Currently, researchers at Sandia National Laboratories are creating software that is designed to determine the source of a toxic release given sensor readings of the toxin concentration at fixed locations in the building. One of the most important concerns in solving such problems is computation time since even a crude approximation to the source, if found in a timely manner, will give emergency personnel the chance to take appropriate actions to contain the substance. The manner in which the toxin spreads depends on the air flow within the building. Due to the turbulence in the air flow, it is necessary to calculate the flow field on a fine mesh. Unfortunately, using a fine mesh for every calculation in this problem may result in prohibitively long computation times when other features are incorporated into the model. The goal of this thesis is to reduce the computation time required by the software mentioned above by applying two different mesh coarsening strategies after the flow field is computed. The first of these strategies is to use a uniformly coarse mesh and the second is to use our knowledge of the air flow in the building to construct an adaptive mesh. The objective of the latter strategy is to use a fine mesh only in areas where it is absolutely necessary, i.e., in areas where there is a great change in the flow field.

Made available in DSpace on 2017-07-21T20:31:59Z (GMT). No. of bitstreams: 1 Mariana Ferreira.pdf: 1101451 bytes, checksum: 311578c4efd5146b9f09dd0ba7c8ff3a (MD5) Previous issue date: 2012-06-28 / This study aims at analyzing the design process of the School Development Plan - SDP (Plano de Desenvolvimento da Escola - PDE Escola), as well as the enactment of such policy in State schools of Guarapuava - PR. The research was based on the policy cycle approach (BOWE et al., 1992; BALL, 1994), on the theory of policy enactment (BALL; MAGUIRE; BRAUN, 2012), and on authors whose ideas underlie the role of the State in the definition of policies (FREITAS et al., 2009; MENDES, 2006), education as a principle of social quality (CAMINI, 2001; BELLONI, 2003), and the role of school education (GIMENO SACRISTÁN, 2007; YOUNG, 2007). The study comprised: a) study on the historical, political, economical and ideological backgrounds of educational policies from the 1990s on (context of influence); b) analysis of official documents which address the organization of educational policies – SDP School, theses and dissertations on the Education Development Plan and the School Development Plan (context of text production); c) analysis of the context of practice through field research carried out in three schools in Guarapuava, involving the analysis of the Implementation Plan of each school and interviews with principals, educators and teachers. Main conclusions were as follow: a) The Federal Education Development Plan - EDP is an attempt to supply articulated actions between the Federal government, States and towns, aimed at improving the quality of public education in Brazil. However, the way it was organized it generated several manifestations among education researchers, both in favor and against it; b) The SDP School is one of the programs which compose the Federal EDP, presented as a management tool, which originated in Fernando Henrique Cardoso’s government as one of the ‘Fundescola’ developments; c) by implementing the SDP School, in Paraná State, some changes were made, aiming at making it suitable to State educational policies; d) in the context of practice, the education professionals created different strategies to implement the policy (translation and interpretation processes). Finally, it was concluded that the SDP School offers relevant contributions regarding planning according to the school reality. However it was also noticed that in the actions proposed by the schools, there is a strong influence of management perspective at different levels of proximity with a conception of democratic education. / A presente pesquisa teve por objetivo analisar o processo de formulação do Plano do Desenvolvimento da Escola - PDE Escola, bem como essa política foi colocada em ação, na rede estadual do município de Guarapuava - Pr. A pesquisa fundamentou-se na abordagem do ciclo de políticas (BOWE et al., 1992; BALL, 1994), na theory of policy enactment - teoria da política em ação (BALL; MAGUIRE; BRAUN, 2012) e nas ideias de autores que fundamentam o papel do Estado na definição das políticas (FREITAS et al., 2009; MENDES, 2006), a educação como princípio de qualidade social (CAMINI, 2001; BELLONI, 2003), o papel da educação escolar (GIMENO SACRISTÁN, 2007; YOUNG, 2007). A pesquisa envolveu: a) estudo sobre os antecedentes históricos, políticos, econômicos e ideológicos das políticas educacionais a partir da década de 1990 (contexto de influência); b) análise de textos oficiais que tratam da organização das políticas educacionais – PDE Escola; teses e dissertações sobre o Plano de Desenvolvimento da Educação e o Plano de Desenvolvimento da Escola (contexto da produção de texto); c) análise do contexto da prática por meio de pesquisa de campo realizada em três escolas do município de Guarapuava, envolvendo a análise do Plano de Ação de cada escola e entrevistas com diretores, pedagogos e professores. As principais conclusões foram: a) O PDE Federal é uma tentativa de prover ações articuladas entre o governo federal, os estados e municípios, com a finalidade de melhorar a qualidade da educação pública no país, porém da forma como foi organizado gerou várias manifestações tanto favoráveis como desfavoráveis, entre os pesquisadores em educação; b) O programa PDE Escola é um dos programas que compõem o PDE Federal, apresentado como uma ferramenta gerencial, que teve suas raízes no governo de Fernando Henrique Cardoso como uma das ações do Fundescola; c) ao implantar o PDE Escola, no Estado do Paraná, algumas alterações foram feitas, com o objetivo de adequá-lo às políticas educacionais estaduais; d) no contexto da prática, os profissionais da educação criam diferentes estratégias para colocar a política em ação (processos de tradução e interpretação). Finalmente, conclui-se que o PDE Escola oferece contribuições relevantes no que se refere ao planejamento de acordo com realidade da escola. No entanto, percebeu-se, nas ações propostas pelas escolas, uma forte influência da perspectiva gerencial, com diferentes níveis de aproximação de uma concepção de educação democrática.

