As interações moleculares, em especial as de caráter não-covalente, são processos-chave em vários aspectos da biologia celular e molecular, desde a comunicação entre as células ou da velocidade e especificidade das reações enzimáticas. Portanto, há a necessidade de estudar e criar métodos preditivos para calcular a afinidade entre moléculas nos processos de interação, os quais encontram uma gama de aplicações, incluindo a descoberta de novos fármacos. No geral, entre esses valores de afinidade, o mais importante é a energia livre de ligação, que normalmente é determinada por modos computacionalmente rápidos, porém sem uma forte base teórica, ou por cálculos muito complexos, utilizando dinâmica molecular, onde mesmo com um grande poder de determinação da afinidade, é muito custoso computacionalmente. O objetivo deste trabalho é avaliar um modelo menos custoso computacionalmente e que promova um aprofundamento na avaliação de resultados obtidos a partir de simulações de docking molecular. Para esta finalidade, o método de Monte Carlo é empregado para a amostragem de orientações e conformações do ligante do sítio ativo macromolecular. A avaliação desta metodologia demonstrou que é possível calcular grandezas entrópicas e entálpicas e analisar a capacidade interativa entre complexos proteína-ligante de forma satisfatória para o complexo lisozima do bacteriófago T4. / The molecular interactions, especially the ones with a non-covalent nature, are key processes in general aspects of cellular and molecular biology, including cellular communication and velocity and specificity of enzymatic reactions. So, there is a strong need for studies and development of methods for the calculation of the affinity on interaction processes, since these have a wide range of applications like rational drug design. The free energy of binding is the most important measure among the affinity measurements. It can be calculated by quick computational means, but lacking on strong theoretical basis or by complex calculations using molecular dynamics, where one can compute accurate results but at the price of an increased computer power. The aim of this project is to evaluate a computationally inexpensive model which can improve the results from molecular docking simulations. For this end, the Monte Carlo method is implemented to sample different ligand configurations inside the macromolecular binding site. The evaluation of this methodology showed that is possible to calculate entropy and enthalpy, along analyzing the interactive capacity between receptor-ligands complexes in a satisfactory way for the bacteriophage T4.

As interações moleculares, em especial as de caráter não-covalente, são processos-chave em vários aspectos da biologia celular e molecular, desde a comunicação entre as células ou da velocidade e especificidade das reações enzimáticas. Portanto, há a necessidade de estudar e criar métodos preditivos para calcular a afinidade entre moléculas nos processos de interação, os quais encontram uma gama de aplicações, incluindo a descoberta de novos fármacos. No geral, entre esses valores de afinidade, o mais importante é a energia livre de ligação, que normalmente é determinada por modos computacionalmente rápidos, porém sem uma forte base teórica, ou por cálculos muito complexos, utilizando dinâmica molecular, onde mesmo com um grande poder de determinação da afinidade, é muito custoso computacionalmente. O objetivo deste trabalho é avaliar um modelo menos custoso computacionalmente e que promova um aprofundamento na avaliação de resultados obtidos a partir de simulações de docking molecular. Para esta finalidade, o método de Monte Carlo é empregado para a amostragem de orientações e conformações do ligante do sítio ativo macromolecular. A avaliação desta metodologia demonstrou que é possível calcular grandezas entrópicas e entálpicas e analisar a capacidade interativa entre complexos proteína-ligante de forma satisfatória para o complexo lisozima do bacteriófago T4. / The molecular interactions, especially the ones with a non-covalent nature, are key processes in general aspects of cellular and molecular biology, including cellular communication and velocity and specificity of enzymatic reactions. So, there is a strong need for studies and development of methods for the calculation of the affinity on interaction processes, since these have a wide range of applications like rational drug design. The free energy of binding is the most important measure among the affinity measurements. It can be calculated by quick computational means, but lacking on strong theoretical basis or by complex calculations using molecular dynamics, where one can compute accurate results but at the price of an increased computer power. The aim of this project is to evaluate a computationally inexpensive model which can improve the results from molecular docking simulations. For this end, the Monte Carlo method is implemented to sample different ligand configurations inside the macromolecular binding site. The evaluation of this methodology showed that is possible to calculate entropy and enthalpy, along analyzing the interactive capacity between receptor-ligands complexes in a satisfactory way for the bacteriophage T4.