Type 1 diabetes (T1D) is an auto-immune disease characterized by insulin-deficiency. Insulin is a metabolic hormone that is involved in lowering blood glucose (BG) levels in order to control BG level to a tight range. In T1D this glycemic control is lost, causing chronic hyperglycemia (excess glucose in blood stream). Chronic hyperglycemia damages vital tissues. Therefore, glycemic control must be restored. A common therapy for restoring glycemic control is intensive insulin therapy, where the missing insulin is replaced with regular insulin injections. When dosing this compensatory insulin many factors that affect glucose metabolism must be considered. Linkura is a company that has developed tools for monitoring the most important factors, which are meals and exercise. In the Linkura meal and exercise tools, the nutrition content in meals and the calorie consumption during exercise are estimated. Another tool designed to aid control of BG is the bolus calculator. Bolus calculators use input of BG level, carbohydrate intake, and insulin history to estimate insulin need. The accuracy of these insulin bolus calculations suffer from two problems. First, errors occur when users inaccurately estimate the carbohydrate content in meals. Second, exercise is not included in bolus calculations. To reduce these problems, it was suggested that the Linkura web tools could be utilized in combination with a bolus calculator. For this purpose, a bolus calculator was developed. The bolus calculator was based on existing models that utilize clinical parameters to relate changes in BG levels to meals, insulin, and exercise stimulations. The bolus calculator was evaluated using data collected from Linkura's web tools. The collected data showed some inconsistencies which cannot be explained by any model.  The performance of the bolus calculator in predicting BG levels using general equations to derive the clinical parameters was inadequate. Performance was increased by adopting an update-algorithm where the clinical parameters were updated daily using previous data. Still, better model performance is prefered for use in a bolus calculator.   The results show potential in developing bolus calculator tools combined with the Linkura tools. For such bolus calculator, further evaluation on modeling long-term exercise and additional safety features minimizing risk of hypoglycemia are required.

In the dissertation, we study the statistical evaluation of treatment comparisons by evaluating the relative comparison of survival experiences between two treatment groups. We construct confidence interval and simultaneous confidence bands for the ratio and odds ratio of two survival functions through both parametric and nonparametric approaches.We first construct empirical likelihood confidence interval and simultaneous confidence bands for the odds ratio of two survival functions to address small sample efficacy and sufficiency. The empirical log-likelihood ratio is developed, and the corresponding asymptotic distribution is derived. Simulation studies show that the proposed empirical likelihood band has outperformed the normal approximation band in small sample size cases in the sense that it yields closer coverage probabilities to chosen nominal levels.Furthermore, in order to incorporate prognostic factors for the adjustment of survival functions in the comparison, we construct simultaneous confidence bands for the ratio and odds ratio of survival functions based on both the Cox model and the additive risk model. We develop simultaneous confidence bands by approximating the limiting distribution of cumulative hazard functions by zero-mean Gaussian processes whose distributions can be generated through Monte Carlo simulations. Simulation studies are conducted to evaluate the performance for proposed models. Real applications on published clinical trial data sets are also studied for further illustration purposes.In the end, the population attributable fraction function is studied to measure the impact of risk factors on disease incidence in the population. We develop semiparametric estimation of attributable fraction functions for cohort studies with potentially censored event time under the additive risk model.

In the dissertation, we study the statistical evaluation of treatment comparisons by evaluating the relative comparison of survival experiences between two treatment groups. We construct confidence interval and simultaneous confidence bands for the ratio and odds ratio of two survival functions through both parametric and nonparametric approaches.We first construct empirical likelihood confidence interval and simultaneous confidence bands for the odds ratio of two survival functions to address small sample efficacy and sufficiency. The empirical log-likelihood ratio is developed, and the corresponding asymptotic distribution is derived. Simulation studies show that the proposed empirical likelihood band has outperformed the normal approximation band in small sample size cases in the sense that it yields closer coverage probabilities to chosen nominal levels.Furthermore, in order to incorporate prognostic factors for the adjustment of survival functions in the comparison, we construct simultaneous confidence bands for the ratio and odds ratio of survival functions based on both the Cox model and the additive risk model. We develop simultaneous confidence bands by approximating the limiting distribution of cumulative hazard functions by zero-mean Gaussian processes whose distributions can be generated through Monte Carlo simulations. Simulation studies are conducted to evaluate the performance for proposed models. Real applications on published clinical trial data sets are also studied for further illustration purposes.In the end, the population attributable fraction function is studied to measure the impact of risk factors on disease incidence in the population. We develop semiparametric estimation of attributable fraction functions for cohort studies with potentially censored event time under the additive risk model.

