Geometric optimization methods for the analysis of gene expression data

DNA microarrays provide such a huge amount of data that unsupervised methods are required to reduce the dimension of the data set and to extract meaningful biological information. This work shows that Independent Component Analysis (ICA) is a promising approach for the analysis of genome-wide transcriptomic data. The paper first presents an overview of the most popular algorithms to perform ICA. These algorithms are then applied on a microarray breast-cancer data set. Some issues about the application of ICA and the evaluation of biological relevance of the results are discussed. This study indicates that ICA significantly outperforms Principal Component Analysis (PCA).

Geometric optimization methods for independent component analysis applied on gene expression data

DNA microarrays provide a huge amount of data and require therefore dimensionality reduction methods to extract meaningful biological information. Independent Component Analysis (ICA) was proposed by several authors as an interesting means. Unfortunately, experimental data are usually of poor quality- because of noise, outliers and lack of samples. Robustness to these hurdles will thus be a key feature for an ICA algorithm. This paper identifies a robust contrast function and proposes a new ICA algorithm. © 2007 IEEE.

Geometric optimization on visibility problems: metaheuristic and exact solutions

Os problemas de visibilidade têm diversas aplicações a situações reais. Entre os mais conhecidos, e exaustivamente estudados, estão os que envolvem os conceitos de vigilância e ocultação em estruturas geométricas (problemas de vigilância e ocultação). Neste trabalho são estudados problemas de visibilidade em estruturas geométricas conhecidas como polígonos, uma vez que estes podem representar, de forma apropriada, muitos dos objectos reais e são de fácil manipulação computacional. O objectivo dos problemas de vigilância é a determinação do número mínimo de posições para a colocação de dispositivos num dado polígono, de modo a que estes dispositivos consigam “ver” a totalidade do polígono. Por outro lado, o objectivo dos problemas de ocultação é a determinação do número máximo de posições num dado polígono, de modo a que quaisquer duas posições não se consigam “ver”. Infelizmente, a maior parte dos problemas de visibilidade em polígonos são NP-difíceis, o que dá origem a duas linhas de investigação: o desenvolvimento de algoritmos que estabelecem soluções aproximadas e a determinação de soluções exactas para classes especiais de polígonos. Atendendo a estas duas linhas de investigação, o trabalho é dividido em duas partes. Na primeira parte são propostos algoritmos aproximados, baseados essencialmente em metaheurísticas e metaheurísticas híbridas, para resolver alguns problemas de visibilidade, tanto em polígonos arbitrários como ortogonais. Os problemas estudados são os seguintes: “Maximum Hidden Vertex Set problem”, “Minimum Vertex Guard Set problem”, “Minimum Vertex Floodlight Set problem” e “Minimum Vertex k-Modem Set problem”. São também desenvolvidos métodos que permitem determinar a razão de aproximação dos algoritmos propostos. Para cada problema são implementados os algoritmos apresentados e é realizado um estudo estatístico para estabelecer qual o algoritmo que obtém as melhores soluções num tempo razoável. Este estudo permite concluir que as metaheurísticas híbridas são, em geral, as melhores estratégias para resolver os problemas de visibilidade estudados. Na segunda parte desta dissertação são abordados os problemas “Minimum Vertex Guard Set”, “Maximum Hidden Set” e “Maximum Hidden Vertex Set”, onde são identificadas e estudadas algumas classes de polígonos para as quais são determinadas soluções exactas e/ou limites combinatórios.

Maximum Margin Classifiers with Specified False Positive and False Negative Error Rates

This paper addresses the problem of maximum margin classification given the moments of class conditional densities and the false positive and false negative error rates. Using Chebyshev inequalities, the problem can be posed as a second order cone programming problem. The dual of the formulation leads to a geometric optimization problem, that of computing the distance between two ellipsoids, which is solved by an iterative algorithm. The formulation is extended to non-linear classifiers using kernel methods. The resultant classifiers are applied to the case of classification of unbalanced datasets with asymmetric costs for misclassification. Experimental results on benchmark datasets show the efficacy of the proposed method.

