<p>The famous Black-Scholes (BS) model used in the option pricing theory</p><p>contains two parameters - a volatility and an interest rate. Both</p><p>parameters should be determined before the price evaluation procedure</p><p>starts. Usually one use the historical data to guess the value of these</p><p>parameters. For short lifetime options the interest rate can be estimated</p><p>in proper way, but the volatility estimation is, as well in this case,</p><p>more demanding. It turns out that the volatility should be considered</p><p>as a function of the asset prices and time to make the valuation self</p><p>consistent. One of the approaches to this problem is the method of</p><p>uncertain volatility and the static hedging. In this case the envelopes</p><p>for the maximal and minimal estimated option price will be introduced.</p><p>The envelopes will be described by the Black - Scholes - Barenblatt</p><p>(BSB) equations. The existence of the upper and lower bounds for the</p><p>option price makes it possible to develop the worse and the best cases</p><p>scenario for the given portfolio. These estimations will be financially</p><p>relevant if the upper and lower envelopes lie relatively narrow to each</p><p>other. One of the ideas to converge envelopes to an unknown solution</p><p>is the possibility to introduce an optimal static hedged portfolio.</p>

The famous Black-Scholes (BS) model used in the option pricing theory contains two parameters - a volatility and an interest rate. Both parameters should be determined before the price evaluation procedure starts. Usually one use the historical data to guess the value of these parameters. For short lifetime options the interest rate can be estimated in proper way, but the volatility estimation is, as well in this case, more demanding. It turns out that the volatility should be considered as a function of the asset prices and time to make the valuation self consistent. One of the approaches to this problem is the method of uncertain volatility and the static hedging. In this case the envelopes for the maximal and minimal estimated option price will be introduced. The envelopes will be described by the Black - Scholes - Barenblatt (BSB) equations. The existence of the upper and lower bounds for the option price makes it possible to develop the worse and the best cases scenario for the given portfolio. These estimations will be financially relevant if the upper and lower envelopes lie relatively narrow to each other. One of the ideas to converge envelopes to an unknown solution is the possibility to introduce an optimal static hedged portfolio.

This thesis provides insight into methods for estimating blood perfusion, emphasizing the need for accurate modeling in dynamic physiological environments. The thesis critically examines conventional error function solutions used in steady state or gradually changing blood flow scenarios, revealing their shortcomings in accurately reflecting more rapid changes in blood perfusion. To address this limitation, this study introduces a novel prediction model based on the finite-difference method (FDM) specifically designed to produce accurate results under different blood flow perfusion conditions. A comparative analysis concludes that the FDM-based model is consistent with traditional error function methods under constant blood perfusion conditions, thus establishing its validity under dynamic and steady blood flow conditions. In addition, the study attempts to determine whether analytical solutions exist that are suitable for changing perfusion conditions. Three alternative analytical estimation methods were explored, each exposing the common thread of inadequate responsiveness to sudden changes in blood perfusion. Based on the advantages and disadvantages of the error function and FDM estimation, a combination of these two methods was developed. Utilizing the simplicity and efficiency of the error function, the prediction of contact resistance and core temperature along with the initial blood perfusion was first made at the beginning of the data. Then the subsequent blood perfusion values were predicted using the FDM, as the FDM can effectively respond to changing blood perfusion values. / Master of Science / Blood perfusion, the process of blood flowing through our body's tissues, is crucial for our health. It's like monitoring traffic flow on roads, which is especially important during rapid changes, such as during exercise or medical treatments. Traditional methods for estimating blood perfusion, akin to older traffic monitoring techniques, struggle to keep up with these rapid changes. This research introduces a new approach, using a method often found in engineering and physics, called the finite-difference method (FDM), to create more accurate models of blood flow in various conditions. This study puts this new method to the test against the old standards. We discover that while both are effective under steady conditions, the FDM shines when blood flow changes quickly. We also examined three other methods, but they, too, fell short in these fast-changing scenarios. This work is more than just numbers and models; it's about potentially transforming how we understand and manage health. By combining the simplicity of traditional methods for initial blood flow estimates with the dynamic capabilities of the FDM, we're paving the way for more precise medical diagnostics and treatments.

