Lookback option is a well-known path-dependent option where its payoff depends on the historical extremum prices. The thesis focuses on the binomial pricing of the American floating strike lookback put options with payoff at time $t$ (if exercise) characterized by \[ \max_{k=0, \ldots, t} S_k - S_t, \] where $S_t$ denotes the price of the underlying stock at time $t$. Build upon the idea of \hyperlink{RBCV}{Reiner Babbs Cheuk and Vorst} (RBCV, 1992) who proposed a transformed binomial lattice model for efficient pricing of this class of option, this thesis extends and enhances their binomial recursive algorithm by exploiting the additional combinatorial properties of the lattice structure. The proposed algorithm is not only computational efficient but it also significantly reduces the memory constraint. As a result, the proposed algorithm is more than 1000 times faster than the original RBCV algorithm and it can compute a binomial lattice with one million time steps in less than two seconds. This algorithm enables us to extrapolate the limiting (American) option value up to 4 or 5 decimal accuracy in real time.

We propose a lattice model for three stochastically interacting components that mimicsthe formation of the internal structure of adhesive bands via evaporating one component(the solvent) by thermal gradient. We use high-performance computing resources toinvestigate the formation of rubber-acrylate morphologies. We pay special attentionto the role of varying temperature as well as of the changing the solvent interaction inconnection to the shape of the obtained rubber morphologies.In the lattice model, we start with microscopic spins of three particles in the latticewith short-range interactions between them. This microscopic model is approximatednumerically via a Monte Carlo Metropolis-based algorithm. High-performancecomputing resources and Python-based implementations have been used for thenumerical simulation of the lattice model. The numerical implementation highlights theeffect of the model parameters (volatility of the Solvent, temperature, and interactionbetween the particles) on the structure of the obtained morphologies. We demonstratethat one can utilize a reasonably simple model to explain the impact of parameters onthe creation of morphology in ternary systems when one component evaporates.

No description available.

Porous materials have long been a research interest due to their practical importance in traditional chemical industries such as catalysis and separation processes. The successful synthesis of porous materials requires further understanding of the fundamental physics that govern the formation of these materials. In this thesis, we apply molecular modeling methods and develop novel models to study the formation mechanism of ordered porous materials. The improved understanding provides an opportunity to rational control pore size, pore shape, surface reactivity and may lead to new design of tailor-made materials. To attain detailed structural evolution of silicate materials, an atomistic model with explicitly representation of silicon and oxygen atoms is developed. Our model is based on rigid tetrahedra (representing SiO4) occupying the sites of a body centered cubic (bcc) lattice. The model serves as the base model to study the formation of silica materials. We first carried out Monte Carlo simulations to describe the polymerization process of silica without template molecules starting from a solution of silicic acid in water at pH 2. We predicted Qn evolutions during silica polymerization and good agreement was found compared with experimental data, where Qn is the fraction of Si atoms with n bridging oxygens. The model captures the basic kinetics of silica polymerization and provides structural evolution information. Next we generalize the application of this atomic lattice model to materials with tetrahedral (T) and bridging (B) atoms and apply parallel tempering Monte Carlo methods to search for ground states. We show that the atomic lattice model can be applied to silica and related materials with a rich variety of structures including known chalcogenides, zeolite analogs, and layered materials. We find that whereas canonical Monte Carlo simulations of the model consistently produce the amorphous solids studied in our previous work, parallel tempering Monte Carlo gives rise to ordered nanoporous solids. The utility of parallel tempering highlights the existence of barriers between amorphous and crystalline phases of our model. The role of template molecules during synthesis of ordered mesoporous materials was investigated. Implemented surfactant lattice model of Larson, together with atomic tetrahedral model for silica, we successfully modeled the formation of surfactant-templated mesoporous silica (MCM-41), with explicit representation of silicic acid condensation and surfactant self-assembly. Lamellar and hexagonal mesophases form spontaneously at different synthesis conditions, consistent with published experimental observations. Under conditions where silica polymerization is negligible, reversible transformation between hexagonal and lamellar phases were observed by changing synthesis temperatures. Upon long-time simulation that allows condensation of silanol groups, the inorganic phases of mesoporous structures were found with thicker walls that are amorphous and lack of crystallinity. Compared with bulk amorphous silica, the wall-domain of mesoporous silicas are less ordered withlarger fractions of three- and four-membered rings and wider ring-size distributions. It is the first molecular simulation study of explicit representations of both silicic acid condensation and surfactant self-assembly.

