in order to split the overall rate constants of the reaction of MCC into contributions from the discrete OH groups. For the model compounds, we have found that k((Prim-OH))/k((Sec-OH)) > 1, akin to reactions of cellulose under heterogeneous conditions; this ratio increases as a function of increasing Nc. The overall, and partial rate constants of the acylation of MCC decrease from ethanoic- to butanoic-anhydride and then increase for pentanoic- and hexanoic anhydride, due to subtle changes in- and compensations of the enthalpy and entropy of activation.

Further results in J and CTOD estimation procedures for SE(T) fracture specimens - Part I: Homogeneous materials

This study provides further developments of the evaluation procedure for J and CTOD in SE(T) fracture specimens based on plastic eta-factors and load separation analysis. Non-linear finite element analyses for plane-strain and 3-D models provide the relationship between plastic work and crack driving forces which define the eta-values. Further analyses based on the load separation method define alternative eta-values for the analyzed specimen configurations. Overall, the present results provide improved estimation equations for J and CTOD as a function of loading condition (pin load vs. clamp ends), crack geometry and strain hardening properties. (C) 2011 Elsevier Ltd. All rights reserved.

Homogeneous structures and rigidity of isoparametric submanifolds in Hilbert space

We study isoparametric submanifolds of rank at least two in a separable Hilbert space, which are known to be homogeneous by the main result in [E. Heintze and X. Liu, Ann. of Math. (2), 149 (1999), 149-181], and with such a submanifold M and a point x in M we associate a canonical homogeneous structure I" (x) (a certain bilinear map defined on a subspace of T (x) M x T (x) M). We prove that I" (x) , together with the second fundamental form alpha (x) , encodes all the information about M, and we deduce from this the rigidity result that M is completely determined by alpha (x) and (Delta alpha) (x) , thereby making such submanifolds accessible to classification. As an essential step, we show that the one-parameter groups of isometries constructed in [E. Heintze and X. Liu, Ann. of Math. (2), 149 (1999), 149-181] to prove their homogeneity induce smooth and hence everywhere defined Killing fields, implying the continuity of I" (this result also seems to close a gap in [U. Christ, J. Differential Geom., 62 (2002), 1-15]). Here an important tool is the introduction of affine root systems of isoparametric submanifolds.

Identification and characterization of drought/wet events homogeneous environments based on regional climate simulations

The objective of this study was to identify and characterize homogeneous environments based on the probability of drought/wet occurrence in the central-northern Brazil, considering Rondonia, Mato Grosso, Goias and Tocantins States. The drought index denominated the moisture anomaly Z-index (Z-index) was used. The input climate data for the drought index was generated by the regional climate model RegCM3 for the period from 1975 to 1989. As result of cluster analysis, it was identified 13 homogeneous environments. These environments were characterized based on the probability of drought/wet, relative density of drought/wet occurrence, annual rainfall variability and probability of drought occurrence during the rainy season (October to March). The Mato Grosso State had the highest number of homogeneous environments and the environment 11, located at southwest of this State had the highest probability of drought occurrence, 9%. The environment 10, located at the extreme east of Goias State, showed the lowest median for the total annual rainfall. The climatic event with the highest probability of occurrence in the study area is close to normal or normality moisture.

STABLE PIECEWISE POLYNOMIAL VECTOR FIELDS

Let N = {y > 0} and S = {y < 0} be the semi-planes of R-2 having as common boundary the line D = {y = 0}. Let X and Y be polynomial vector fields defined in N and S, respectively, leading to a discontinuous piecewise polynomial vector field Z = (X, Y). This work pursues the stability and the transition analysis of solutions of Z between N and S, started by Filippov (1988) and Kozlova (1984) and reformulated by Sotomayor-Teixeira (1995) in terms of the regularization method. This method consists in analyzing a one parameter family of continuous vector fields Z(epsilon), defined by averaging X and Y. This family approaches Z when the parameter goes to zero. The results of Sotomayor-Teixeira and Sotomayor-Machado (2002) providing conditions on (X, Y) for the regularized vector fields to be structurally stable on planar compact connected regions are extended to discontinuous piecewise polynomial vector fields on R-2. Pertinent genericity results for vector fields satisfying the above stability conditions are also extended to the present case. A procedure for the study of discontinuous piecewise vector fields at infinity through a compactification is proposed here.