This thesis introduces models for pricing credit default swaps (CDS) and evaluating the counterparty risk when buying a CDS in the over-the-counter (OTC) market from a counterpart subjected to default risk. Rather than assuming that the default of the referencing firm of the CDS is independent of the trading parties in the CDS, this thesis proposes models that capture the default correlation amongst the three parties involved in the trade, namely the referencing firm, the buyer and the seller. We investigate how the counterparty risk that CDS buyers face can be affected by default correlation and how their balance sheet could be influenced by the changes in counterparty risk. The correlation of corporate default events has been frequently observed in credit markets due to the close business relationships of certain firms in the economy. One of the many mathematical approaches to model that correlation is default contagion. We propose an innovative model of default contagion which provides more flexibility by allowing the affected firm to recover from a default contagion event. We give a detailed derivation of the partial differential equations (PDE) for valuing both the CDS and the credit value adjustment (CVA). Numerical techniques are exploited to solve these PDEs. We compare our model against other models from the literature when measuring the CVA of an OTC CDS when the default risk of the referencing firm and the CDS seller is correlated. Further, the model is extended to incorporate economy-wide events that will damage all firms' credit at the same time-this is another kind of default correlation. Advanced numerical techniques are proposed to solve the resulting partial-integro differential equations (PIDE). We focus on investigating the different role of default contagion and economy-wide events have in terms of shaping the default correlation and counterparty risk. We complete the study by extending the model to include bilateral counterparty risk, which considers the default of the buyer and the correlation among the three parties. Again, our extension leads to a higher-dimensional problem that we must tackle with hybrid numerical schemes. The CVA and debit value adjustment (DVA) are analysed in detail and we are able to value the profit and loss to the investor's balance sheet due to CVA and DVA profit and loss under different market circumstances including default contagion.

We develop novel numerical methods for optimization problems subject to constraints given by nonlinear hyperbolic systems of conservation and balance laws in one space dimension. These types of control problems arise in a variety of applications, in which inverse problems for the corresponding initial value problems are to be solved. The optimization method can be seen as a block Gauss-Seidel iteration. The optimization requires one to numerically solve the hyperbolic system forward in time and the corresponding linear adjoint system backward in time. We test the optimization method on a number of control problems constrained by nonlinear hyperbolic systems of PDEs with both smooth and discontinuous prescribed terminal states. The theoretical foundation of the introduced scheme is provided in the case of scalar hyperbolic conservation laws on an unbounded domain with a strictly convex flux. In addition, we empirically demonstrate that using a higher-order temporal discretization helps to substantially improve both the efficiency and accuracy of the overall numerical method. / acase@tulane.edu

This thesis makes significant contributions to the object detection problem in computer vision. The object detection problem is, given a digital image of a scene, to detect the relevant object in the image. One technique for performing object detection, called ``active contours,' optimizes a constructed energy that is defined on contours (closed curves) and is tailored to image features. An optimization method can be used to perform the optimization of the energy, and thereby deform an initially placed contour to the relevant object. The typical optimization technique used in almost every active contour paper is evolving the contour by the energy's gradient descent flow, i.e., the steepest descent flow, in order to drive the initial contour to (hopefully) the minimum curve. The problem with this technique is that often times the contour becomes stuck in a sub-optimal and undesirable local minimum of the energy. This problem can be partially attributed to the fact that the gradient flows of these energies make use of only local image and contour information. By local, we mean that in order to evolve a point on the contour, only information local to that point is used. Therefore, in this thesis, we introduce a new class of flows that are global in that the evolution of a point on the contour depends on global information from the entire curve. These flows help avoid a number of problems with traditional flows including helping in avoiding undesirable local minima. We demonstrate practical applications of these flows for the object detection problem, including applications to both image segmentation and visual object tracking.