How does basis set superposition error change the potential surfaces for hydrogen-bonded dimers?

We describe a simple method to automate the geometric optimization of molecular orbital calculations of supermolecules on potential surfaces that are corrected for basis set superposition error using the counterpoise (CP) method. This method is applied to the H-bonding complexes HF/HCN, HF/H2O, and HCCH/H2O using the 6-31G(d,p) and D95 + + (d,p) basis sets at both the Hartree-Fock and second-order Møller-Plesset levels. We report the interaction energies, geometries, and vibrational frequencies of these complexes on the CP-optimized surfaces; and compare them with similar values calculated using traditional methods, including the (more traditional) single point CP correction. Upon optimization on the CP-corrected surface, the interaction energies become more negative (before vibrational corrections) and the H-bonding stretching vibrations decrease in all cases. The extent of the effects vary from extremely small to quite large depending on the complex and the calculational method. The relative magnitudes of the vibrational corrections cannot be predicted from the H-bond stretching frequencies alone

Disparity estimation using TI multi-wavelet transform

A multi-resolution image matching technique based on translation invariant discrete multi-wavelet transform followed by a coarse to fine matching strategy is presented. The technique addresses the estimation of optimal corresponding points and the corresponding disparity maps in the presence of occlusion, ambiguity and illuminative variations in the two perspective views taken by two different cameras or at different lighting conditions. The problem of occlusion and ambiguity is addressed explicitly by a geometric optimization approach along with the uniqueness constraint whereas the illuminative variation is dealt with by using windowed normalized correlation on the discrete multi-wavelet coefficients.

Modelagem molecular na caracterização eletrônica de oligopeptídeos e na descrição quântica da interação fármaco-receptor

In this dissertation, the theoretical principles governing the molecular modeling were applied for electronic characterization of oligopeptide α3 and its variants (5Q, 7Q)-α3, as well as in the quantum description of the interaction of the aminoglycoside hygromycin B and the 30S subunit of bacterial ribosome. In the first study, the linear and neutral dipeptides which make up the mentioned oligopeptides were modeled and then optimized for a structure of lower potential energy and appropriate dihedral angles. In this case, three subsequent geometric optimization processes, based on classical Newtonian theory, the semi-empirical and density functional theory (DFT), explore the energy landscape of each dipeptide during the search of ideal minimum energy structures. Finally, great conformers were described about its electrostatic potential, ionization energy (amino acids), and frontier molecular orbitals and hopping term. From the hopping terms described in this study, it was possible in subsequent studies to characterize the charge transport propertie of these peptides models. It envisioned a new biosensor technology capable of diagnosing amyloid diseases, related to an accumulation of misshapen proteins, based on the conductivity displayed by proteins of the patient. In a second step of this dissertation, a study carried out by quantum molecular modeling of the interaction energy of an antibiotic ribosomal aminoglicosídico on your receiver. It is known that the hygromycin B (hygB) is an aminoglycoside antibiotic that affects ribosomal translocation by direct interaction with the small subunit of the bacterial ribosome (30S), specifically with nucleotides in helix 44 of the 16S ribosomal RNA (16S rRNA). Due to strong electrostatic character of this connection, it was proposed an energetic investigation of the binding mechanism of this complex using different values of dielectric constants (ε = 0, 4, 10, 20 and 40), which have been widely used to study the electrostatic properties of biomolecules. For this, increasing radii centered on the hygB centroid were measured from the 30S-hygB crystal structure (1HNZ.pdb), and only the individual interaction energy of each enclosed nucleotide was determined for quantum calculations using molecular fractionation with conjugate caps (MFCC) strategy. It was noticed that the dielectric constants underestimated the energies of individual interactions, allowing the convergence state is achieved quickly. But only for ε = 40, the total binding energy of drug-receptor interaction is stabilized at r = 18A, which provided an appropriate binding pocket because it encompassed the main residues that interact more strongly with the hygB - C1403, C1404, G1405, A1493, G1494, U1495, U1498 and C1496. Thus, the dielectric constant ≈ 40 is ideal for the treatment of systems with many electrical charges. By comparing the individual binding energies of 16S rRNA nucleotides with the experimental tests that determine the minimum inhibitory concentration (MIC) of hygB, it is believed that those residues with high binding values generated bacterial resistance to the drug when mutated. With the same reasoning, since those with low interaction energy do not influence effectively the affinity of the hygB in its binding site, there is no loss of effectiveness if they were replaced.