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-06-08T13:54:44Z No. of bitstreams: 1 evertonluizmartinsdapaixao.pdf: 7260792 bytes, checksum: 8a1a1accd3cfb65d925f1429e761f688 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-06-26T19:03:05Z (GMT) No. of bitstreams: 1 evertonluizmartinsdapaixao.pdf: 7260792 bytes, checksum: 8a1a1accd3cfb65d925f1429e761f688 (MD5) / Made available in DSpace on 2017-06-26T19:03:05Z (GMT). No. of bitstreams: 1 evertonluizmartinsdapaixao.pdf: 7260792 bytes, checksum: 8a1a1accd3cfb65d925f1429e761f688 (MD5) Previous issue date: 2013-04-19 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho usamos o método de Monte Carlo Metropolis aplicado em sistemas magnéticos para estudar nanoestruturas como nanodiscos e nanofios de Permalloy. Dividimos em duas partes. Primeiramente, estudou-se o comportamento do núcleo do vórtice rodeado por anéis de impurezas em nanodiscos de permalloy. Variamos o raio e a espessura dos anéis e medimos o limite do campo aplicado para que o núcleo do vórtice passe através destes anéis. Em segundo lugar, temos estudado os estados fundamentais (de menor energia) para nanofios para uma pequena região do espaço de fase. Podemos identificar as configurações de rotação associadas a estes estados. / In this work we have used Monte Carlo Metropolis method applied in magnetic systems to study nanostructures like permalloy nanodisks and nanowires. We divided it in two parts. First, we have studied the behavior of the vortex core surrounded by rings of the impurities in permalloy nanodisks. We have varied the radius and the thickness of the rings and we measure the limit of the applied field for that the vortex core passes through the ring. Second, we have studied the ground states (lowest-energy state) for nanowires to a small region of the phase space. We can identify the spin configurations associated to the these states.

Bayesian modelling, in which our prior belief about the distribution on model parameters is updated by observed data, is a popular approach to statistical data analysis. However, writing specific inference algorithms for Bayesian models by hand is time-consuming and requires significant machine learning expertise. Probabilistic programming promises to make Bayesian modelling easier and more accessible by letting the user express a generative model as a short computer program (with random variables), leaving inference to the generic algorithm provided by the compiler of the given language. However, it is not easy to design a probabilistic programming language correctly and define the meaning of programs expressible in it. Moreover, the inference algorithms used by probabilistic programming systems usually lack formal correctness proofs and bugs have been found in some of them, which limits the confidence one can have in the results they return. In this work, we apply ideas from the areas of programming language theory and statistics to show that probabilistic programming can be a reliable tool for Bayesian inference. The first part of this dissertation concerns the design, semantics and type system of a new, substantially enhanced version of the Tabular language. Tabular is a schema-based probabilistic language, which means that instead of writing a full program, the user only has to annotate the columns of a schema with expressions generating corresponding values. By adopting this paradigm, Tabular aims to be user-friendly, but this unusual design also makes it harder to define the syntax and semantics correctly and reason about the language. We define the syntax of a version of Tabular extended with user-defined functions and pseudo-deterministic queries, design a dependent type system for this language and endow it with a precise semantics. We also extend Tabular with a concise formula notation for hierarchical linear regressions, define the type system of this extended language and show how to reduce it to pure Tabular. In the second part of this dissertation, we present the first correctness proof for a Metropolis-Hastings sampling algorithm for a higher-order probabilistic language. We define a measure-theoretic semantics of the language by means of an operationally-defined density function on program traces (sequences of random variables) and a map from traces to program outputs. We then show that the distribution of samples returned by our algorithm (a variant of “Trace MCMC” used by the Church language) matches the program semantics in the limit.