Made available in DSpace on 2014-12-17T15:01:32Z (GMT). No. of bitstreams: 1 HannielFSF_DISSERT.pdf: 2655706 bytes, checksum: fff21ca883e2c0c137ef98496660b572 (MD5) Previous issue date: 2013-07-05 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / The present work has the main goal to study the modeling and simulation of a biphasic separator with induced phase inversion, the MDIF, with the utilization of the finite differences method for the resolution of the partial differencial equations which describe the transport of contaminant s mass fraction inside the equipment s settling chamber. With this aim, was developed the deterministic differential model AMADDA, wich was admensionalizated and then semidiscretizated with the method of lines. The integration of the resultant system of ordinary differential equations was realized by means of a modified algorithm of the Adam-Bashfort- Moulton method, and the sthocastic optimization routine of Basin-Hopping was used in the model s parameter estimation procedure . With the aim to establish a comparative referential for the results obtained with the model AMADDA, were used experimental data presented in previous works of the MDIF s research group. The experimental data and those obtained with the model was assessed regarding its normality by means of the Shapiro-Wilk s test, and validated against the experimental results with the Student s t test and the Kruskal-Wallis s test, depending on the result. The results showed satisfactory performance of the model AMADDA in the evaluation of the MDIF s separation efficiency, being possible to determinate that at 1% significance level the calculated results are equivalent to those determinated experimentally in the reference works / O presente trabalho tem como objetivo estudar a modelagem e simula??o de um separador bif?sico com invers?o de fases induzida, o MDIF (Misturador Decantador ? Invers?o de Fases), por meio da utiliza??o do m?todo das diferen?as finitas para a resolu??o das equa??es diferenciais parciais que descrevem o transporte da fra??o m?ssica do contaminante no interior da c?mara de decanta??o do equipamento. Com esse intuito, foi desenvolvido o modelo determin?stico diferencial AMADDA, o qual foi admensionalizado e ent?o semidiscretizado atrav?s do m?todo das linhas. A integra??o do sistema de equa??es diferenciais ordin?rias resultante foi realizada atrav?s de um algoritmo modificado do m?todo de Adam-Bashfort-Moulton, e a rotina de otimiza??o estoc?stica de Basin-Hopping foi utilizada no procedimento de estima??o de par?metros do modelo. Com o intuito de estabelecer um referencial comparativo para a valida??o dos resultados obtidos com o modelo AMADDA, foram utilizados dados experimentais apresentados na literatura (FERNANDES JR, 2002; FERNANDES JR, 2006; MEDEIROS, 2008). Os resultados experimentais e aqueles obtidos com o modelo foram avaliados quanto ? sua normalidade por meio do teste de Shapiro-Wilk, e validados frente aos resultados experimentais atrav?s do teste t de Student e o o teste de Kruskal-Wallis, ? depender do resultado. Os resultados obtidos atrav?s do modelo AMADDA mostraram um desempenho satisfat?rio na determina??o da efici?ncia de separa??o do MDIF, sendo poss?vel determinar que, a um n?vel de signific?ncia de 1%, os resultados calculados s?o equivalentes ?queles determinados experimentalmente nos trabalhos de refer?ncia

Submitted by Celso Magalhaes (celsomagalhaes@ufrrj.br) on 2017-05-19T12:03:19Z No. of bitstreams: 1 2016 - Pablo Amauri Carvalho de Ara?jo e Souza.pdf: 3429164 bytes, checksum: c1da6eb8bb41fc96de0b7e5ca2a9570f (MD5) / Made available in DSpace on 2017-05-19T12:03:19Z (GMT). No. of bitstreams: 1 2016 - Pablo Amauri Carvalho de Ara?jo e Souza.pdf: 3429164 bytes, checksum: c1da6eb8bb41fc96de0b7e5ca2a9570f (MD5) Previous issue date: 2016-06-13 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior - CAPES / This work highlights the importance of well administrated vaccination as prophylactic activity, making it a key element of mathematical modeling about the spreading of an infection by Influenza H1N1 virus in a human population. The model counts with Optimal Control theory to achieve a vaccination strategy that balance infection?s prevention and your own cost in a hypothetical population exposed to a virus. The numerical solutions of ordinary differential equations systems generated by model is given via Finite Difference Method, that reveals the populational dynamics during the time while the vaccine is distributed, in various different situations of virus exposition and vaccination cost. / Este trabalho ressalta a import?ncia da vacina??o bem administrada como atividade profil?tica, tornando-a elemento chave da modelagem matem?tica do espalhamento da infec??o pelo v?rus Influenza H1N1 em uma popula??o humana. O modelo conta com a teoria de Controle ?timo para alcan?ar uma estrat?gia de vacina??o, que equilibre a preven??o da infec??o e seu pr?prio custo em uma popula??o hipot?tica exposta ao v?rus. As solu??es num?ricas dos sistemas de equa??es diferenciais ordin?rias gerados pelo modelo ficam a cargo do M?todo das Diferen?as Finitas, revelando a din?mica populacional no per?odo de tempo em que a vacina ? distribu?da, em distintas situa??es de exposi??o ao v?rus e custo da vacina??o.