EQUIVALENCE OF REAL MILNOR FIBRATIONS FOR QUASI-HOMOGENEOUS SINGULARITIES

We show that for real quasi-homogeneous singularities f : (R-m, 0) -> (R-2, 0) with isolated singular point at the origin, the projection map of the Milnor fibration S-epsilon(m-1) \ K-epsilon -> S-1 is given by f/parallel to f parallel to. Moreover, for these singularities the two versions of the Milnor fibration, on the sphere and on a Milnor tube, are equivalent. In order to prove this, we show that the flow of the Euler vector field plays and important role. In addition, we present, in an easy way, a characterization of the critical points of the projection (f/parallel to f parallel to) : S-epsilon(m-1) \ K-epsilon -> S-1.

Homogeneous metallicities and radial velocities for Galactic globular clusters

Well determined radial velocities and abundances are essential for analyzing the properties of the globular cluster system of the Milky Way. However more than 50% of these clusters have no spectroscopic measure of their metallicity. In this context, this work provides new radial velocities and abundances for twenty Milky Way globular clusters which lack or have poorly known values for these quantities. The radial velocities and abundances are derived from spectra obtained at the Ca II triplet using the FORS2 imager and spectrograph at the VLT, calibrated with spectra of red giants in a number of clusters with well determined abundances. For about half of the clusters in our sample we present significant revisions of the existing velocities or abundances, or both. We also confirm the existence of a sizable abundance spread in the globular cluster M 54, which lies at the center of the Sagittarius dwarf galaxy. In addition evidence is provided for the existence of a small intrinsic internal abundance spread (sigma[Fe/H](int) approximate to 0.11-0.14 dex, similar to that of M 54) in the luminous distant globular cluster NGC 5824. This cluster thus joins the small number of Galactic globular clusters known to possess internal metallicity ([Fe/H]) spreads.

Polynomial and Poisson dependence in free Poisson algebras and free Poisson fields

We prove that any two Poisson dependent elements in a free Poisson algebra and a free Poisson field of characteristic zero are algebraically dependent, thus answering positively a question from Makar-Limanov and Umirbaev (2007) [8]. We apply this result to give a new proof of the tameness of automorphisms for free Poisson algebras of rank two (see Makar-Limanov and Umirbaev (2011) [9], Makar-Limanov et al. (2009) [10]). (C) 2011 Elsevier Inc. All rights reserved.

Modeling random corrosion processes via polynomial chaos expansion

Polynomial Chaos Expansion (PCE) is widely recognized as a flexible tool to represent different types of random variables/processes. However, applications to real, experimental data are still limited. In this article, PCE is used to represent the random time-evolution of metal corrosion growth in marine environments. The PCE coefficients are determined in order to represent data of 45 corrosion coupons tested by Jeffrey and Melchers (2001) at Taylors Beach, Australia. Accuracy of the representation and possibilities for model extrapolation are considered in the study. Results show that reasonably accurate smooth representations of the corrosion process can be obtained. The representation is not better because a smooth model is used to represent non-smooth corrosion data. Random corrosion leads to time-variant reliability problems, due to resistance degradation over time. Time variant reliability problems are not trivial to solve, especially under random process loading. Two example problems are solved herein, showing how the developed PCE representations can be employed in reliability analysis of structures subject to marine corrosion. Monte Carlo Simulation is used to solve the resulting time-variant reliability problems. However, an accurate and more computationally efficient solution is also presented.

Figures of equilibrium for tidally deformed non-homogeneous celestial bodies

Abstract (2,250 Maximum Characters): Several theories of tidal evolution, since the theory developed by Darwin in the XIX century, are based on the figure of equilibrium of the tidally deformed body. Frequently the adopted figure is a Jeans prolate spheroid. In some case, however, the rotation is important and Roche ellipsoids are used. The main limitations of these models are (a) they refer to homogeneous bodies; (b) the rotation axis is perpendicular to the plane of the orbit. This communication aims at presenting several results in which these hypotheses are not done. In what concerns the non-homogeneity, the presented results concerns initially bodies formed by N homogeneous layers and we study the non sphericity of each layer and relate them to the density distribution. The result is similar to the Clairaut figure of equilibrium, often used in planetary sciences, but taking into full account the tidal deformation. The case of the rotation axis non perpendicular to the orbital plane is much more complex and the study has been restricted for the moment to the case of homogeneous bodies.

Construction of polynomial spline spaces over quadtree and octree T-meshes

[EN]We present a new strategy for constructing tensor product spline spaces over quadtree and octree T-meshes. The proposed technique includes some simple rules for inferring local knot vectors to define spline blending functions. These rules allow to obtain for a given T-mesh a set of cubic spline functions that span a space with nice properties: it can reproduce cubic polynomials, the functions are C2-continuous, linearly independent, and spaces spanned by nested T-meshes are also nested. In order to span spaces with these properties applying the proposed rules, the T-mesh should fulfill the only requirement of being a 0-balanced quadtree or octree. ..