Estudamos uma classe de sistemas elípticos - \'elipson POT 2\' \'DELTA\' u + u = g(v) em \'ÔMEGA\' - \'elipson POT 2\' \'DELTA\' v + v f(u) em ÔMEGA \' PARTIAL\'u SOBRE \'PARTIAL n = \'PARTIAL v SOBRE PARTIAL n = O sobre \"PARTIAL\'\' ÔMEGA\' onde \' ÔMEGA ESTA CONTIDO EM R POT. N\' é um domínio limitado, com bordo regular e N \' > ou =\' 3. As não linearidades f e g são funções com crescimento superlinear e subcrítico no infinito. Estudamos resultados sobre a existência de uma sequência de soluções que se concentram, quando o parâmetro \'epsilon\' tende a zero, em um ponto da fronteira que maximiza a sua curvatura. Para isso utilizamos um resultado abstrato sobre existência de pontos críticos para funcionais fortemente indefinidos / We study an singularly perturbed Hamiltonean elliptic system - \'elipson POT 2\' \'DELTA\' u + u = g(v) in \'ÔMEGA\' - \'elipson POT 2\' \'DELTA\' v + v f(u) in ÔMEGA \' PARTIAL\'u ON \'PARTIAL n = \'PARTIAL v ON PARTIAL n\' = O sobre \"PARTIAL\'\' ÔMEGA\' when \'ÔMEGA THIS CONTAINED R POT. N\' is a smooth bounded domain, N \' > or =\' 3 and f and g are nonlinearities having superlinear and subcritical growth at infinity. We study an abstract result about existence of critical points of strongly as \' epsilon\' goes to zero, at a point of the boundary which maximizes the mean curvature of the boundary

Na primeira parte desta tese, estudamos os princípios operacionais das decisões celulares mediadas pelo sistema de sinalização Notch. Este sistema tem papel importante nas decisões celulares que ocorrem durante o desenvolvimento embrionário, cicatrização de feridas e na formação de tumores. O circuito de sinalização é ativado quando o receptor Notch de uma célula interage com um dos ligantes - Delta ou Jagged - de uma célula vizinha. O circuito Notch-Delta forma um comutador intercelular, e duas células vizinhas tendem a adotar estados diferentes - Emissor (muito ligante e pouco receptor) e Recebedor (pouco ligante e muito receptor). Neste manuscrito, apresentamos uma nova abordagem teórica que integra ambos Delta e Jagged no circuito Notch. Mostramos que o circuito Notch-Delta-Jagged permite um novo estado - um híbrido Emissor/Recebedor (E/R) com concentrações intermediárias de receptores e ligantes, e portanto o circuito é age como uma chave de três vias. Em seguida, observamos que a taxa de produção de ambos os ligantes, assim como a modulação assimétrica da afinidade de ligação do Notch com seus ligantes mediada pela glicosiltransferase Fringe, afeta severamente o intervalo de existência dos estados e sua relativa estabilidade - altos níveis de Jagged, mas não de Fringe ou Delta, promovem o estado híbrido E/R e o processo de indução lateral. Nós elucidamos o papel de Jagged na determinação dos estados celulares e discutimos sua possível implicação no entendimento da comunicação entre tumor e estroma, que frequentemente envolve comunicação via interações Notch-Jagged. Posteriormente, avaliamos a interação entre Notch, inflamação e a população de Células Cancerígenas Estaminais (CCE). Mostramos que inflamação pode expandir a população de CCE por meio do aumento dos níveis de produção de Jagged que posteriormente ativa o sistema de sinalização Notch em células vizinhas não-CCE. Nossos resultados sugerem que a inibição da produção de Jagged atenua o efeito da expansão de CCE devido a inflamação, indicando que inflamação cresce a população de CCE via interações Notch-Jagged. Nossos resultados são consistentes com observações em câncer de mama do subtipo basal (triplo negativo), onde a perda de Fringe e a ativação constitutiva do eixo NF-kB - Jag1 promove a expansão da população de CCE. Nossa abordagem computacional pode ser adaptada para incluir circuitos adicionais tais como p53 e hipóxia, que afetam a plasticidade celular, proporcionando assim uma plataforma útil para a projeção de novas terapias. Na segunda parte desta tese, introduzimos um novo método para seleção de características: Suvrel. Este é um método variacional, inspirado em aprendizado de relevância, para determinar tensores métricos para definição de distâncias baseadas em similaridades, para utilização em métodos de classificação. Nós introduzimos uma nova metodologia na qual o