Relativistic LCAO with Minimax Principle and New Balanced Basis Sets

Relativistic density functional theory is widely applied in molecular calculations with heavy atoms, where relativistic and correlation effects are on the same footing. Variational stability of the Dirac Hamiltonian is a very important field of research from the beginning of relativistic molecular calculations on, among efforts for accuracy, efficiency, and density functional formulation, etc. Approximations of one- or two-component methods and searching for suitable basis sets are two major means for good projection power against the negative continuum. The minimax two-component spinor linear combination of atomic orbitals (LCAO) is applied in the present work for both light and super-heavy one-electron systems, providing good approximations in the whole energy spectrum, being close to the benchmark minimax finite element method (FEM) values and without spurious and contaminated states, in contrast to the presence of these artifacts in the traditional four-component spinor LCAO. The variational stability assures that minimax LCAO is bounded from below. New balanced basis sets, kinetic and potential defect balanced (TVDB), following the minimax idea, are applied with the Dirac Hamiltonian. Its performance in the same super-heavy one-electron quasi-molecules shows also very good projection capability against variational collapse, as the minimax LCAO is taken as the best projection to compare with. The TVDB method has twice as many basis coefficients as four-component spinor LCAO, which becomes now linear and overcomes the disadvantage of great time-consumption in the minimax method. The calculation with both the TVDB method and the traditional LCAO method for the dimers with elements in group 11 of the periodic table investigates their difference. New bigger basis sets are constructed than in previous research, achieving high accuracy within the functionals involved. Their difference in total energy is much smaller than the basis incompleteness error, showing that the traditional four-spinor LCAO keeps enough projection power from the numerical atomic orbitals and is suitable in research on relativistic quantum chemistry. In scattering investigations for the same comparison purpose, the failure of the traditional LCAO method of providing a stable spectrum with increasing size of basis sets is contrasted to the TVDB method, which contains no spurious states already without pre-orthogonalization of basis sets. Keeping the same conditions including the accuracy of matrix elements shows that the variational instability prevails over the linear dependence of the basis sets. The success of the TVDB method manifests its capability not only in relativistic quantum chemistry but also for scattering and under the influence of strong external electronic and magnetic fields. The good accuracy in total energy with large basis sets and the good projection property encourage wider research on different molecules, with better functionals, and on small effects.

On Solution Sets of Information Inequalities

We investigate solution sets of a special kind of linear inequality systems. In particular, we derive characterizations of these sets in terms of minimal solution sets. The studied inequalities emerge as information inequalities in the context of Bayesian networks. This allows to deduce important properties of Bayesian networks, which is important within causal inference.

Evaluation of sets of oriented and non-oriented receptive fields as local descriptors

Local descriptors are increasingly used for the task of object recognition because of their perceived robustness with respect to occlusions and to global geometrical deformations. We propose a performance criterion for a local descriptor based on the tradeoff between selectivity and invariance. In this paper, we evaluate several local descriptors with respect to selectivity and invariance. The descriptors that we evaluated are Gaussian derivatives up to the third order, gray image patches, and Laplacian-based descriptors with either three scales or one scale filters. We compare selectivity and invariance to several affine changes such as rotation, scale, brightness, and viewpoint. Comparisons have been made keeping the dimensionality of the descriptors roughly constant. The overall results indicate a good performance by the descriptor based on a set of oriented Gaussian filters. It is interesting that oriented receptive fields similar to the Gaussian derivatives as well as receptive fields similar to the Laplacian are found in primate visual cortex.

Implementación de sistemas de información en los procesos de logística inversa de los Sets Quirúrgicos de Ortopedia

El presente documento es el producto de un análisis en cuanto al área de Logística Inversa del grupo empresarial AMAREY, el cual cuenta en la actualidad con más de dieciséis sistemas de sets quirúrgicos de ortopedia, es decir: sistema para mano, pie, radio, cadera, tibia, hombro, entre otros; de los cuales se tienen una cantidad específica de cada sistema, es decir: 4 sets del sistema Axsos. Se encuentra que la compañía no cuenta con ningún tipo de ayuda que le pueda brindar información exacta y a tiempo sobre las entradas y las salidas de los equipos de cirugía. Por lo anterior el resultado de la investigación está orientada a proponer la implementación de sistemas de información en los proceso de logística inversa de los sets quirúrgicos de ortopedia, con el fin de obtener una mejor gestión de la calidad al realizar la trazabilidad del material crítico y del set en general.

Confidence sets for asset correlations in portfolio credit risk

Asset correlations are of critical importance in quantifying portfolio credit risk and economic capitalin financial institutions. Estimation of asset correlation with rating transition data has focusedon the point estimation of the correlation without giving any consideration to the uncertaintyaround these point estimates. In this article we use Bayesian methods to estimate a dynamicfactor model for default risk using rating data (McNeil et al., 2005; McNeil and Wendin, 2007).Bayesian methods allow us to formally incorporate human judgement in the estimation of assetcorrelation, through the prior distribution and fully characterize a confidence set for the correlations.Results indicate: i) a two factor model rather than the one factor model, as proposed bythe Basel II framework, better represents the historical default data. ii) importance of unobservedfactors in this type of models is reinforced and point out that the levels of the implied asset correlationscritically depend on the latent state variable used to capture the dynamics of default,as well as other assumptions on the statistical model. iii) the posterior distributions of the assetcorrelations show that the Basel recommended bounds, for this parameter, undermine the levelof systemic risk.

