Évolution moléculaire : un modèle Markov-modulé pour les processus de substitution

Les processus Markoviens continus en temps sont largement utilisés pour tenter d’expliquer l’évolution des séquences protéiques et nucléotidiques le long des phylogénies. Des modèles probabilistes reposant sur de telles hypothèses sont conçus pour satisfaire la non-homogénéité spatiale des contraintes fonctionnelles et environnementales agissant sur celles-ci. Récemment, des modèles Markov-modulés ont été introduits pour décrire les changements temporels dans les taux d’évolution site-spécifiques (hétérotachie). Des études ont d’autre part démontré que non seulement la force mais également la nature de la contrainte sélective agissant sur un site peut varier à travers le temps. Ici nous proposons de prendre en charge cette réalité évolutive avec un modèle Markov-modulé pour les protéines sous lequel les sites sont autorisés à modifier leurs préférences en acides aminés au cours du temps. L’estimation a posteriori des différents paramètres modulants du noyau stochastique avec les méthodes de Monte Carlo est un défi de taille que nous avons su relever partiellement grâce à la programmation parallèle. Des réglages computationnels sont par ailleurs envisagés pour accélérer la convergence vers l’optimum global de ce paysage multidimensionnel relativement complexe. Qualitativement, notre modèle semble être capable de saisir des signaux d’hétérogénéité temporelle à partir d’un jeu de données dont l’histoire évolutive est reconnue pour être riche en changements de régimes substitutionnels. Des tests de performance suggèrent de plus qu’il serait mieux ajusté aux données qu’un modèle équivalent homogène en temps. Néanmoins, les histoires substitutionnelles tirées de la distribution postérieure sont bruitées et restent difficilement interprétables du point de vue biologique.

Lactide polymerization with iron alkoxide complexes

Les essais préliminaires pour préparer des alcoolates de fer à partir du bichlorure ou bibromure de fer (II), en les combinant avec des ligands de type diimino pyridine, ont engendré la formation de complexes homoleptiques et hétéroleptiques, dépendant des substituants sur les branches imines du ligand. Ces complexes homoleptiques octaédriques et paramagnétiques ont été étudiés par rapport à leurs propriétés spectroscopiques et cristallographiques. De plus, la synthèse des complexes de fer hétéroleptique a engendré de bons précurseurs penta-coordonnés pour les réactions de substitution de ligands avec des alcoolates de métaux alcalins, de manière à produire les dialcoolates de fer (II) désirés. Des techniques d’analyse telles que la spectroscopie UV-vis, l’analyse élémentaire, la spectrométrie de masse à haute résolution et la cristallographie aux rayons X ont été utilisées pour caractériser ces complexes de fer. L’activité catalytique de ces complexes de fer (II) a aussi été étudiée par rapport à la polymérisation du lactide; les dialcoolates convoités ont été générés in-situ en raison de la difficulté à produire et à isoler les dérivés alcoolates des complexes diimino pyridine de fer. Une étude approfondie a aussi été faite sur les réactions de polymérisation, surtout par rapport aux valeurs de conversion à l’échelle du temps, ainsi qu’à la tacticité des chaines de polymères obtenues. Ces analyses ont été effectuées par l’entremise de la spectroscopie de résonance magnétique nucléaire, de la chromatographie d’exclusion stérique, et de la spectrométrie de masse MALDI (désorption-ionisation laser assistée par matrice).

Non invasive classification system of scoliosis curve types using least-squares support vector machines

Objective To determine scoliosis curve types using non invasive surface acquisition, without prior knowledge from X-ray data. Methods Classification of scoliosis deformities according to curve type is used in the clinical management of scoliotic patients. In this work, we propose a robust system that can determine the scoliosis curve type from non invasive acquisition of the 3D back surface of the patients. The 3D image of the surface of the trunk is divided into patches and local geometric descriptors characterizing the back surface are computed from each patch and constitute the features. We reduce the dimensionality by using principal component analysis and retain 53 components using an overlap criterion combined with the total variance in the observed variables. In this work, a multi-class classifier is built with least-squares support vector machines (LS-SVM). The original LS-SVM formulation was modified by weighting the positive and negative samples differently and a new kernel was designed in order to achieve a robust classifier. The proposed system is validated using data from 165 patients with different scoliosis curve types. The results of our non invasive classification were compared with those obtained by an expert using X-ray images. Results The average rate of successful classification was computed using a leave-one-out cross-validation procedure. The overall accuracy of the system was 95%. As for the correct classification rates per class, we obtained 96%, 84% and 97% for the thoracic, double major and lumbar/thoracolumbar curve types, respectively. Conclusion This study shows that it is possible to find a relationship between the internal deformity and the back surface deformity in scoliosis with machine learning methods. The proposed system uses non invasive surface acquisition, which is safe for the patient as it involves no radiation. Also, the design of a specific kernel improved classification performance.