O entendimento dos princípios básicos do enovelamento protéico pode conduzir a muitas aplicações importantes. Embora não se conheçam todos os aspectos significativos envolvidos neste problema, experimentos e aproximações teóricas têm produzido avanços relevantes na sua compreensão. Um fato experimental importante tem sido a descoberta de que o logaritmo da taxa de enovelamento log kf se correlaciona linearmente com parâmetros estruturais globais, como a ordem de contato relativa c. Com o propósito de contribuir para o entendimento do processo de enovelamento, o objetivo primordial deste trabalho consiste em explicar o porquê de certas proteínas não seguirem o comportamento linear entre log kf e c, verificado para outras proteínas da mesma classe (usualmente proteínas pequenas e com termodinâmica descrita pela aproximação de dois estados). Para isso foi necessário identificar os parâmetros topológicos da estrutura nativa que constituíssem importantes determinantes da cinética do enovelamento de proteínas globulares. Também se estudou como as especificidades estéricas dos aminoácidos afetam o processo do enovelamento de proteínas, assim como influenciam na correlação entre a ordem de contato relativo e a taxa de enovelamento. Empregou-se neste estudo um modelo simplificado em rede cúbica, que foi tratado por meio de simulações Monte Carlo. Um conjunto de 52 estruturas maximamente compactas, correspondendo a cadeias de tamanho L = 27 monômeros, foi usado para representar estados nativos; estas estruturas foram escolhidas de forma a representar uma variedade significativa de padrões estruturais, independentemente de c. Através de uma análise detalhada da influência de parâmetros topológicos das configurações nativas na cinética do enovelamento, conclui-se que a taxa de enovelamento é fortemente dependente daquilo que denominamos aqui como “conteúdo de estruturas tipo-secundárias" da estrutura nativa. Adicionalmente, observou-se que aquela (taxa), independentemente do valor da ordem de contato relativo, é fortemente influenciada pelos padrões confíguracionais e suas combinações presentes na nativa. Por meio dessa premissa, foi então possível explicar de forma consistente os casos que não obedecem a pretensa relação linear entre log kf e c, levando a concluir que o logaritmo da taxa de enovelamento e a ordem de contato relativo são linearmente dependentes somente para aquelas configurações em que há uma certa quantidade equilibrada (que depende de c) de padrões estruturais, mesclando contatos efetivos de curto alcance (alto conteúdo de estruturas tipo-secundárias), com outros de longo alcance (baixo conteúdo de estruturas tipo-secundárias). Estruturas nativas que quebram este equilíbrio têm sua cinética de enovelamento afetada com respeito à reta de regressão linear ajustada para o conjunto de todas as configurações consideradas. Dessa forma, verificou-se que o mecanismo físico básico que relaciona o conteúdo de estruturas tipo-secundárias e a taxa de enovelamento, envolve o conceito de cooperatividade: se a estrutura nativa é rica em combinações de padrões estruturais ricos em contatos efetivos de curto alcance, o processo de enovelamento é mais rápido porque contatos locais são naturalmente estimulados por flutuações térmicas. / The understanding of basic principles of the protein folding problem can lead to many important applications. Although not all the involved significant aspects of this problem are known, experiments and theoretical approaches have produced important advances in its understanding. An important experimental fact has been the discovery that the logarithm of the folding rate log kf correlates linearly with global structural parameters, like the relative contact order c. In order to contribute for the understanding of folding process, the primordial goal of this work consists in to explain why certain proteins do not follow the linear behavior between log kf and c, as verified to other proteins from the same class (usually small two states proteins). For this, it was necessary to identify those topological parameters of the native structure that are important to the folding kinetic of globular protein. It was also studied how steric specificities of the aminoacids affect the protein folding process, as well how they influence the correlation between the relative contact order and the folding rate. It was employed in this study a simplified cubic lattice model, treated by Monte Carlo simulation. A set of 52 maximum compact structures, corresponding to chains of size L = 27 monomers, was used to represent the native states; these structures were chosen in such a way to represent a significant diversity of structural patterns, independently of c. Through a detailed analysis of the influence of topological parameters of the native configurations on the folding kinetic, it was concluded that the folding rate is strongly dependent of what we call here as “content of type-secondary" of the native. Additionally, it was observed that log kf is, independently of c, strongly influenced by the configurational patterns and its combinations in the native. Through this premise it was possible to consistently explain the cases that do not obey the pretense linear relation between log kf and c, leading to conclude that the logarithm of the folding rate and the relative contact order are linearly related only for those configurations in that there is a certain balanced amount of structural patterns (which depend on c) mixing short-range effective contacts (high contents of secondary-type structures) and long-range contacts (low contents of secondary-type structures). Structures that break this balance have its folding kinetic affected with respect to the linear fitting adjusted for the set of all the considered configurations. Of this form, it was verified that basic physical mechanism that relates the content of type-secondary structures and the folding rate involves the cooperativety concept: if the native structure presents combinations of structural standards rich in effective contacts of short-range, the folding process is faster because local contacts are naturally stimulated by thermal fluctuations.