Internal test sets studies in a group of antimalarials

Topological indices have been applied to build QSAR models for a set of 20 antimalarial cyclic peroxy cetals. In order to evaluate the reliability of the proposed linear models leave-n-out and Internal Test Sets (ITS) approaches have been considered. The proposed procedure resulted in a robust and consensued prediction equation and here it is shown why it is superior to the employed standard cross-validation algorithms involving multilinear regression models

The formation of learning sets by the chinchilla in an auditory discrimination procedure

This paper discusses a study conducted to test sound discrimination abilities of the chinchilla.

Preparation of consistent soil data sets for modelling purposes: Secondary SOTER data for four case study areas

The common GIS-based approach to regional analyses of soil organic carbon (SOC) stocks and changes is to define geographic layers for which unique sets of driving variables are derived, which include land use, climate, and soils. These GIS layers, with their associated attribute data, can then be fed into a range of empirical and dynamic models. Common methodologies for collating and formatting regional data sets on land use, climate, and soils were adopted for the project Assessment of Soil Organic Carbon Stocks and Changes at National Scale (GEFSOC). This permitted the development of a uniform protocol for handling the various input for the dynamic GEFSOC Modelling System. Consistent soil data sets for Amazon-Brazil, the Indo-Gangetic Plains (IGP) of India, Jordan and Kenya, the case study areas considered in the GEFSOC project, were prepared using methodologies developed for the World Soils and Terrain Database (SOTER). The approach involved three main stages: (1) compiling new soil geographic and attribute data in SOTER format; (2) using expert estimates and common sense to fill selected gaps in the measured or primary data; (3) using a scheme of taxonomy-based pedotransfer rules and expert-rules to derive soil parameter estimates for similar soil units with missing soil analytical data. The most appropriate approach varied from country to country, depending largely on the overall accessibility and quality of the primary soil data available in the case study areas. The secondary SOTER data sets discussed here are appropriate for a wide range of environmental applications at national scale. These include agro-ecological zoning, land evaluation, modelling of soil C stocks and changes, and studies of soil vulnerability to pollution. Estimates of national-scale stocks of SOC, calculated using SOTER methods, are presented as a first example of database application. Independent estimates of SOC stocks are needed to evaluate the outcome of the GEFSOC Modelling System for current conditions of land use and climate. (C) 2007 Elsevier B.V. All rights reserved.

Copper(II) complexes of tetradentate N2S2 donor sets: synthesis, crystal structure characterization and reactivity

Two mononuclear and one dinuclear copper(II) complexes, containing neutral tetradentate NSSN type ligands, of formulation [Cu-II(L-1)Cl]ClO4 (1), [Cu-II(L-2)Cl]ClO4 (2) and [Cu-2(II)(L-3)(2)Cl-2](ClO4)(2) (3) were synthesized and isolated in pure form [where L-1 = 1,2-bis(2-pyridylmethylthio)ethane, L-2 = 1,3-bis(2-pyridylmethylthio)propane and L-3 = 1,4-bis(2-pyridylmethylthio)butane]. All these green colored copper(II) complexes were characterized by physicochemical and spectroscopic methods. The dinuclear copper(II) complex 3 changed to a colorless dinuclear copper(I) species of formula [Cu-2(1)(L-3)(2)](ClO4)(2),0.5H(2)O (4) in dimethylformamide even in the presence of air at ambient temperature, while complexes I and 2 showed no change under similar conditions. The solid-state structures of complexes 1, 2 and 4 were established by X-ray crystallography. The geometry about the copper in complexes 1 and 2 is trigonal bipyramidal whereas the coordination environment about the copper(I) in dinuclear complex 4 is distorted tetrahedral. (C) 2008 Elsevier Ltd. All rights reserved.

A kernel-based two-class classifier for imbalanced data sets

Many kernel classifier construction algorithms adopt classification accuracy as performance metrics in model evaluation. Moreover, equal weighting is often applied to each data sample in parameter estimation. These modeling practices often become problematic if the data sets are imbalanced. We present a kernel classifier construction algorithm using orthogonal forward selection (OFS) in order to optimize the model generalization for imbalanced two-class data sets. This kernel classifier identification algorithm is based on a new regularized orthogonal weighted least squares (ROWLS) estimator and the model selection criterion of maximal leave-one-out area under curve (LOO-AUC) of the receiver operating characteristics (ROCs). It is shown that, owing to the orthogonalization procedure, the LOO-AUC can be calculated via an analytic formula based on the new regularized orthogonal weighted least squares parameter estimator, without actually splitting the estimation data set. The proposed algorithm can achieve minimal computational expense via a set of forward recursive updating formula in searching model terms with maximal incremental LOO-AUC value. Numerical examples are used to demonstrate the efficacy of the algorithm.