Development of the advanced, real-time methods for monitoring of bioaerosols is becoming increasingly important. At present, the Ultraviolet Aerodynamic Particle Sizer (UVAPS, Model 3312, TSI, St. Paul., MN) is the only commercially available method for in-situ, continuous measurements of viable airborne microorganisms. Research included in this thesis aimed towards comprehensive evaluation of the method over a wide range of operating conditions, linking the experimental results to the theoretical basis of its design and operation, and to developing a scientific basis for its application to real-time monitoring of bioaerosols. Specifically, due to a growing concern in the general community about the environmental and health aspects of biological aerosols originated from various types of agricultural operations including animal farming, this research was focussed on developing a research methodology/strategy for applying the method to the investigation of bioaerosols in the swine confinement buildings (SCB). Investigations under controlled laboratory conditions were primarily concerned with selectivity, sensitivity, counting efficiency, and detection limits of the spectrometer. This study also examined the effect of physiological state (metabolic activity) of bacteria on the performance characteristics of the method. The practical implications of the research findings are discussed in this thesis. Further field investigations undertaken on a pig farm advanced understanding of the UVAPS performance in the real-life environmental settings. The research also provided a new insight on the particle size distribution and the effect of on-farm-activities on aerosol load inside the SCBs, for both biological and non-biological aerosols. This study has proved that the UVAPS is a powerful tool for investigation of viable bioaerosols in the environment. However, this method is limited to detection of active metabolising bacteria that excludes dormant bacterial spores. In addition, the method is very sensitive to physiological state of bacteria and to the effect of adverse environmental conditions on metabolic activity of airborne bacteria, which may decrease the amount of the intrinsic fluorophores in the cells below sensitivity level iv of the monitor. Possible limitations of this technology include also the lack of selectivity and thus interferences from the non-microbial organic components of airborne particles. In addition, the sensitivity of the method is insufficient for monitoring viable bacteria in the environments with relatively low concentrations of bioaerosols. In order to increase sensitivity of the method, it would be desirable to concentrate the bioaerosols into a smaller volume with the aim of high-volume virtual impactors (aerosol concentrators) prior to the monitoring. Therefore, in the indoor environments where an application of the concentrator is not feasible, the utilisation of the UVAPS may be problematic. Due to the intrinsic limitations, the method is not recommended for the direct measurements of viable bioaerosols and should be used in conjunction with the conventional biosamplers for obtaining more realistic insights into the microbial air quality. Nevertheless, the UVAPS has been found to be an adequate method for the investigation of the dynamics of biological aerosols in real-time. Overall, this thesis contributes to the advancing of the understanding of the method and may assist in developing new, more advanced technologies for the real-time monitoring of viable bioaerosols, as well as in developing sampling strategies for the application of the method to various bioaerosol studies.

