Cancer is one of the leading causes of premature deaths across the world today, and there is an urgent need for imaging techniques that can help in early diagnosis and treatment planning for cancer patients. In the last four decades, magnetic resonance imaging (MRI) has emerged as one of the leading modalities for non-invasive imaging of tumours. By using dynamic contrast-enhanced magnetic resonance imaging (DCEMRI), this modality can be used to acquire information about perfusion and vascularity of tumours, which can help in predicting response to treatment. There are many factors that complicate the analysis of DCE-MRI data, and make clinical predictions based on it unreliable. During data acquisition, there are many sources of uncertainties and errors, especially patient motion, which result in the same image position being representative of many different anatomical locations across time. Apart from motion, there are also other inherent uncertainties and noise associated with the measurement of DCE-MRI parameters, which contribute to the model-fitting error observed when trying to apply pharmacokinetic (PK) models to the data. In this thesis, a probabilistic, model-based registration and parameter estimation (MoRPE) framework for motion correction and PK-parameter estimation in DCE-MRI sequences is presented. The MoRPE framework is first compared with conventional motion correction methods on simulated data, and then applied to data from a clinical trial involving twenty colorectal cancer patients. On clinical data, the ability of MoRPE to discriminate between responders and non-responders to combined chemoand radiotherapy is tested, and found to be superior to other methods. The effect of incorporating different arterial input functions within MoRPE is also assessed. Following this, a quantitative analysis of the uncertainties associated with the different PK parameters is performed using a variational Bayes mathematical framework. This analysis provides a quantitative estimate of the extent to which motion correction affects the uncertainties associated with different parameters. Finally, the importance of estimating spatial heterogeneity of PK parameters within tumours is assessed. The efficacy of different measures of spatial heterogeneity, in predicting response to therapy based on the pre-therapy scan alone are compared, and the prognostic value of a new derived PK parameter the 'acceleration constant' is investigated. The integration of uncertainty estimates of different DCE-MRI parameters into the calculation of their heterogeneity measures is also shown to improve the prediction of response to therapy.

Este trabalho foi conduzido com o objetivo de comparar a formulação de ração por meio da programação linear (custo mínimo) e programação não linear (lucro máximo) para poedeiras comerciais. Utilizou-se 288 poedeiras da linhagem Hisex® White de 33 a 45 semanas de idade, com 1,540 ± 0,1167 kg de peso corporal. As aves foram distribuídas em delineamento em blocos ao acaso, com seis tratamentos com seis repetições de oito aves cada, totalizando 36 parcelas. Os tratamentos experimentais foram: 1) ração de custo mínimo com exigências nutricionais das Tabelas Brasileiras para Aves e Suínos; 2) ração de custo mínimo com as exigências nutricionais recomendadas pelo Manual da Linhagem; 3) ração de custo mínimo com exigências nutricionais obtidas de modelos matemáticos para otimização de desempenho; 4) ração de lucro máximo em cenário de mercado normal; 5) ração de lucro máximo em cenário de mercado favorável; e 6) ração de lucro máximo em cenário de mercado desfavorável. O desempenho foi avaliado por meio do consumo de ração, produção de ovos, peso dos ovos, massa de ovos e conversão alimentar. Na qualidade interna e externa, em quatro ovos por parcela, foram avaliadas o peso do ovo, gravidade específica, resistência à quebra da casca, peso da casca, espessura da casca, coloração da gema, altura de albúmen e unidade Haugh. Para avaliação econômica calculou-se o lucro. Os dados foram submetidos a análise de variância e em caso de significância (P<0,05) foi aplicado o teste de Scott-Knott (5%). Não houve diferença estatística (P>0,05) para a unidade Haugh, altura do albúmen e para as características de qualidade externa de ovos. Verificou-se efeito de tratamento (P<0,05) nas características de desempenho e qualidade de ovos por meio do valor absoluto e relativos de albúmen e gema. De forma geral, os tratamentos com as exigências obtidas pelos modelos matemáticos seguido das obtidas pelo manual da linhagem, ambos da programação linear, proporcionaram melhores resultados de desempenho, pois as rações foram nutricionalmente mais densas, no entanto, pioraram os resultados econômicos. Conclui-se que rações formuladas por meio de programação linear propiciaram as aves melhor desempenho, todavia, sem correspondente benefício econômico comparadas as rações formuladas por meio de programação não linear. / This study aimed to compares the feed formulation using linear (minimal cost) and non-linear (maximum profit) programming for commercial hens. Thus, 288 Hisex® white layer hens, from 33 to 45 weeks old, with 1,54 ± 0,12 kg of BWwere used. The hens were distributed in randomized blocks, with six treatments and six replicates with eight birds per replicate, totaling 36 plots. The treatments were: 1) minimum cost feed formulation, with nutritional requirements proposed by Rostagno et al. (2011); 2) minimum cost feed formulation, with nutritional requirements recommended by strain management guide; 3) minimum cost feed formulation, with nutritional requirements obtained from mathematical models for performance optimization; 4) maximum profit feed formulation in normal market scenario; 5) maximum profit feed formulation in favorable market scenario; and 6) maximum profit feed formulation in an unfavorable market scenario. The performance was evaluated from feed intake, egg production, egg weight, egg mass and feed conversion ratio. In four eggs per pen was evaluated the internal and external egg quality: egg weight, specific gravity, shell resistance, shell weight, shell thickness, yolk color, albumen height and Haugh unit. To economic evaluation, profit was calculated. Data were submitted to variance analyses and when significant (P<0.05) Scott-Knott test (5%) was applied. There was no statistical difference (P>0.05) for Haugh unit, albumen height and external quality of the eggs. There was effect of treatment (P<0.05) on performance and eggs quality from absolute and relative values of yolk and albumen. In general, treatments with requirements obtained by mathematical models or by strain management guide, both from linear programming, improved the performance results, since diets were denser nutritionally, however, worsened the economic results. In summary, feed formulated by linear programming improves performance, however, worsens economic results compared with nonlinear programming.