tensor métrico pode ser calculado analiticamente. O preprocessamento das características por uma transformação linear utilizando o tensor métrico calculado via Suvrel melhora a eficiência dos classificadores. Testamos nosso método para conjuntos de dados públicos, utilizando os classificadores mais comumente utilizados. Nós também aplicamos esta metodologia no estudo da relação entre parâmetros estruturais globais e o sistema de classificação de função enzimática. Por último, introduzimos uma nova metodologia para a identificação de genes diferencialmente expressos utilizando a tecnologia de microarranjos de DNA. Diferentemente das abordagens tradicionais, nossa metodologia evita passos intermediários de preprocessamento que são desnecessários e devido a isto não acumula erros destas análises, o que resulta em um método mais sensível e robusto. / In the first part of this thesis, we studied the operating principles of cell fate decisions mediated by Notch signaling pathway. This pathway have important role in cell fate determination during embryonic development, wound healing and tumorigenesis. Notch signaling is activated by binding of Notch receptor of one cell to either of its ligand- Delta or Jagged- of another cell. Notch-Delta circuit forms an intercellular toggle switch, and two neighboring cells tend to adopt different fates - Sender (high ligand, low receptor) and Receiver (low ligand, high receptor). Here, we present a new tractable theoretical framework that incorporates both Delta and Jagged in Notch signaling, and show that Notch-Delta-Jagged circuit enables an additional fate - hybrid Sender/Receiver (S/R) (medium ligand, medium receptor) and behaves as a three-way switch. Further, we found that production rates of both the ligands and the asymmetric modulation of binding affinity of Notch to its ligands by glycosyltransferase Fringe severely affects the parameter range of the existence of these states and their relative stability - high levels of Jagged, but not that of Fringe or Delta, promote hybrid S/R state and lateral induction. We elucidate the role of Jagged in cell fate determination and discuss its possible implications in understanding tumor-stroma crosstalk, which frequently entails Notch-Jagged communication. We further evaluate the interplay among Notch signaling, inflamation and Cancer Stem Cell population. We show that inflammation can expand the population of Cancer Stem Cells (CSCs) by increasing the levels of Jagged in cells that can further activate Notch signaling pathway in neighboring non-CSCs. Our results suggest that, inhibiting the production of Jagged dampens the effect of inflammation in expanding the CSC population, indicating that inflammatory signal function through Notch-Jagged signaling to increase CSCs. Our results are consistent with observations in basal-like breast cancer, where loss of Fringe and constitutive activation of NF-kB-Jag1 axis promotes CSC population. Our computational framework can be tailored to include additional signals such as p53 and hypoxia that affect this plasticity to gain stemness, thus providing a platform that can be useful in designing novel therapies. In the second part of the thesis, we introduce a new method for feature selection: Supervised Variational Relevance Learning (Suvrel). This is a variational method to determine metric tensors to define distance based similarity in pattern classification, inspired in relevance learning. We propose a new methodology where the metric tensor can be calculated analytically. Preprocessing the patterns by doing linear transformations using the metric tensor yields a dataset which can be more efficiently classified. We test our methods using publicly available datasets, for some standard classifiers. We also applied this methodology to study the relationship between global structural parameters and the Enzyme Commission hierarchy. Lastly, we propose a new methodology for identifying the differentially expressed genes using DNA microarray technology. Unlike traditional approaches, our methodology skips intermediate unnecessary preprocessing steps and therefore does not accumulate errors due to these analysis, resulting in a more sensitive and robust method.