No description available.

O entendimento dos princípios básicos do enovelamento protéico pode conduzir a muitas aplicações importantes. Embora não se conheçam todos os aspectos significativos envolvidos neste problema, experimentos e aproximações teóricas têm produzido avanços relevantes na sua compreensão. Um fato experimental importante tem sido a descoberta de que o logaritmo da taxa de enovelamento log kf se correlaciona linearmente com parâmetros estruturais globais, como a ordem de contato relativa c. Com o propósito de contribuir para o entendimento do processo de enovelamento, o objetivo primordial deste trabalho consiste em explicar o porquê de certas proteínas não seguirem o comportamento linear entre log kf e c, verificado para outras proteínas da mesma classe (usualmente proteínas pequenas e com termodinâmica descrita pela aproximação de dois estados). Para isso foi necessário identificar os parâmetros topológicos da estrutura nativa que constituíssem importantes determinantes da cinética do enovelamento de proteínas globulares. Também se estudou como as especificidades estéricas dos aminoácidos afetam o processo do enovelamento de proteínas, assim como influenciam na correlação entre a ordem de contato relativo e a taxa de enovelamento. Empregou-se neste estudo um modelo simplificado em rede cúbica, que foi tratado por meio de simulações Monte Carlo. Um conjunto de 52 estruturas maximamente compactas, correspondendo a cadeias de tamanho L = 27 monômeros, foi usado para representar estados nativos; estas estruturas foram escolhidas de forma a representar uma variedade significativa de padrões estruturais, independentemente de c. Através de uma análise detalhada da influência de parâmetros topológicos das configurações nativas na cinética do enovelamento, conclui-se que a taxa de enovelamento é fortemente dependente daquilo que denominamos aqui como “conteúdo de estruturas tipo-secundárias” da estrutura nativa. Adicionalmente, observou-se que aquela (taxa), independentemente do valor da ordem de contato relativo, é fortemente influenciada pelos padrões confíguracionais e suas combinações presentes na nativa. Por meio dessa premissa, foi então possível explicar de forma consistente os casos que não obedecem a pretensa relação linear entre log kf e c, levando a concluir que o logaritmo da taxa de enovelamento e a ordem de contato relativo são linearmente dependentes somente para aquelas configurações em que há uma certa quantidade equilibrada (que depende de c) de padrões estruturais, mesclando contatos efetivos de curto alcance (alto conteúdo de estruturas tipo-secundárias), com outros de longo alcance (baixo conteúdo de estruturas tipo-secundárias). Estruturas nativas que quebram este equilíbrio têm sua cinética de enovelamento afetada com respeito à reta de regressão linear ajustada para o conjunto de todas as configurações consideradas. Dessa forma, verificou-se que o mecanismo físico básico que relaciona o conteúdo de estruturas tipo-secundárias e a taxa de enovelamento, envolve o conceito de cooperatividade: se a estrutura nativa é rica em combinações de padrões estruturais ricos em contatos efetivos de curto alcance, o processo de enovelamento é mais rápido porque contatos locais são naturalmente estimulados por flutuações térmicas. / The understanding of basic principles of the protein folding problem can lead to many important applications. Although not all the involved significant aspects of this problem are known, experiments and theoretical approaches have produced important advances in its understanding. An important experimental fact has been the discovery that the logarithm of the folding rate log kf correlates linearly with global structural parameters, like the relative contact order c. In order to contribute for the understanding of folding process, the primordial goal of this work consists in to explain why certain proteins do not follow the linear behavior between log kf and c, as verified to other proteins from the same class (usually small two states proteins). For this, it was necessary to identify those topological parameters of the native structure that are important to the folding kinetic of globular protein. It was also studied how steric specificities of the aminoacids affect the protein folding process, as well how they influence the correlation between the relative contact order and the folding rate. It was employed in this study a simplified cubic lattice model, treated by Monte Carlo simulation. A set of 52 maximum compact structures, corresponding to chains of size L = 27 monomers, was used to represent the native states; these structures were chosen in such a way to represent a significant diversity of structural patterns, independently of c. Through a detailed analysis of the influence of topological parameters of the native configurations on the folding kinetic, it was concluded that the folding rate is strongly dependent of what we call here as “content of type-secondary” of the native. Additionally, it was observed that log kf is, independently of c, strongly influenced by the configurational patterns and its combinations in the native. Through this premise it was possible to consistently explain the cases that do not obey the pretense linear relation between log kf and c, leading to conclude that the logarithm of the folding rate and the relative contact order are linearly related only for those configurations in that there is a certain balanced amount of structural patterns (which depend on c) mixing short-range effective contacts (high contents of secondary-type structures) and long-range contacts (low contents of secondary-type structures). Structures that break this balance have its folding kinetic affected with respect to the linear fitting adjusted for the set of all the considered configurations. Of this form, it was verified that basic physical mechanism that relates the content of type-secondary structures and the folding rate involves the cooperativety concept: if the native structure presents combinations of structural standards rich in effective contacts of short-range, the folding process is faster because local contacts are naturally stimulated by thermal fluctuations.