Análise vibracional do α-tocoferol

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Análisis experimental y por el método de los elementos finitos del estado de tensiones en uniones carpinteras de empalme de llave

In this research, the halved and tabled traditional timber scarf joint is analyzed. This joint consists in two end joint pieces usually subjected to tension. Initially, the study is discussed from an experimental point of view. In this way, 3 critical cross-sections are established (section of the notch, section of the horizontal plane and reduced section) and mechanical tests are performed to achieve the failure on each of critical sections by changing the geometry of the joint. The study is completed by developing a finite element model which allows verify experimental results and extend the analysis to other geometries. This model has to simulate the real behavior of the material which is being studied, so mechanical tests are performed to obtain the elastic constants and the coefficients of friction of the material. In the reduced section, an abrupt decrease of the effective cross-section takes place, and this effect is also experimentally analyzed. These tests indicate that a crack is initiated before the bending-tension failure occurs in the reduced section. The test material consists of wood of Pinus sylvestris L. coming from the “Valsaín´s Sawmill” (Segovia) with “premium quality” according to the nonstructural wood visual classification of sawmill. It is observed that initiation of a crack, in the mortise (bottom of reduced section), and shear stress concentration, at the initial part of the heel (beginning of horizontal plane), completely determine the mechanical behaviour of the joint, resulting in 3 failure modes: local compression failure in the section of the notch, shear failure in the horizontal plane, and failure of stresses concentration, mainly perpendicular to the grain tension, at the bottom of reduced section. The geometric optimization is obtained for halved and tabled traditional scarf joint, when the joint has made with similar properties of wood than tested specimens, for any height and width of the cross-section. It is considered the failure due to the initiation of a crack in reduced section, by applying a correction coefficient into the usual equation used to design the members subjected to both tension and bending. Therefore, it is possible to obtain, analytically, the design conditions to be met of the 3 critical cross-sections. According to the theoretical optimization, the tension strength of complete cross-section is reduced until 14%, when using this type of joint. The experimental optimization indicates even a greater reduction, until 6%. En el presente trabajo de investigación se analiza el comportamiento mecánico de las uniones tradicionales de empalme de llave, que consisten en dos piezas unidas por sus testas transmitiéndose entre ellas principalmente un esfuerzo de tracción. Inicialmente, el estudio se aborda desde un punto de vista experimental. De este modo, se establecen las 3 secciones críticas o de estudio (sección del encaje, sección rasante del cogote y sección reducida) y se realizan ensayos mecánicos, variando la geometría de la unión, para alcanzar la rotura en cada una de ellas. Se completa el estudio mediante la elaboración de un modelo por elementos finitos que permite verificar los resultados experimentales y ampliar el análisis a otras geometrías. Este modelo debe simular el comportamiento real del material objeto de estudio, por lo que se realizan ensayos para obtener las constantes elásticas y los coeficientes de rozamiento del mismo. También se analiza, experimentalmente, el efecto entalladura que reduce bruscamente la sección completa del tirante, estableciendo que el fallo por flexotracción en la sección reducida de la pieza, no llega a producirse por el inicio previo de una grieta. El material de ensayo consiste en madera de Pinus sylvestris L. (pino silvestre) procedente del Aserradero de Valsaín (Segovia) y de calidad “Extra” o “Primera” según la clasificación visual no estructural del aserradero. Se observa que el inicio de una grieta en la mortaja del rediente y la concentración de tensiones tangenciales en la parte inicial del cogote, determinan completamente el comportamiento mecánico de la unión, dando lugar a 3 modos distintos de rotura: fallo por compresión en la sección del encaje, fallo por cortante en la sección rasante y fallo por concentración de tensiones, principalmente tracciones perpendiculares, en el rebaje de la sección reducida. Se consigue optimizar geométricamente cualquier empalme de llave confeccionado con madera de características similares a la ensayada, para cualquier valor de la altura y de la anchura de la sección. Se considera el agotamiento en la sección reducida causado por el inicio de grieta, mediante la aplicación de un coeficiente corrector en la expresión habitual de agotamiento por flexotracción, en consecuencia, finalmente es posible obtener, de modo analítico, un valor del índice de agotamiento en cada una de las 3 secciones de estudio. La optimización teórica del empalme de llave indica que la capacidad resistente del tirante bruto se reduce al 14%, cuando se coloca este tipo de unión tradicional. Experimentalmente se obtiene, que, para la sección ensayada, la capacidad resistente del tirante bruto se reduce todavía más, llegando al 6%.