by Yan Shing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 78-80). / Abstract also in Chinese. / Chapter 1 --- Admissible Points of Convex Sets --- p.7 / Chapter 1.1 --- Introduction and Notations --- p.7 / Chapter 1.2 --- The Main Result --- p.7 / Chapter 1.2.1 --- The Proof of Theoreml.2.1 --- p.8 / Chapter 1.3 --- An Application --- p.10 / Chapter 2 --- A Generalization on The Theorems of Admissible Points --- p.12 / Chapter 2.1 --- Introduction and Notations --- p.12 / Chapter 2.2 --- Fundamental Lemmas --- p.14 / Chapter 2.3 --- The Main Result --- p.16 / Chapter 3 --- Introduction to Variational Inequalities --- p.21 / Chapter 3.1 --- Variational Inequalities in Finite Dimensional Space --- p.21 / Chapter 3.2 --- Problems Which Relate to Variational Inequalities --- p.25 / Chapter 3.3 --- Some Variations on Variational Inequality --- p.28 / Chapter 3.4 --- The Vector Variational Inequality Problem and Its Relation with The Vector Optimization Problem --- p.29 / Chapter 3.5 --- Variational Inequalities in Hilbert Space --- p.31 / Chapter 4 --- Vector Variational Inequalities --- p.36 / Chapter 4.1 --- Preliminaries --- p.36 / Chapter 4.2 --- Notations --- p.37 / Chapter 4.3 --- Existence Results of Vector Variational Inequality --- p.38 / Chapter 5 --- The Generalized Quasi-Variational Inequalities --- p.44 / Chapter 5.1 --- Introduction --- p.44 / Chapter 5.2 --- Properties of The Class F0 --- p.46 / Chapter 5.3 --- Main Theorem --- p.53 / Chapter 5.4 --- Remarks --- p.58 / Chapter 6 --- A set-valued open mapping theorem and related re- sults --- p.61 / Chapter 6.1 --- Introduction and Notations --- p.61 / Chapter 6.2 --- An Open Mapping Theorem --- p.62 / Chapter 6.3 --- Main Result --- p.63 / Chapter 6.4 --- An Application on Ordered Normed Spaces --- p.66 / Chapter 6.5 --- An Application on Open Decomposition --- p.70 / Chapter 6.6 --- An Application on Continuous Mappings from Order- infrabarreled Spaces --- p.72 / Bibliography

Deep neural networks (DNNs) have recently been used to solve complex perceptual and decision tasks. In particular, convolutional neural networks (CNN) have been extremely successful for visual perception. In addition to performing well on the trained object recognition task, these CNNs also model brain data throughout the visual hierarchy better than previous models. However, these DNNs are still far from completely explaining visual perception in the human brain. In this thesis, we investigated two methods with the goal of improving DNNs’ capabilities to model human visual perception: (1) deep representational distance learning (RDL), a method for driving representational spaces in deep nets into alignment with other (e.g. brain) representational spaces and (2) variational DNNs that use sampling to perform approximate Bayesian inference. In the first investigation, RDL successfully transferred information from a teacher model to a student DNN. This was achieved by driving the student DNN’s representational distance matrix (RDM), which characterises the representational geometry, into alignment with that of the teacher. This led to a significant increase in test accuracy on machine learning benchmarks. In the future, we plan to use this method to simultaneously train DNNs to perform complex tasks and to predict neural data. In the second investigation, we showed that sampling during learning and inference using simple Bernoulli- and Gaussian-based noise improved a CNN’s representation of its own uncertainty for object recognition. We also found that sampling during learning and inference with Gaussian noise improved how well CNNs predict human behavioural data for image classification. While these methods alone do not fully explain human vision, they allow for training CNNs that better model several features of human visual perception.