The ligating versatility of halides and pseudohalides in copper(II) complexes- monomers, dimers and chains”

The work embodied in this thesis was carried out by the author in the Department of Applied Chemistry, CUSAT, Kochi, during the period 2008-2013. The thesis brings to light, our attempts to evaluate the coordination behavior of some compounds of interest. The biological activities of semicarbazones and their metal complexes have been an active area of research during the past years because of their significant role in naturally occurring biological systems. Tridentate NNO and ONO semicarbazone systems formed from heterocyclic and aromatic carbonyl compounds and their transition metal complexes are well-authenticated compounds in this field and their synthesis, crystal structures and spectral studies are well desirable. Hence, we decided to develop a research program aimed at the syntheses, crystal structures and spectral studies of copper complexes with halides and pseudohalides. In addition to single crystal X-ray diffraction studies, various physico-chemical methods of analysis were also used for the characterization of the complexes

CBIR Using Local and Global Properties of Image Sub-blocks

This paper proposes a content based image retrieval (CBIR) system using the local colour and texture features of selected image sub-blocks and global colour and shape features of the image. The image sub-blocks are roughly identified by segmenting the image into partitions of different configuration, finding the edge density in each partition using edge thresholding, morphological dilation and finding the corner density in each partition. The colour and texture features of the identified regions are computed from the histograms of the quantized HSV colour space and Gray Level Co- occurrence Matrix (GLCM) respectively. A combined colour and texture feature vector is computed for each region. The shape features are computed from the Edge Histogram Descriptor (EHD). Euclidean distance measure is used for computing the distance between the features of the query and target image. Experimental results show that the proposed method provides better retrieving result than retrieval using some of the existing methods

A Sub-block Based Image Retrieval Using Modified Integrated Region Matching.

This paper proposes a content based image retrieval (CBIR) system using the local colour and texture features of selected image sub-blocks and global colour and shape features of the image. The image sub-blocks are roughly identified by segmenting the image into partitions of different configuration, finding the edge density in each partition using edge thresholding, morphological dilation. The colour and texture features of the identified regions are computed from the histograms of the quantized HSV colour space and Gray Level Co- occurrence Matrix (GLCM) respectively. A combined colour and texture feature vector is computed for each region. The shape features are computed from the Edge Histogram Descriptor (EHD). A modified Integrated Region Matching (IRM) algorithm is used for finding the minimum distance between the sub-blocks of the query and target image. Experimental results show that the proposed method provides better retrieving result than retrieval using some of the existing methods

Bayes quadratic unbiased estimator of spatial covariance parameters

This work presents Bayes invariant quadratic unbiased estimator, for short BAIQUE. Bayesian approach is used here to estimate the covariance functions of the regionalized variables which appear in the spatial covariance structure in mixed linear model. Firstly a brief review of spatial process, variance covariance components structure and Bayesian inference is given, since this project deals with these concepts. Then the linear equations model corresponding to BAIQUE in the general case is formulated. That Bayes estimator of variance components with too many unknown parameters is complicated to be solved analytically. Hence, in order to facilitate the handling with this system, BAIQUE of spatial covariance model with two parameters is considered. Bayesian estimation arises as a solution of a linear equations system which requires the linearity of the covariance functions in the parameters. Here the availability of prior information on the parameters is assumed. This information includes apriori distribution functions which enable to find the first and the second moments matrix. The Bayesian estimation suggested here depends only on the second moment of the prior distribution. The estimation appears as a quadratic form y'Ay , where y is the vector of filtered data observations. This quadratic estimator is used to estimate the linear function of unknown variance components. The matrix A of BAIQUE plays an important role. If such a symmetrical matrix exists, then Bayes risk becomes minimal and the unbiasedness conditions are fulfilled. Therefore, the symmetry of this matrix is elaborated in this work. Through dealing with the infinite series of matrices, a representation of the matrix A is obtained which shows the symmetry of A. In this context, the largest singular value of the decomposed matrix of the infinite series is considered to deal with the convergence condition and also it is connected with Gerschgorin Discs and Poincare theorem. Then the BAIQUE model for some experimental designs is computed and compared. The comparison deals with different aspects, such as the influence of the position of the design points in a fixed interval. The designs that are considered are those with their points distributed in the interval [0, 1]. These experimental structures are compared with respect to the Bayes risk and norms of the matrices corresponding to distances, covariance structures and matrices which have to satisfy the convergence condition. Also different types of the regression functions and distance measurements are handled. The influence of scaling on the design points is studied, moreover, the influence of the covariance structure on the best design is investigated and different covariance structures are considered. Finally, BAIQUE is applied for real data. The corresponding outcomes are compared with the results of other methods for the same data. Thereby, the special BAIQUE, which estimates the general variance of the data, achieves a very close result to the classical empirical variance.

