The objective of this thesis is to develop a sequential algorithm to determine accurately and quickly, at which point in time a product is well mixed or reaches a steady state plateau, in terms of the Refractive Index (RI). An algorithm using sequential non-linear model fitting and prediction is proposed. A simulation study representing typical scenarios in a liquid manufacturing process in pharmaceutical industries was performed to evaluate the proposed algorithm. The data simulated included autocorrelated normal errors and used the Gompertz model. A set of 27 different combinations of the parameters of the Gompertz function were considered. The results from the simulation study suggest that the algorithm is insensitive to the functional form and achieves the goal consistently with least number of time points.

Orientador: Jamil Viana Pereira / Resumo: Neste trabalho, será abordada a teoria matemática utilizada no estudo de quatro modelos clássicos de crescimento populacional: Malthus, Verhulst, Gompertz e Montroll. Serão apresentadas e/ou discutidas algumas de suas características, propriedades, diferenças e diferentes métodos para obtenção de seus parâmetros. Posteriormente, estes modelos e métodos serão aplicados a um conjunto de dados relativos ao crescimento populacional do Brasil. Também foi elaborada uma atividade para ser aplicada no Ensino Médio, na qual se explora, por tabelas e gráficos, a forma como os alunos observam certos fenômenos de crescimento, bem como, construtivamente e com auxílio de dados, a forma como ocorrem esses crescimentos de fato. / Abstract: In this work, the mathematical theory of four classic population growth models (Malthus, Verhulst, Gompertz and Montroll) will be addressed. Some of their characteristics, properties, differences and different methods for obtaining their parameters will be presented and/or discussed. Subsequently, these models and methods will be applied to a Brazilian population growth data set. An activity was also elaborated to be applied in high school. It explores, by tables and graphs, how students observe some growth phenomena, as well as, constructively and with the help of data, how these growths really occur. / Mestre

Immersive applications, such as computer gaming, computer vision and video codecs, are an important emerging class of applications with QoS requirements that are difficult to characterize and control using traditional methods. This thesis proposes new techniques reliant on execution-time variance to both characterize and control program behavior. The proposed techniques are intended to be broadly applicable to a wide variety of immersive applications and are intended to be easy for programmers to apply without needing to gain specialized expertise. First, we create new QoS controllers that programmers can easily apply to their applications to achieve desired application-specific QoS objectives on any platform or application data-set, provided the programmers verify that their applications satisfy some simple domain requirements specific to immersive applications. The controllers adjust programmer-identified knobs every application frame to effect desired values for programmer-identified QoS metrics. The control techniques are novel in that they do not require the user to provide any kind of application behavior models, and are effective for immersive applications that defy the traditional requirements for feedback controller construction. Second, we create new profiling techniques that provide visibility into the behavior of a large complex application, inferring behavior relationships across application components based on the execution-time variance observed at all levels of granularity of the application functionality. Additionally for immersive applications, some of the most important QoS requirements relate to managing the execution-time variance of key application components, for example, the frame-rate. The profiling techniques not only identify and summarize behavior directly relevant to the QoS aspects related to timing, but also indirectly reveal non-timing related properties of behavior, such as the identification of components that are sensitive to data, or those whose behavior changes based on the call-context.