This research shows optimization approaches to protein folding. The protein folding problem is to predict the compact three dimensional structure of a protein based on its amino acid sequence. This research focuses on ab-initio mathematical models to find provably optimal solutions to the 2D HP-lattice protein folding model. We built two integer programming (IP) models and five constraint programming (CP) models. All the models give provably optimal solutions. We also developed some CP techniques to solve the problem faster and then compared their computational times. We tested the models with several protein instances. My models, while they are probably too slow to use in practice, are significantly faster than the alternatives, and thus are mathematically relevant. We also provided reasons why protein folding is hard using complexity analysis. This research will contribute to showing whether CP can be an alternative to or a complement of IP in the future. Moreover, figuring out techniques combining CP and IP is a prominent research issue and our work will contribute to that literature. It also shows which IP/CP strategies can speed up the running time for this type of problem. Finally, it shows why a mathematical approach to protein folding is especially hard not only mathematically, i.e. NP-hard, but also practically.

Resumo: O enovelamento de proteinas é um problema fundamental em Biofísica Molecular. O processo de enovelamento é, em geral, mapeado através de uma equação de difusão aplicada ao longo da coordenada de reação Q, a qual descreve o grau de similaridade de uma determinada configuração com o estado nativo da proteína. Os tempos de enovelamento podem ser calculados a partir dos potenciais efetivos e do coeficiente de difusão D. Na literatura, D é assumido constante. Usando modelos de rede, mostramos neste trabalho variações desse coeficiente de difusão em função de Q e calculamos os novos tempos de enovelamento. / Abstract: The protein folding is a fundamental problem in Molecular Biophysics. The folding process is, in general, mapped in a diffusion equation through the reaction coordinate Q, that is the similarity degree of a state with the native state. The folding times can be calculated with effective potencials and the diffusion coef- ficient D. In the literature, D is assumed constant. Using lattice models, we show in this work its variations in function of Q and we calculate the new folding times. / Orientador: Vitor Barbanti Pereira Leite / Coorientador: Jorge Chahine / Banca: Antonio Francisco Pereira de Araújo / Banca: Antonio Caliri / Mestre

Made available in DSpace on 2014-06-11T19:22:54Z (GMT). No. of bitstreams: 0 Previous issue date: 2007-03-30Bitstream added on 2014-06-13T19:08:27Z : No. of bitstreams: 1 oliveira_rj_me_sjrp.pdf: 1282528 bytes, checksum: f1be25a39f095b823d25acad1b0e4ae8 (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / O enovelamento de proteinas é um problema fundamental em Biofísica Molecular. O processo de enovelamento é, em geral, mapeado através de uma equação de difusão aplicada ao longo da coordenada de reação Q, a qual descreve o grau de similaridade de uma determinada configuração com o estado nativo da proteína. Os tempos de enovelamento podem ser calculados a partir dos potenciais efetivos e do coeficiente de difusão D. Na literatura, D é assumido constante. Usando modelos de rede, mostramos neste trabalho variações desse coeficiente de difusão em função de Q e calculamos os novos tempos de enovelamento. / The protein folding is a fundamental problem in Molecular Biophysics. The folding process is, in general, mapped in a diffusion equation through the reaction coordinate Q, that is the similarity degree of a state with the native state. The folding times can be calculated with effective potencials and the diffusion coef- ficient D. In the literature, D is assumed constant. Using lattice models, we show in this work its variations in function of Q and we calculate the new folding times.