From the viewpoint of the adaptive solution of partial differential equations a finit e element method on hierarchical triangular meshes is developed permitting hanging nodes arising from nonuniform hierarchical refinement. Construction, extension and restriction of the nonuniform hierarchical basis and the accompanying mesh are described by graphs. The corresponding FE basis is generated by hierarchical transformation. The characteristic feature of the generalizable concept is the combination of the conforming hierarchical basis for easily defining and changing the FE space with an accompanying nonconforming FE basis for the easy assembly of a FE equations system. For an elliptic model the conforming FEM problem is solved by an iterative method applied to this nonconforming FEM equations system and modified by projection into the subspace of conforming basis functions. The iterative method used is the Yserentant- or BPX-preconditioned conjugate gradient algorithm. On a MIMD computer system the parallelization by domain decomposition is easy and efficient to organize both for the generation and solution of the equations system and for the change of basis and mesh.

Projecting the ice sheets' contribution to sea-level rise is difficult because of the complexity of accurately modeling ice sheet dynamics for the full polar ice sheets, because of the uncertainty in key, unobservable parameters governing those dynamics, and because quantifying the uncertainty in projections is necessary when determining the confidence to place in them. This work presents the formulation and solution of the Bayesian inverse problem of inferring, from observations, a probability distribution for the basal sliding parameter field beneath the Antarctic ice sheet. The basal sliding parameter is used within a high-fidelity nonlinear Stokes model of ice sheet dynamics. This model maps the parameters "forward" onto a velocity field that is compared against observations. Due to the continental-scale of the model, both the parameter field and the state variables of the forward problem have a large number of degrees of freedom: we consider discretizations in which the parameter has more than 1 million degrees of freedom. The Bayesian inverse problem is thus to characterize an implicitly defined distribution in a high-dimensional space. This is a computationally demanding problem that requires scalable and efficient numerical methods be used throughout: in discretizing the forward model; in solving the resulting nonlinear equations; in solving the Bayesian inverse problem; and in propagating the uncertainty encoded in the posterior distribution of the inverse problem forward onto important quantities of interest. To address discretization, a hybrid parallel adaptive mesh refinement format is designed and implemented for ice sheets that is suited to the large width-to-height aspect ratios of the polar ice sheets. An efficient solver for the nonlinear Stokes equations is designed for high-order, stable, mixed finite-element discretizations on these adaptively refined meshes. A Gaussian approximation of the posterior distribution of parameters is defined, whose mean and covariance can be efficiently and scalably computed using adjoint-based methods from PDE-constrained optimization. Using a low-rank approximation of the covariance of this distribution, the covariance of the parameter is pushed forward onto quantities of interest.

The new parallelization technology is presented in this work. The technology is suitable for parallelization of linear algebra problems that arise during solution of PDE and PDE systems. The new technology combines the strong points of "data parallel" and "global memory" parallel programming models. Using the pecularities of the problems of a given class, the technology allows to write effective code easily, with the addition of the possibility for semi-automatic parallelization. The work consists of 3 parts: the review of existing technologies, the description of the new one, various applications. / Šiame darbe pateikiama nauja tiesinės algebros algoritmų, atsirandančių sprendžiant dif. lygtis ir jų sistemas, lygiagretinimo technologija. Ši technologija apjungia "lygiagrečiųjų duomenų" ir "globalios atminties" lygiagretinimo modelių privalumus, ir, naudojant apibrėžtos klasės uždavinių yptaumus, leidžia lengvai gauti efektyvų programos kodą, kuris pusiau automatiškai lygiagretinamas. Darbas susideda iš 3 dalių: egzistuojančių priemonių apžvalga, naujos technologijos aprašymas, įvairūs taikymai.

Šiame darbe pateikiama nauja tiesinės algebros algoritmų, atsirandančių sprendžiant dif. lygtis ir jų sistemas, lygiagretinimo technologija. Ši technologija apjungia "lygiagrečiųjų duomenų" ir "globalios atminties" lygiagretinimo modelių privalumus, ir, naudojant apibrėžtos klasės uždavinių yptaumus, leidžia lengvai gauti efektyvų programos kodą, kuris pusiau automatiškai lygiagretinamas. Darbas susideda iš 3 dalių: egzistuojančių priemonių apžvalga, naujos technologijos aprašymas, įvairūs taikymai. / The new parallelization technology is presented in this work. The technology is suitable for parallelization of linear algebra problems that arise during solution of PDE and PDE systems. The new technology combines the strong points of "data parallel" and "global memory" parallel programming models. Using the pecularities of the problems of a given class, the technology allows to write effective code easily, with the addition of the possibility for semi-automatic parallelization. The work consists of 3 parts: the review of existing technologies, the description of the new one, various applications.

No description available.