"Recently, sequencing technologies have generated massive and heterogeneous data sets. However, interpretation of these data sets is a major barrier to understand genomic heterogeneity in complex diseases. In this dissertation, we develop a Bayesian statistical method for single nucleotide level analysis and a global optimization method for gene expression level analysis to characterize genomic heterogeneity in mixed samples. The detection of rare single nucleotide variants (SNVs) is important for understanding genetic heterogeneity using next-generation sequencing (NGS) data. Various computational algorithms have been proposed to detect variants at the single nucleotide level in mixed samples. Yet, the noise inherent in the biological processes involved in NGS technology necessitates the development of statistically accurate methods to identify true rare variants. At the single nucleotide level, we propose a Bayesian probabilistic model and a variational expectation maximization (EM) algorithm to estimate non-reference allele frequency (NRAF) and identify SNVs in heterogeneous cell populations. We demonstrate that our variational EM algorithm has comparable sensitivity and specificity compared with a Markov Chain Monte Carlo (MCMC) sampling inference algorithm, and is more computationally efficient on tests of relatively low coverage (27x and 298x) data. Furthermore, we show that our model with a variational EM inference algorithm has higher specificity than many state-of-the-art algorithms. In an analysis of a directed evolution longitudinal yeast data set, we are able to identify a time-series trend in non-reference allele frequency and detect novel variants that have not yet been reported. Our model also detects the emergence of a beneficial variant earlier than was previously shown, and a pair of concomitant variants. Characterization of heterogeneity in gene expression data is a critical challenge for personalized treatment and drug resistance due to intra-tumor heterogeneity. Mixed membership factorization has become popular for analyzing data sets that have within-sample heterogeneity. In recent years, several algorithms have been developed for mixed membership matrix factorization, but they only guarantee estimates from a local optimum. At the gene expression level, we derive a global optimization (GOP) algorithm that provides a guaranteed epsilon-global optimum for a sparse mixed membership matrix factorization problem for molecular subtype classification. We test the algorithm on simulated data and find the algorithm always bounds the global optimum across random initializations and explores multiple modes efficiently. The GOP algorithm is well-suited for parallel computations in the key optimization steps. "

He Yiran. / Includes index. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (p. 74-80) and index.. / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

L'objectif de cette thèse est d'étudier des propriétés des points d'équilibre dans des réseaux de transport multi-critères et de développer des méthodes numériques permettant de trouver l'ensemble des points d'équilibre ou une partie représentative de cet ensemble. Le travail est structure comme suit. Dans le premier chapitre nous donnons une introduction de la thèse. Le chapitre 2 est un rappel de certaines notions que nous utilisons dans les autres. Nous y rappelons le concept de point optimal de Pareto, les fonctions multivoques et les problèmes d'inégalité variationnelle. Nous introduisons certaines fonctions de scalarisation et puis établissons quelques propriétés importantes. Dans le chapitre 3, nous décrivons les réseaux de transport qui sont étudiés dans cette thèse. Dans chaque modèle, nous rappelons les définitions des points d'équilibre et donnons une relation entre ces définitions. Dans le chapitre 4 nous traitons les réseaux de transport multi-critères mono-produit sans contraintes de capacité. Tout d'abord, nous construisons deux problèmes d'optimisation dont les solutions sont exactement l'ensemble des points d'équilibre du modèle initiale et établissons certaines propriétés importantes de continuité et de dérivabilité génériques des fonctions objectifs. Puis nous donnons une formule permettant de calculer le gradient des fonctions objectifs. Nous proposons également un algorithme et prouvons sa convergence pour générer une représentation de l'ensemble des points d'équilibre. Puisque les fonctions objectifs de nos problèmes d'optimisation ne sont pas continues, une méthode de lissage est également considérée afin d'utiliser quelques techniques d'optimisation globale. En fin, nous introduisons le concept de point d'équilibre robuste, puis nous établissons des critères de robustesse et une formule permettant de calculer le rayon de robustesse. Dans le chapitre 5 nous étudions des points d'équilibre vectoriel dans le réseau de transport multi-critères mono-produit sous contraintes de capacité.Tout d'abord, nous proposons un problème d'optimisation équivalent. En utilisant des techniques analogues à celles du chapitre 4 nous obtenons également un sous-ensemble des points d'équilibre du modèle proposé. Dans le dernier chapitre nous considérons des points d'équilibre fort dans le réseau de transport multi-critères multi-produit sous contraintes de