Submitted by Silvana Teresinha Dornelles Studzinski (sstudzinski) on 2016-05-25T12:28:08Z No. of bitstreams: 1 Jean Carlos Araújo Costa_.pdf: 1155126 bytes, checksum: 15210c31e7d20bb22cb98f8732173d6d (MD5) / Made available in DSpace on 2016-05-25T12:28:09Z (GMT). No. of bitstreams: 1 Jean Carlos Araújo Costa_.pdf: 1155126 bytes, checksum: 15210c31e7d20bb22cb98f8732173d6d (MD5) Previous issue date: 2016-03-01 / Nenhuma / Técnicas de visualização de dados podem auxiliar nas mais diversas áreas de atuação humana, em especial na compreensão de dados e informações de diferentes fenômenos que se quer estudar. Quanto mais variáveis estão relacionadas com esse fenômeno, mais desafiador se torna seu tratamento e representação visual. Pensando em educação no Brasil e suas bases de dados abertas, bem como em bases de dados acadêmicas existentes nas instituições, o uso de técnicas matemáticas para correlacionar conjuntos de dados e métodos de visualização para apresentar essas correlações, disponíveis em uma ferramenta de fácil acesso e operação, podem tornar públicas informações sobre a qualidade da educação de determinada região, estado, município e instituição de ensino. Outro benefício pode ser a indicação de fatores que antes eram ignorados, como alvos de investimento e ainda ajudar na elaboração de políticas públicas, nacionais ou regionais, que tornem a educação mais eficiente, abrangente e inclusiva. Iniciativas de organizações não governamentais e algumas vinculadas ao governo brasileiro tem elaborado ferramentas de filtragem de informações e divulgação de dados sobre qualidade e investimento de recursos na educação. O governo brasileiro usa índices de desempenho para avaliar suas Instituições de Ensino Superior. O Conceito Preliminar de Curso é um desses. Este trabalho apresenta uma solução, visando elaborar uma metodologia de visualização de dados através de uma aplicação web, com tecnologias open source, utilizando o método de análise de componentes principais (ACP) como técnica matemática de correlação de variáveis, e distribuindo resultados sobre um mapa com a utilização da API do Google Maps, porém, tendo como foco, a busca do nível de influência de diferentes fatores, inclusive de alguns não ligados diretamente à educação, na performance de instituições de ensino e no rendimento acadêmico de alunos, tendo como estudo de caso, a análise de um índice de desempenho na educação superior. / Data visualization techniques can help in several areas of human activity, especially in understanding data and information from different phenomena to be studied. The more variables are related to this phenomenon, the more challenging it becomes their treatment and visual representation. Thinking about education in Brazil and its open databases, as well as in existing academic databases in institutions, using mathematical techniques to correlate data sets and visualization methods to present these correlations available in an easy tool access and operation may disclose information on the quality of education in a region, state, county and educational institution. Another benefit coud be the indication of factors that were ignored, as investment targets and also help in the development of public policies, national or regional, that make more efficient, comprehensive and inclusive education. Initiatives of non-governmental organizations and some linked to the Brazilian government has prepared information filtering tools and dissemination of data on quality and investment of resources in education. Brazilian government uses performance indicators to assess their undergraduation institutions. Course Preliminar Concept (CPC) is one of those. This paper presents a solution to this profile, aiming to develop a data visualization methodology through a web application with open source technologies, using principal component analysis method (PCA) as mathematical technique of variable correlation, and distributing results on a map using the Google Maps API, however, focusing on the search for the level of influence of different factors, including some not directly related to education, performance of educational institutions and the academic performance of students, taking as a case study, the analysis of a performance index in undergraduation.