Submitted by Marlene Santos (marlene.bc.ufg@gmail.com) on 2016-08-05T17:38:42Z No. of bitstreams: 2 Dissertação - Alexandre Barbosa de Almeida - 2016.pdf: 11943401 bytes, checksum: 94f2e941bbde05e098c40f40f0f2f69c (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-08-09T11:57:53Z (GMT) No. of bitstreams: 2 Dissertação - Alexandre Barbosa de Almeida - 2016.pdf: 11943401 bytes, checksum: 94f2e941bbde05e098c40f40f0f2f69c (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2016-08-09T11:57:53Z (GMT). No. of bitstreams: 2 Dissertação - Alexandre Barbosa de Almeida - 2016.pdf: 11943401 bytes, checksum: 94f2e941bbde05e098c40f40f0f2f69c (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-06-17 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / Proteins are vital for the biological functions of all living beings on Earth. However, they only have an active biological function in their native structure, which is a state of minimum energy. Therefore, protein functionality depends almost exclusively on the size and shape of its native conformation. However, less than 1% of all known proteins in the world has its structure solved. In this way, various methods for determining protein structures have been proposed, either in vitro or in silico experiments. This work proposes a new in silico method called Monte Carlo with Dominance, which addresses the problem of protein structure prediction from the point of view of ab initio and multi-objective optimization, considering both protein energetic and structural aspects. The software GROMACS was used for the ab initio treatment to perform Molecular Dynamics simulations, while the framework ProtPred-GROMACS (2PG) was used for the multi-objective optimization problem, employing genetic algorithms techniques as heuristic solutions. Monte Carlo with Dominance, in this sense, is like a variant of the traditional Monte Carlo Metropolis method. The aim is to check if protein tertiary structure prediction is improved when structural aspects are taken into account. The energy criterion of Metropolis and energy and structural criteria of Dominance were compared using RMSD calculation between the predicted and native structures. It was found that Monte Carlo with Dominance obtained better solutions for two of three proteins analyzed, reaching a difference about 53% in relation to the prediction by Metropolis. / As proteínas são vitais para as funções biológicas de todos os seres na Terra. Entretanto, somente apresentam função biológica ativa quando encontram-se em sua estrutura nativa, que é o seu estado de mínima energia. Portanto, a funcionalidade de uma proteína depende, quase que exclusivamente, do tamanho e da forma de sua conformação nativa. Porém, de todas as proteínas conhecidas no mundo, menos de 1% tem a sua estrutura resolvida. Deste modo, vários métodos de determinação de estruturas de proteínas têm sido propostos, tanto para experimentos in vitro quanto in silico. Este trabalho propõe um novo método in silico denominado Monte Carlo com Dominância, o qual aborda o problema da predição de estrutura de proteínas sob o ponto de vista ab initio e de otimização multiobjetivo, considerando, simultaneamente, os aspectos energéticos e estruturais da proteína. Para o tratamento ab initio utiliza-se o software GROMACS para executar as simulações de Dinâmica Molecular, enquanto que para o problema da otimização multiobjetivo emprega-se o framework ProtPred-GROMACS (2PG), o qual utiliza algoritmos genéticos como técnica de soluções heurísticas. O Monte Carlo com Dominância, nesse sentido, é como uma variante do tradicional método de Monte Carlo Metropolis. Assim, o objetivo é o de verificar se a predição da estrutura terciária de proteínas é aprimorada levando-se em conta também os aspectos estruturais. O critério energético de Metropolis e os critérios energéticos e estruturais da Dominância foram comparados empregando o cálculo de RMSD entre as estruturas preditas e as nativas. Foi verificado que o método de Monte Carlo com Dominância obteve melhores soluções para duas de três proteínas analisadas, chegando a cerca de 53% de diferença da predição por Metropolis.

The multinomial logit model (MNL) possesses a latent variable representation in terms of random variables following a multivariate logistic distribution. Based on multivariate finite mixture approximations of the multivariate logistic distribution, various data-augmented Metropolis-Hastings algorithms are developed for a Bayesian inference of the MNL model.

Selon la théorie de Cottrell et Bilby, les dislocations à travers leur champ de contrainte interagissent avec les atomes de soluté qui s’agrègent au cœur et autour des dislocations (atmosphère de Cottrell). Ces atmosphères « bloquent » les dislocations et fragilisent le matériau. Dans cette thèse, les techniques de simulations à l’échelle atomique telles que la Dynamique Moléculaire, les simulations Monte Carlo Cinétique, Monte Carlo Métropolis ont été développées qui permettent de prendre en compte les interactions entre plusieurs centaines d’atomes de carbone et la dislocation, pour étudier la cinétique de formation ainsi que la structure d’une atmosphère de Cottrell. Par ailleurs, la technique de simulation est appliquée à deux autres problématiques: premièrement, il est connu que les atomes de C dans la ferrite se mettent en ordre (mise en ordre de Zener). La stabilité de cette phase est étudiée en fonction de la température et la concentration de C. Deuxièmement, la ségrégation des atomes de soluté dans les nano-cristaux de Ni ainsi que la stabilité des nano-cristaux avec les atomes de soluté dans les joints de grain à haute température est étudiée. / The objective of the thesis was to understand the microscopic features at the origin of ageing in metals. The originality of this contribution was the com- bination of three complementary computational techniques : (1) Metropolis Monte Carlo (MMC), (2) Atomic Kinetic Monte Carlo (AKMC), and, (3) Molecular Dynamics (MD). It consisted of four main sections : Firstly the ordering occurring in bulk alpha-iron via MMC and MD was studied. Various carbon contents and temperatures were investigated in order to obtain a “phase diagram”. Secondly, the generation of systems containing a dislocation interacting with many carbon atoms, namely a Cottrell Atmosphere, with MMC technique was described. The equilibrium structure of the atmosphere and the stress field around the atmospheres proves that the stress field around the dislocation was affected but not cancelled out by the atmosphere. Thirdly, the kinetics of the carbon migration and Cottrell atmosphere evolution were investigated via AKMC. The activation energies for carbon atom migration were calculated from the local stress field and the arrangement of the neigh- bouring carbon atoms. Lastly, an application of the combined use of MMC and MD to describe grain boundary segregation of solute atoms in fcc nickel was presented. The grain growth was inhibited due to the solute atoms in the grain boundary.