capacité. Nous établissons des conditions d'existence des points d'équilibre fort, des relations entre des points d'équilibre fort et des points d'équilibre par rapport à une famille de fonctions ainsi qu'une relation entre des points d'équilibre fort et les points efficaces de l'ensemble des valeurs de la fonction de coût. En plus nous construisons des problèmes d'inéqualité variationnellle, dont les solutions sont les points d'équilibre fort. La dernière partie de ce chapitre est consacrée à un algorithme permettant de trouver des points d'équilibre d'un réseau multi-critères sous contraintes de capacité. Certains exemples numériques sont donnés pour illustrer notre méthode. Nous fermons la thèse avec une liste de références et appendice contenant le code matlab de nos algorithmes. / The purpose of this thesis is to study equilibria in multi-criteria trafficnetworks and develop numerical methods to find the set of all equilibria oronly one representative part of this set. The thesis is structured as follows.In the first chapter we present an introduction of the thesis. Chapter 2is of preliminary character. We recall the concept of Pareto minimal pointsand some notions related to set-valued maps and variational inequality pro-blem. We introduce some scalarizing functions, in particular the so-calledaugmented biggest/smallest monotone functions and augmented signed distance functions, and establish some properties we shall use later.Chapter 3 describes the traffic network models to be studied in this thesis.We define equilibrium for each model and determine a relationship betweenthem. We also give some counter examples for some existing results in therecent literature on this topic.In Chapter 4 we develop a new solution method for multi-criteria net-work equilibrium problems without capacity constraints. To this end we shallconstruct two optimization problems the solutions of which are exactly theset of equilibria of the model, and establish some important generic conti-nuity and differentiability properties of the objective functions. Then we givethe formula to calculate the gradient of the objective functions which enablesus to modify Frank-Wolfe's reduced gradient method to get descent directiontoward an optimal solution. We prove the convergence of the method whichgenerates a nice representative set of equilibria. Since the objective functionsof our optimization problems are not continuous, a method of smoothingthem is also considered in order to see how global optimization algorithmsmay help.We shall also introduce the concept of robust equilibrium, establishcriteria for robustness and a formula to compute the radius of robustness.In Chapter 5 we consider vector equilibrium in the multi-criteria single-product traffic network with capacity constraints.We propose an equivalent optimization problem and establish some im-portant generic continuity and differentiability properties of the objectivefunction. Then we give a formula which allows us to calculate the gradientof the objective function. After that we apply the approach of Chapter 4 toobtain an algorithm for generating equilibria of this network. We also givesome numerical examples to illustrate our approach.In the last chapter we consider strong vector equilibrium in the multi-criteria multi-product traffic network with capacity constraints.We establish conditions for existence of strong vector equilibrium.We alsoestablish relations between equilibrium and efficient points of the value set ofthe cost function and with equilibrium with respect to a family of functions.Moreover we exploit particular increasing functions discussed in Chapter 2 toconstruct variational inequality problems, solutions of which are equilibriumflows. The final part of this chapter is devoted to an algorithm for findingequilibrium flows of a multi-criteria network with capacity constraints. Somenumerical examples are given to illustrate our method and its applicability.A list of references and appendices containing the code Matlab of ouralgorithms follow.

Neste trabalho desenvolvemos o formalismo do Método Celular Variacional para ser aplicado à estruturas cristalinas com vários átomos por célula unitária. O método foi usado para determinar a estrutura elementar do silício, com a célula unitária dividida em quatro poliedros, sendo dois átomos e dois intersticiais. As células intersticiais foram incluídas com o fim de melhorar a média esférica do potencial cristalino. Os resultados obtidos concordam muito bem com os experimentais, mostrando que, mesmo para estruturas periódicas mais complexas, o método exige apenas um pequeno número de funções de base para a expansão das funções de onda celulares. / In this work we developed the Variational Cellular Method formalism applied to three-dimensional periodic structures with an arbitrary number of atoms per unit cell. The Method was used to determine the eletronic structure of silicon, with the unit cell partitional into four space-filling polyhedra: two intersticial polyhedra. The intersticial cells were included in order to improve the spherical cellular potentials. The obtained results are in very good agreement with the experimental results, showing that even for more complex periodic structures the Method requires only a few number of base functions.