PhD (Mathematics) / Department of Mathematics and Applied Mathematics / In this study, we developed multiscale models of vector-borne diseases. In general, the transmission of vector-borne diseases can be considered as falling into two categories, i.e. direct transmission and environmental transmission. Two representative vector-borne diseases, namely; malaria which represents all directly transmitted vector-borne diseases and schistosomiasis which represents all environmentally transmitted vector-borne diseases were studied. Based on existing mathematical modelling science base, we established a new multiscale modelling framework that can be used to evaluate the effectiveness of vector-borne diseases treatment and preventive interventions. The multiscale models consisted of systems of nonlinear ordinary differential equations which were studied for the provision of solutions to the underlying problem of the disease transmission dynamics. Relying on the fact that there is still serious lack of knowledge pertaining to mathematical techniques for the representation and construction of multiscale models of vector-bone diseases, we have developed some grand ideas to placate this gap. The central idea in multiscale modelling is to divide a modelling problem such as a vector-bone disease system into a family of sub-models that exist at different scales and then attempt to study the problem at these scales while simultaneously linking the sub-models across these scales. For malaria, we formulated the multiscale models by integrating four submodels which are: (i) a sub-model for the mosquito-to-human transmission of malaria parasite, (ii) a sub-model for the human-to-mosquito transmission of malaria parasite, (iii) a within-mosquito malaria parasite population dynamics sub-model and (iv) a within-human malaria parasite population dynamics sub-model. For schistosomiasis, we integrated the two subsystems (within-host and between-host sub-models) by identifying the within-host and between-host variables and parameters associated with the environmental dynamics of the pathogen and then designed a feedback of the variables and parameters across the within-host and between-host sub-models. Using a combination of analytical and computational tools we adequately accounted for the influence of the sub-models in the different multiscale models. The multiscale models were then used to evaluate the effectiveness of the control and prevention interventions that operate at different scales of a vector-bone disease system. Although the results obtained in this study are specific to malaria and schistosomiasis, the multiscale modelling frameworks developed are robust enough to be applicable to other vector-borne diseases. / NRF

This thesis is in the field of non-linear partial differential equations (PDE), focusing on problems which show some type of phase-transition. A single phase Hele-Shaw flow models a Newtoninan fluid which is being injected in the space between two narrowly separated parallel planes. The time evolution of the space that the fluid occupies can be modelled by a semi-linear PDE. This is a problem within the field of free boundary problems. In the multi-phase problem we consider the time-evolution of a system of phases which interact according to the principle that the joint boundary which emerges when two phases meet is fixed for all future times. The problem is handled by introducing a parameterized equation which is regularized and penalized. The penalization is non-local in time and tracks the history of the system, penalizing the joint support of two different phases in space-time. The main result in the first paper is the existence theory of a weak solution to the parameterized equations in a Bochner space using the implicit function theorem. The family of solutions to the parameterized problem is uniformly bounded allowing us to extract a weakly convergent subsequence for the case when the penalization tends to infinity. The second problem deals with a parameterized highly oscillatory quasi-linear elliptic equation in divergence form. As the regularization parameter tends to zero the equation gets a jump in the conductivity which occur at the level set of a locally periodic function, the obstacle. As the oscillations in the problem data increases the solution to the equation experiences high frequency jumps in the conductivity, resulting in the corresponding solutions showing an effective global behaviour. The global behavior is related to the so called homogenized solution. We show that the parameterized equation has a weak solution in a Sobolev space and derive bounds on the solutions used in the analysis for the case when the regularization is lost. Surprisingly, the limiting problem in this case includes an extra term describing the interaction between the solution and the obstacle, not appearing in the case when obstacle is the zero level-set. The oscillatory nature of the problem makes standard numerical algorithms computationally expensive, since the global domain needs to be resolved on the micro scale. We develop a multi scale method for this problem based on the heterogeneous multiscale method (HMM) framework and using a finite element (FE) approach to capture the macroscopic variations of the solutions at a significantly lower cost. We numerically investigate the effect of the obstacle on the homogenized solution, finding empirical proof that certain choices of obstacles make the limiting problem have a form structurally different from that of the parameterized problem. / <p>QC 20180222</p>