Michael Souza

Solving the molecular distance geometry problem with inaccurate distance data

We present a new iterative algorithm for the molecular distance geometry problem with inaccurate and sparse data, which is based on the solution of linear systems, maximum cliques, and a minimization of nonlinear least-squares function. Computational results with real protein structures are presented in order to validate our approach.

Hyperbolic smoothing and penalty techniques applied to molecular structure determination

Abstract This work considers the problem of estimating the relative positions of all atoms of a protein, given a subset of all the pair-wise distances between the atoms. This problem is NP-hard, and the usual formulations are nonsmoothed and nonconvex, having a high number of local minima. Our contribution is an efficient method that combines the hyperbolic smoothing and the penalty techniques that are useful in obtaining differentiability and reducing the number of local minima.

Pb(II) adsorption by biomass from chemically modified aquatic macrophytes, Salvinia sp. and Pistia stratiotes

This study used two biosorbents obtained from the aquatic plants Salvinia sp. and Pistia stratiotes to establish a sustainable and alternative treatment for industrial wastewater and other water bodies that contain Pb(II). The biosorbent named Salvinia with NaOH (SOH) was obtained from Salvinia sp., and Salvinia and Pistia mixture with NaOH (SPOH) was obtained from a mixture of the two plants in a 1:1 ratio. The biosorbents were characterized by zeta potential, infrared (IR) spectroscopy, scanning electron microscopy (SEM), energy-dispersive spectroscopy and Boehm titration. The results of Boehm titration and IR analysis indicated the presence of basic functional groups, whereas those of SEM analysis indicated that the biosorbents have a structure conducive to adsorption. Batch adsorption experiments were performed to observe the effects of pH, contact time, initial lead concentration and temperature on the metal removal process. The results revealed that the biosorbents efficiently removed Pb(II) from aqueous solutions, with a maximum observed adsorption capacity (saturation limits, qmax) of 202 mg g(-1) and 210.1 mg g(-1) for SPOH and SOH, respectively. The Freundlich, Langmuir and Dubinin-Radushkevich models were applied to the data; these biosorbent studies did not satisfactorily adjust to either of the models, but the information obtained helped us understand the adsorption mechanism.

Logarithmic quasi-distance proximal point scalarization method for multi-objective programming

Recently, Gregorio and Oliveira developed a proximal point scalarization method (applied to multi-objective optimization problems) for an abstract strict scalar representation with a variant of the logarithmic-quadratic function of Auslender et?al. as regularization. In this study, a variation of this method is proposed, using the regularization with logarithm and quasi-distance. By restricting it to a certain class of quasi-distances that are Lipschitz continuous and coercive in any of their arguments, we show that any sequence { ( x k , z k ) } ? R n × R + + m generated by the method satisfies: {zk} is convergent; and {xk} is bounded and its accumulation points are weak Pareto solutions of the unconstrained multi-objective optimization problem

Estratégias para Mitigação de Erros Numéricos em Algoritmos de Determinação de Estruturas Proteicas

Apresentamos duas estrategias de para mitigacao de erros numericos em algoritmos iterativos que usam apenas informacoes locais para o problema de geometria de distâncias moleculares. Alem disso, realizamos experimentos numericos em instâncias construidas a partir de proteinas reais, envolvendo milhares de atomos, e mostramos que as estrategias propostas conjugadas em um novo algoritmo BuildUpOpt sao capazes de resolver instâncias de grande porte.

Modeling the Molecular Distance Geometry Problem Using Dihedral Angles

An alternative formulation based on dihedral angles to the molecular distance geometry problem with imprecise distance data is presented. This formulation considers the additional hypothesis of a particular ordering such that all distances \(||x_i-x_j||=d_{ij}\), \(|i-j|<3\), are known. Considering that bond length and angles are given a priori in a protein backbone, there is always at least one of such ordering in instances involving real protein data. This hypothesis reduces by 2/3 the number of variables of the problem and allows us to calculate the derivatives of the standard Cartesian coordinates representation with respect to the dihedral angles. Numerical experiments illustrate the correctness and viability of the proposed formulation.

Um Método para o Cálculo da Inversa de Matrizes Simétricas e Positivas Definidas em Bloco

Nosso objetivo e propor um novo algoritmo para o calculo de inversas de matrizes simetricas e positivas definidas (SPD) em bloco. Em [1], os autores propoem um algoritmo baseado no processo de Gram-Schmidt, utilizando um produto interno induzido por uma matriz SPD, para ser usado como precondicionador para o Metodo de Gradientes Conjugados. Aqui propomos uma generalizacao desse processo para matrizes SPD em bloco, que tambem sera utilizado, posteriormente, como precondicionador.

Método de Precondicionamento CPR em Simulações de Reservatório de Petróleo

Este trabalho apresenta a implementacao, em MATLAB, de um esquema de dois estagios do tipo CPR (do ingles Constrained Pressure Residual) [5], para a resolucao de sistemas lineares de grande porte oriundos de simulacoes de extracao de reservatorios de petroleo. Vamos descrever o metodo CPR, seus dois estagios e apresentar resultados para matrizes de problemas reais, comparando-os com resultados utilizando precondicionadores classicos.

Implementação paralela de um precondicionador algébrico de dois níveis de decomposição de domínios baseado em ILU(k)

Discutimos a implementacao paralela em Message-Passing Interface (MPI) de um precondicionador algebrico de dois niveis de decomposicao de dominios baseado em fatoracao incompleta LU (ILU(k)) utilizando a biblioteca PETSc e estrategias para melhorar a performance e reduzir a comunicacao entre os processadores durante a construcao e aplicacao.

Nova implementação do precondicionador AINV em acelerador NVIDIA utilizando a biblioteca CUSP

Comparamos o desempenho em placa grafica (GPU) do precondicionador AINV baseado na aproximacao da inversa. Os resultados de nossos experimentos numericos e computacionais indicam que nossa implementacao e competitiva e possui resultados melhores do que a versao disponivel na biblioteca CUSP largamente utilizada em aplicacoes com aceleradores NVIDIA. Alem disso, apresentamos as ideias principais na definicao do precondicionador e detalhes sobre a implementacao.