Made available in DSpace on 2015-04-22T22:07:20Z (GMT). No. of bitstreams: 1 orlando.pdf: 5376505 bytes, checksum: 0fe38436ca5d2157e6047c3b7a23d9ef (MD5) Previous issue date: 2012-10-22 / Recently, the quantum spin ½ Heisenberg model with antiferromagnetic competitive interactions between first (J1) and second (J2) neighbors on a square lattice (called J1-J2 Heisenberg model) has been extensively studied by several methods, where the critical properties are relatively well known at T = 0. For small (α < α1c) and large (α > α2c) values of the parameter of frustration α = J2/J1 we ordered two states: the state of Néel (or antiferromagnetic-AF) and collinear antiferromagnetic (CAF), respectively, which are separated by a disordered state (spin-liquid SL). The CAF state consists of spins oriented parallel along the chain and antiparalelamente between chains, whereas the SL state is believed to be represented by the settings singlet states of dimers or platelets randomly oriented over the entire square lattice. Many debates were devoted to that kind of phase transition order at points α = α1c and α = α2c, concluding in a first-order one, respectively. Years ago, Oliveira [Phys. Rev. B 43, 6181 (1991)] proposed a variational method which uses as its starting point the ground state of the product states of isolated platelets (singlets), thus obtaining the magnetization subnet A, mA, and average internal energy as a function of α. Qualitative results described above were observed with values for points of the same phase transitions α1c ≈ 0.41 and α2c ≈ 0.68. In this work we will generalize this variational method to include a spatial anisotropy for the exchange, which consists of interactions of different first neighbors J1 - horizontal (vertical) and J1 = λJ1 - vertical (horizontal), with all interactions seconds to neighbors along the diagonals with the same intensity J2 (called model J1-J1 -J2 Heisenberg). We discuss the phase diagram at T = 0 plane λ-α, the behavior of order parameters and average internal energy AF and CAF phases as a function of α for various values of the spatial anisotropy λ. Our goal is to analyze the effect of anisotropy on the disordered state (SL), in which some methods (nonlinear waves spins, expanding in series) have provided that this state exist each value of 0<λ≤1, whereas other ones (field effective spin waves linear, coupled cluster) are foreseen only the SL state to high anisotropy values (λ>λ1) and a first-order phase transition between the phases AF and CAF. / Recentemente, o modelo de Heisenberg quântico antiferromagnético de spin ½ com interações competitivas entre primeiros (J1) e segundos (J2) vizinhos numa rede quadrada (o chamado modelo J1−J2 Heisenberg) tem sido exaustivamente estudado por diversos métodos, onde as propriedades críticas são relativamente bem conhecidas em T = 0. Para pequenos (α < α1c) e grandes (α > α2c) valores do parâmetro de frustração α = J2/J1 temos dois estados ordenados: o estado de Néel (ou antiferromagnético-AF) e colinear antiferromagnético (CAF), respectivamente, que são separados por um estado desordenado (spin líquido-SL). O estado CAF é caracterizado com os spins orientados paralelamente ao longo da cadeia e antiparalelamente entre cadeias, enquanto o estado SL acredita-se que seja representado por configurações de estados singletos de dímeros ou plaquetas orientados aleatoriamente sobre toda a rede quadrada. Muitos debates foram dedicados à que tipo de ordem da transição de fase nos pontos α= α1c e α= α2c, tendo como conclusão sendo de segunda e primeira ordem, respectivamente. Anos atrás, de Oliveira [Phys. Rev. B 43, 6181 (1991)] propôs um método variacional onde usa como ponto de partida o estado fundamental do produto de estados isolados de plaquetas (singletos), obtendo assim a magnetização de sub-rede A, mA, e a energia interna média como uma função de α. Os resultados qualitativos descritos acima foram observados, com os valores para os pontos de transições de fases iguais a α1c ≈ 0,41 e α2c ≈ 0,68. Neste trabalho generalizaremos este método variacional para incluir uma anisotropia espacial no exchange, que consiste em interações de primeiros vizinhos diferentes J1 - na horizontal (vertical) e J1 = λ J1 - na vertical (horizontal), com todas as interações de segundos vizinhos ao longo das diagonais com a mesma intensidade J2 (o chamado modelo J1-J1 -J2 Heisenberg). Discutiremos o diagrama de fase em T=0 no plano λ-α, o comportamento dos parâmetros de ordem e energia interna média nas fases AF e CAF como uma função de α para vários valores da anisotropia espacial λ. Nosso objetivo é analisar o efeito desta anisotropia sobre o estado desordenado (SL), onde alguns métodos (ondas de spins não linear, expansão em séries) têm previsto que este estado existe para todo valor de 0<λ≤1, enquanto outros métodos (campo efetivo, ondas de spin linear, cluster acoplado) têm previsto apenas este estado SL para altos valores de anisotropia (λ>λ1) e uma transição de fase de primeira ordem entre as fases AF e CAF.