Bayesian inference occurs when prior knowledge about uncertain parameters in mathematical models is merged with new observational data related to the model outcome. In this thesis we focus on models given by partial differential equations where the uncertain parameters are coefficient functions belonging to infinite dimensional function spaces. The result of the Bayesian inference is then a well-defined posterior probability measure on a function space describing the updated knowledge about the uncertain coefficient. For decision making and post-processing it is often required to sample or integrate wit resprect to the posterior measure. This calls for sampling or numerical methods which are suitable for infinite dimensional spaces. In this work we focus on Kalman filter techniques based on ensembles or polynomial chaos expansions as well as Markov chain Monte Carlo methods. We analyze the Kalman filters by proving convergence and discussing their applicability in the context of Bayesian inference. Moreover, we develop and study an improved dimension-independent Metropolis-Hastings algorithm. Here, we show geometric ergodicity of the new method by a spectral gap approach using a novel comparison result for spectral gaps. Besides that, we observe and further analyze the robustness of the proposed algorithm with respect to decreasing observational noise. This robustness is another desirable property of numerical methods for Bayesian inference. The work concludes with the application of the discussed methods to a real-world groundwater flow problem illustrating, in particular, the Bayesian approach for uncertainty quantification in practice. / Bayessche Inferenz besteht daraus, vorhandenes a-priori Wissen über unsichere Parameter in mathematischen Modellen mit neuen Beobachtungen messbarer Modellgrößen zusammenzuführen. In dieser Dissertation beschäftigen wir uns mit Modellen, die durch partielle Differentialgleichungen beschrieben sind. Die unbekannten Parameter sind dabei Koeffizientenfunktionen, die aus einem unendlich dimensionalen Funktionenraum kommen. Das Resultat der Bayesschen Inferenz ist dann eine wohldefinierte a-posteriori Wahrscheinlichkeitsverteilung auf diesem Funktionenraum, welche das aktualisierte Wissen über den unsicheren Koeffizienten beschreibt. Für Entscheidungsverfahren oder Postprocessing ist es oft notwendig die a-posteriori Verteilung zu simulieren oder bzgl. dieser zu integrieren. Dies verlangt nach numerischen Verfahren, welche sich zur Simulation in unendlich dimensionalen Räumen eignen. In dieser Arbeit betrachten wir Kalmanfiltertechniken, die auf Ensembles oder polynomiellen Chaosentwicklungen basieren, sowie Markowketten-Monte-Carlo-Methoden. Wir analysieren die erwähnte Kalmanfilter, indem wir deren Konvergenz zeigen und ihre Anwendbarkeit im Kontext Bayesscher Inferenz diskutieren. Weiterhin entwickeln und studieren wir einen verbesserten dimensionsunabhängigen Metropolis-Hastings-Algorithmus. Hierbei weisen wir geometrische Ergodizität mit Hilfe eines neuen Resultates zum Vergleich der Spektrallücken von Markowketten nach. Zusätzlich beobachten und analysieren wir die Robustheit der neuen Methode bzgl. eines fallenden Beobachtungsfehlers. Diese Robustheit ist eine weitere wünschenswerte Eigenschaft numerischer Methoden für Bayessche Inferenz. Den Abschluss der Arbeit bildet die Anwendung der diskutierten Methoden auf ein reales Grundwasserproblem, was insbesondere den Bayesschen Zugang zur Unsicherheitsquantifizierung in der Praxis illustriert.