This study presents a model for the organization of educational content customized for environments of individual studies. For many students the availability of content in general form can not be efficient. It proposed a multilevel structure of concepts to provide the development of different combinations to show the same content. The work shows that it is possible to customize the content in order to encourage other students with the use of proximal learning standards. These patterns are obtained from the analysis of the action of students with positive results in the individual organization of the content. The formal representation establishes the definition of the student profile, multi-level content, the distribution plan of correction of concepts and teaching career. The structure of the trajectory of student teaching is formally established by the method of finite differences. The system uses artificial intelligence techniques to organize and personalize content reactively. Customization is provided by an artificial neural network that enables the classification of the student profile and assign that profile to a standard proximal learning. To mediate and adjust the contents of a reactive system was inserted into a set of rules from experts in teaching. The experiment showed the applicability and appropriateness of the proposed model. The results indicated the suitability of the approach by automating the organization\'s custom content so adaptive and reactive. The intelligent system to establish the structure of the custom content to be presented was considered efficient, giving the student a better use of the content, with higher and lower final average study time and content presented. / Este trabalho apresenta uma modelagem para a organização personalizada de conteúdos didáticos para ambientes de estudos individuais. Para muitos estudantes a disponibilização do conteúdo em formato generalizado pode não ser eficiente. É proposta uma estrutura multinível de conceitos para proporcionar o desenvolvimento de diferentes combinações para a apresentação do mesmo conteúdo. O trabalho mostra que é possível personalizar o conteúdo de forma a favorecer outros estudantes com o uso de padrões proximais de aprendizagem. Estes padrões são obtidos da análise da ação de estudantes, com resultados positivos na organização individual do conteúdo. A representação formal estabelece a definição do perfil do estudante, o conteúdo multinível, o plano de distribuição dos conceitos e a correção da trajetória didática. A estruturação da trajetória didática do estudante é formalmente estabelecida pelo método das diferenças finitas. O sistema utiliza técnicas de inteligência artificial para organizar e personalizar reativamente o conteúdo. A personalização é proporcionada por uma rede neural artificial que possibilita a classificação do perfil do estudante e associa esse perfil a um padrão proximal de aprendizagem. Para mediar e ajustar o conteúdo de forma reativa foi inserido no sistema um conjunto de regras de especialistas em docência. O experimento realizado mostrou a aplicabilidade e a adequação da modelagem proposta. Os resultados indicaram a adequação da abordagem, automatizando a organização personalizada do conteúdo de forma adaptativa e reativa. O sistema inteligente ao estabelecer a estruturação personalizada do conteúdo a ser apresentado foi considerado eficiente, proporcionando ao estudante um melhor aproveitamento do conteúdo, com maior média final e menor tempo de estudo e conteúdo apresentado. / Doutor em Ciências

Cette thèse vise à étudier le comportement de revêtement articulé du tunnel en développant une nouvelle approche numérique à la Méthode de Réaction Hyperstatique (HRM) et la production des modèles numériques en deux dimensions et trois dimensions à l'aide de la méthode des différences finies (FDM). L'étude a été traitée d'abord sous charges statiques, puis effectuée sous charges dynamiques. Tout d'abord, une étude bibliographique a été effectuée. Une nouvelle approche numérique appliquée à la méthode HRM a ensuite été développée. En même temps, un modèle numérique en deux dimensions est programmé sur les conditions de charge statique dans le but d'évaluer l'influence des joints, en termes de la distribution et des caractéristiques des joints, sur le comportement du revêtement articulé de tunnel. Après cela, des modèles complets en trois dimensions d'un seul tunnel, de deux tunnels horizontaux et de deux tunnels empilés, dans lesquels le système des joints est simulé, ont été développés. Ces modèles en trois dimensions permettent d'étudier le comportement non seulement du revêtement du tunnel, mais encore le déplacement du sol entourant le tunnel lors de l’excavation. Un modèle numérique en trois dimensions simplifié a ensuite été réalisé afin de valider la nouvelle approche numérique appliquée à la méthode HRM.Dans la dernière partie de ce mémoire, la performance du revêtement articulé du tunnel sous chargements dynamiques est prise en compte par l’analyse quasi-statique et dynamique complète en utilisant le modèle numérique en deux dimensions (FDM). Un modèle HRM a également été développé prenant en compte des charges quasi-statiques. Les différences de comportement de tunnel sous chargements statiques et sismiques sont mises en évidence et expliquées. / This PhD thesis has the aim to study the behaviour of segmental tunnel lining by developing a new numerical approach to the Hyperstatic Reaction Method (HRM) and producing two-dimensional (2D) and three-dimensional (3D) numerical models using the finite difference method (FDM). The study first deals with under static loads, and then performs under dynamic loads. Firstly, a literature review has been conducted. A new numerical approach applied to the HRM has then been developed. At the same time, a 2D numerical model is programmed regarding static loading conditions in order to evaluate the influence of the segmental joints, in terms of both joint distribution and joint stiffness characteristics, on the tunnel lining behaviour. After that, full 3D models of a single tunnel, twin horizontal tunnels and twin tunnels stacked over each other, excavated in close proximity in which the joint pattern is simulated, have been developed. These 3D models allow one to investigate the behaviour of not only the tunnel lining but also the displacement of the ground surrounding the tunnel during the tunnel excavation. A simplified 3D numerical model has then been produced in order to validate the new numerical approach applied to the HRM. In the last part of the manuscript, the performance of the segmental tunnel lining exposed to dynamic loading is taken into consideration through quasi-static and full dynamic analyses using 2D numerical models (FDM). A new HRM model has also been developed considering quasi-static loads. The differences of the tunnel behaviour under static and seismic loadings are highlighted.