Submitted by Sandra Pereira (srpereira@ufrrj.br) on 2018-03-15T14:04:44Z No. of bitstreams: 1 2012 - Renato Berutti Neto.pdf: 4059567 bytes, checksum: 6f8cfef981af15e4298a546d0c7563dc (MD5) / Made available in DSpace on 2018-03-15T14:04:44Z (GMT). No. of bitstreams: 1 2012 - Renato Berutti Neto.pdf: 4059567 bytes, checksum: 6f8cfef981af15e4298a546d0c7563dc (MD5) Previous issue date: 2012-03-14 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior, CAPES, Brasil. / This work has been performed at the Laboratory of Chemical Kinetics, located in the Chemistry Department of Universidade Federal Rural do Rio de Janeiro, for the study of unimolecular reactions of formamide in gas phase and on the ground state: (1) CHONH2? CO + NH3 (2) CHONH2? H2 + HNCO and (3) CHONH2? HCO + NH2. Theoretical calculations including geometry optimizations and frequencies, have been performed at CASSCF level, with corrections at MRMP2 level for the electronic energy. The cc-pVDZ, cc and cc-pVTZ basis sets as well as the aug-cc-pVDZ have been used for comparative purposes. The unimolecular reactions were differently treated, depending on the specific topology of the potential energy surface. For the decompositions, corresponding saddle points have been located and the lowest energy paths have been calculated with the intrinsic reaction coordinate (IRC) method. The dissociation reaction has been described in terms of a scanning on the potential curve considering partial geometry optimizations of the fragments NH2 and HCO, keeping the CN distances frozen, those assumed as the internal reaction coordinate. Ab initio calculations were performed with the package GAMESS. The results show that the best description of the molecule has been obtained at CAS(10,9)/CCT level, yielding minimum deviations for the calculated molecular properties in relation to the experimental data available in the literature. The critical energies for the reactions of the decomposition have been determined, being (1): 77.60 kcal / mol and (2): 73.56 kcal / mol, both at level MRMP2/CAS(10,9)/CCT. For these results, it has been observed that the corrections MRMP2 are very important, bringing data calculated values very close to the literature values. From the analysis of the reaction pathways, it can be inferred that the dynamics of decomposition CHONH2 ? CO + NH3 is initiated by the torsional movement along the axis molecular by slightly rotating the fragment HCO in relation to the NH2, while the distance CN extends and the HC distance increases, with decreasing of HCN angle; the hydrogen atom bonds to the nitrogen atom and, with progressive increase of the distance CN, the fragments NH3 and CO are formed, achieving relaxed geometries. The decomposition CHONH2? HNCO + H2, by its turn, is initiated by increasing the distance HC at the HCO fragment, and further hydrogen abstraction of the atom at the NH2 fragment to form H2, which progressively separates from the HNCO, after the saddle point, generating the two products of this reaction. Dissociation is interpreted as the stretching of the CN bond, which promotes the separation of the NH2 and HCO fragments, whose geometries are relaxed along the curve of potential. The dissociation limit, determined at level MRMP2/CAS(10,9)/CCT is 91.52 kcal/mol. The canonical variational constant were calculated in the range of 300 - 