On Nonlinear Preconditioners in Newton-Krylov-Methods for Unsteady Flows

The application of nonlinear schemes like dual time stepping as preconditioners in matrix-free Newton-Krylov-solvers is considered and analyzed. We provide a novel formulation of the left preconditioned operator that says it is in fact linear in the matrix-free sense, but changes the Newton scheme. This allows to get some insight in the convergence properties of these schemes which are demonstrated through numerical results.

Semi-algebraic methods for symbolic analysis of complex reaction networks

The identification of chemical mechanism that can exhibit oscillatory phenomena in reaction networks are currently of intense interest. In particular, the parametric question of the existence of Hopf bifurcations has gained increasing popularity due to its relation to the oscillatory behavior around the fixed points. However, the detection of oscillations in high-dimensional systems and systems with constraints by the available symbolic methods has proven to be difficult. The development of new efficient methods are therefore required to tackle the complexity caused by the high-dimensionality and non-linearity of these systems. In this thesis, we mainly present efficient algorithmic methods to detect Hopf bifurcation fixed points in (bio)-chemical reaction networks with symbolic rate constants, thereby yielding information about their oscillatory behavior of the networks. The methods use the representations of the systems on convex coordinates that arise from stoichiometric network analysis. One of the methods called HoCoQ reduces the problem of determining the existence of Hopf bifurcation fixed points to a first-order formula over the ordered field of the reals that can then be solved using computational-logic packages. The second method called HoCaT uses ideas from tropical geometry to formulate a more efficient method that is incomplete in theory but worked very well for the attempted high-dimensional models involving more than 20 chemical species. The instability of reaction networks may lead to the oscillatory behaviour. Therefore, we investigate some criterions for their stability using convex coordinates and quantifier elimination techniques. We also study Muldowney's extension of the classical Bendixson-Dulac criterion for excluding periodic orbits to higher dimensions for polynomial vector fields and we discuss the use of simple conservation constraints and the use of parametric constraints for describing simple convex polytopes on which periodic orbits can be excluded by Muldowney's criteria. All developed algorithms have been integrated into a common software framework called PoCaB (platform to explore bio- chemical reaction networks by algebraic methods) allowing for automated computation workflows from the problem descriptions. PoCaB also contains a database for the algebraic entities computed from the models of chemical reaction networks.

Preconditioning and iterative solution of symmetric indefinite linear systems arising from interior point methods for linear programming

We study the preconditioning of symmetric indefinite linear systems of equations that arise in interior point solution of linear optimization problems. The preconditioning method that we study exploits the block structure of the augmented matrix to design a similar block structure preconditioner to improve the spectral properties of the resulting preconditioned matrix so as to improve the convergence rate of the iterative solution of the system. We also propose a two-phase algorithm that takes advantage of the spectral properties of the transformed matrix to solve for the Newton directions in the interior-point method. Numerical experiments have been performed on some LP test problems in the NETLIB suite to demonstrate the potential of the preconditioning method discussed.

A survey addressing the fundamental matrix estimation problem

Epipolar geometry is a key point in computer vision and the fundamental matrix estimation is the only way to compute it. This article surveys several methods of fundamental matrix estimation which have been classified into linear methods, iterative methods and robust methods. All of these methods have been programmed and their accuracy analysed using real images. A summary, accompanied with experimental results, is given

MA167exam00pdf

Exam questions and solutions in PDF

MA167exam00

Exam questions and solutions in LaTex. Diagrams for the questions are all together in the support.zip file, as .eps files

MA167exam01pdf

Exam questions and solutions in PDF

MA167exam01

Exam questions and solutions in LaTex. Diagrams for the questions are all together in the support.zip file, as .eps files