Submitted by Alison Vanceto (alison-vanceto@hotmail.com) on 2017-09-13T18:23:58Z No. of bitstreams: 1 DissWML.pdf: 4207155 bytes, checksum: 5811f047e7b65dbd43f52f60e16255ba (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-09-20T13:58:00Z (GMT) No. of bitstreams: 1 DissWML.pdf: 4207155 bytes, checksum: 5811f047e7b65dbd43f52f60e16255ba (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-09-20T13:58:07Z (GMT) No. of bitstreams: 1 DissWML.pdf: 4207155 bytes, checksum: 5811f047e7b65dbd43f52f60e16255ba (MD5) / Made available in DSpace on 2017-09-20T14:05:26Z (GMT). No. of bitstreams: 1 DissWML.pdf: 4207155 bytes, checksum: 5811f047e7b65dbd43f52f60e16255ba (MD5) Previous issue date: 2017-06-29 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / This research was started because of concerns regarding the teaching and learning of Counting Problems in Elementary School. With the intent of contributing to the construction of basic Combinatorial concepts, we elaborated exploratory-investigative tasks and we tried through these tasks, to analyze the answers that were made by students of an 8th grade of Elementary School, in order to answer the following investigative question: what learning occurs with the mobilization of registers of semiotic representation theory to do counting in a scenario of exploratory- investigative tasks in an 8th grade of Elementary School? The theoretical and methodological reference is constituted by the registers of semiotic representation theory propounded by Duval; by the theory of Mathematical Investigations, Ponte et al. Besides that the research also had the collaboration of Pessoa and Borba. We present a brief historical retrospective on the subject, besides a previous analysis of other works in the area and official documents aimed at teaching and learning of Mathematics subject regarding to contents of Counting Problems in Elementary School. The research was developed with a group of 25 students of the 8th grade Elementary School in a public school in São Paulo state, in the year 2016. The data collection was done through field notes (logbook), and from the records written by the students during the development of the sequence of tasks. Through this investigation, we could verify that the study of Counting Problems through exploratory-investigative tasks allows the articulation of different registers of semiotic representation, leading to a better understanding of this topic. / Esta pesquisa originou-se a partir de inquietações relacionadas ao ensino e aprendizagem de Problemas de Contagem no Ensino Fundamental. Com a intenção de contribuir para a construção de conceitos básicos de Combinatória, elaboramos tarefas de natureza exploratório-investigativas e procuramos por meio destas, analisar as respostas produzidas por estudantes de um 8o ano do Ensino Fundamental, com o intuito de responder a seguinte questão de investigação: que aprendizagem ocorre com a mobilização de registros de representação semiótica para a realização de contagens em um cenário de tarefas exploratório-investigativas num 8o ano do Ensino Fundamental? O referencial teórico e metodológico é constituído pela teoria dos registros de representação semiótica proposta por Duval e pela teoria das Investigações Matemáticas, proposta Ponte et al. Além disso o trabalho também contou com a colaboração de Pessoa e Borba. Realizamos um breve retrospecto histórico sobre o tema, além de uma análise previa de outros trabalhos na área, e documentos oficiais voltados para o ensino e aprendizagem da Matemática no que diz respeito a conteúdos relacionados a Problemas de Contagem no Ensino Fundamental. A pesquisa foi desenvolvida em uma turma de 25 alunos do 8o ano Ensino Fundamental de uma escola da rede pública de ensino do estado de São Paulo, no ano de 2016. A coleta de dados se deu por meio de notas de campo (diário de bordo), e dos registros produzidos pelos estudantes ao logo do desenvolvimento da sequência de tarefas. Através desta investigação, pudemos verificar que o estudo de Problemas de Contagem por meio de tarefas exploratório- investigativas possibilita a articulação entre diferentes registros de representação semiótica, o que leva a um melhor entendimento desse tema.

Le problème du cercle de Gauss consiste à compter le nombre de points entiers de longueur bornée dans le plan. Autrement dit, compter le nombre de géodésiques fermées de longueur bornée sur un tore plat bidimensionnel. De très nombreux problèmes de comptage en systèmes dynamiques se sont inspirés de ce problème. Depuis 30 ans, on cherche à comprendre l’asymptotique de géodésiques fermées dans les surfaces de translation. H. Masur a montré que ce nombre a une croissance quadratique. Calculer l’asymptotique quadratique (constante de Siegel–Veech) est un sujet de recherches très actif aujourd’hui. L’objet d’étude de cette thèse est le modèle de windtree, un modèle de billard non compact. Dans le cas classique, on place des obstacles rectangulaires identiques dans le plan en chaque point entier. On joue au billard sur le complémentaire. Nous montrons que le nombre de trajectoires périodiques a une croissance asymptotique quadratique et calculons la constante de Siegel–Veech pour le windtree classique ainsi que pour la généralisation de Delecroix– Zorich. Nous prouvons que, pour le windtree classique, cette constante ne dépend pas des tailles des obstacles (phénomène “non varying” analogue aux résultats de Chen–Möller). Enfin, lorsque la surface de translation compacte sous-jacente est une surface de Veech, nous donnons une version quantitative du comptage. / The Gauss circle problem consists in counting the number of integer points of bounded length in the plane. In other words, counting the number of closed geodesics of bounded length on a flat two dimensional torus. Many counting problems in dynamical systems have been inspired by this problem. For 30 years, the experts try to understand the asymptotic behavior of closed geodesics in translation surfaces. H. Masur proved that this number has quadratic growth rate. Compute the quadratic asymptotic (Siegel–Veech constant) is a very active research domain these days. The object of study in this thesis is the wind-tree model, a non-compact billiard model. In the classical setting, we place identical rectangular obstacles in the plane at each integer point. We play billiard on the complement. We show that the number of periodic trajectories has quadratic asymptotic growth rate and we compute the Siegel–Veech constant for the classical wind-tree model as well as for the Delecroix–Zorich variant. We prove that, for the classical wind-tree model, this constant does not depend on the dimensions of the obstacles (non-varying phenomenon, analogous to results of Chen–Möller). Finally, when the underlying compact translation surface is a Veech surface, we give a quantitative version of the counting.