2000K, being the values, in s-1, obtained at 1600K: (1) k = 5.62 x 103, (2) k = 1.07 x 103 and (3) k = 3.45. It follows that the channel (1) is privileged at a temperature of 1600K, and the decompositions are faster than the dissociation. / O presente trabalho foi realizado no Laborat?rio de Cin?tica, situado no Departamento de Qu?mica da Universidade Federal Rural do Rio de Janeiro, visando o estudo das Rea??es Unimoleculares da Formamida em Fase Gasosa e no Estado Fundamental: (1) CHONH2? CO + NH3, (2) CHONH2? HNCO + H2 e (3) CHONH2? HCO + NH2. C?lculos te?ricos, incluindo otimiza??es de geometria e frequ?ncias, foram procedidos em n?vel CASSCF com corre??es em n?vel MRMP2 para a energia eletr?nica. Bases cc-pVDZ e cc-pVTZ, assim como aug-ccpVDZ foram utilizados para fins comparativos. As rea??es unimoleculares foram tratadas diferentemente, dependendo da topologia espec?fica da superf?cie de energia potencial. Para as decomposi??es, pontos de sela correspondentes foram localizados e caminhos de menor energia foram calculados com o m?todo da coordenada de rea??o intr?nseca (IRC). A rea??o de dissocia??o foi descrita a partir do levantamento da curva de potencial considerando otimiza??es parciais de geometria dos fragmentos NH2 e HCO, mantendo fixas as dist?ncias CN, coordenada interna esta, assumida como a coordenada de rea??o. Os c?lculos ab initio foram realizados com o pacote GAMESS. Os resultados mostram que a melhor descri??o da mol?cula de formamida foi obtida em n?vel CAS(10,9)/CCT, promovendo menores desvios das propriedades moleculares calculadas em rela??o as experimentais dispon?veis na literatura. As energias cr?ticas para as rea??es de decomposi??o foram determinadas, sendo (1): 77,60kcal/mol e (2): 73,56 kcal/mol, ambas em n?vel MRMP2/CAS(10,9)/CCT. Para esses resultados, observou-se que as corre??es MRMP2 foram muito importantes, trazendo esses dados calculados a valores muito pr?ximos aos recomendados na literatura. A partir da an?lise dos caminhos de rea??o, pode-se inferir que a din?mica da decomposi??o CHONH2? CO + NH3 ? iniciada pelo movimento de tor??o ao longo do eixo molecular, fazendo girar levemente o fragmento NH2 em rela??o ao HCO, ao mesmo tempo em que o eixo CN se alonga e a dist?ncia HC aumenta, com a diminui??o do ?ngulo HCN, o ?tomo de hidrog?nio se liga ao nitrog?nio e, a partir do aumento progressivo da dist?ncia CN, os fragmentos NH3 e CO se formam, tendo lentamente suas geometrias relaxadas. J? a decomposi??o CHONH2? HNCO + H2 ? iniciada pelo aumento da dist?ncia HC no radical HCO e posterior abstra??o de um dos ?tomos de hidrog?nio do fragmento NH2 para a forma??o de H2, que se distancia progressivamente, ap?s a regi?o do ponto de sela, do fragmento HNCO, gerando os dois produtos desta rea??o. A dissocia??o, interpretada como o estiramento da liga??o CN, promove a separa??o dos fragmentos NH2 e HCO, cujas geometrias s?o otimizadas ao longo da curva de potencial. O limite de dissocia??o, calculado em n?vel MRMP2/CAS(10,9)/CCT foi determinado como 91,52 kcal/mol. As constantes variacionais can?nicas foram calculadas na faixa de 300 - 2000K com o programa kcvt, sendo os valores, em s-1, obtidos a 1600K: (1) k = 5,62 x 103, (2) k = 1,07 x 103 e (3) k = 3,45. Conclui-se que o canal (1) ? privilegiado na temperatura de 1600K, e que as decomposi??es s?o mais r?pidas que a dissocia??o.