Efeito do substituinte “-F” nas propriedades electrónicas e estruturais de fluoroquinolonas

Este estudo incide sobre as características que a presença do ião flúor em moléculas concede. Mais concretamente em fluoroquinolonas, antibióticos que cada vez são mais utilizados. Fez-se uma analise de vários parâmetros para obtermos informação sobre a interação fármaco-receptor nas fluoroquinolonas. Sendo para isso utilizadas técnicas de caracterização química computacional para conseguirmos caracterizar eletronicamente e estruturalmente (3D) as fluoroquinolonas em complemento aos métodos semi-empíricos utilizados inicialmente. Como é sabido, a especificidade e a afinidade para o sitio alvo, é essencial para eficácia de um fármaco. As fluoroquinolonas sofreram um grande desenvolvimento desde a primeira quinolona sintetizada em 1958, sendo que desde ai foram sintetizadas inúmeros derivados da mesma. Este facto deve-se a serem facilmente manipuladas, derivando fármacos altamente potentes, espectro alargado, factores farmacocinéticos optimizados e efeitos adversos reduzidos. A grande alteração farmacológica para o aumento do interesse neste grupo, foi a substituição em C6 de um átomo de flúor em vez de um de hidrogénio. Para obtermos as informações sobre a influência do ião flúor sobre as propriedades estruturais e electrónicas das fluoroquinolonas, foi feita uma comparação entre a fluoroquinolona com flúor em C6 e com hidrogénio em C6. As quatro fluoroquinolonas presentes neste estudo foram: ciprofloxacina, moxiflocacina, sparfloxacina e pefloxacina. As informações foram obtidas por programas informáticos de mecânica quântica e molecular. Concluiu-se que a presença de substituinte flúor não modificava de forma significativa a geometria das moléculas mas sim a distribuição da carga no carbono vicinal e nos átomos em posição alfa, beta e gama relativamente a este. Esta modificação da distribuição electrónica pode condicionar a ligação do fármaco ao receptor, modificando a sua actividade farmacológica.

Constrained optimization of heat exchangers

Optimizing a shell and tube heat exchanger for a given duty is an important and relatively difficult task. There is a need for a simple, general and reliable method for realizing this task. The authors present here one such method for optimizing single phase shell-and-tube heat exchangers with given geometric and thermohydraulic constraints. They discuss the problem in detail. Then they introduce a basic algorithm for optimizing the exchanger. This algorithm is based on data from an earlier study of a large collection of feasible designs generated for different process specifications. The algorithm ensures a near-optimal design satisfying the given heat duty and geometric constraints. The authors also provide several sub-algorithms to satisfy imposed velocity limitations. They illustrate how useful these sub-algorithms are with several examples where the exchanger weight is minimized.