Este trabalho apresenta os resultados obtidos na elaboração de dois modelos para o fenômeno da dor utilizando-se redes neurais artificiais, de forma a simular computacionalmente as prováveis respostas de um indivíduo na presença de dor. Os modelos são fundamentados na Teoria de Controle da Comporta de dor, onde são analisados os principais componentes envolvidos na percepção/inibição da dor, bem como o funcionamento dos mecanismos biológicos e cognitivos participantes do processo. A escolha do tipo de rede neural é feita a partir das observações realizadas, considerando-se também o número de fatores envolvidos e o comportamento esperado frente a cada conjunto de entrada. O método de treinamento das redes neurais baseia-se no algoritmo de retropropagação. O foco do processamento da rede é responder adequadamente, considerando-se a influência das entradas envolvidas, a eventos posteriores à ocorrência de uma lesão gerando um sinal de alerta a ser utilizado como uma resposta natural do organismo a este dano tecidual. O desempenho de cada modelo é avaliado comparando-se as saídas obtidas com aquelas esperadas para cada padrão de entrada. / This work presents the results of two models that were developed to describe the phenomenon of pain using Artificial Neural Networks, with the final goal to simulate computationally possible answers of an individual in the presence of pain. The models are based on The Gate Control Theory, where the main components involved in the perception/inhibition of pain were analysed, as well as the operation of the biological and cognitive mechanisms involved in the process. The type of neural network was chosen based on accumulated knowledge, considering also the number of involved factors and the expected behaviour response to each set of patterns. The neural networks were trained based on the backpropagation algorithm. The major focus of the network processing was to answer adequately to the occurrence of an injury, considering the role of the involved inputs, and generating an alert signal to this tecidual damage, which could replace the natural reply of the organism. The performance of each model is evaluated comparing the outputs obtained with those expected for each pattern.

Neste trabalho estudou-se a modelagem matemática de processo de produção do antitumoral retamicina produzido pelo microrganismo filamentoso Streptomyces olindensis em cultivos descontínuos, descontínuos alimentados e contínuos. Através da modelagem matemática é possível verificar o comportamento dos fatores que interferem na produção deste metabólito secundário, a fim de identificar as melhores condições de processo. Foram estudados diferentes modelos: modelo morfologicamente estruturado, modelo não estruturado e um modelo híbrido que combina equações de balanço material com redes neurais artificiais. O modelo morfologicamente estruturado é um aperfeiçoamento de um modelo anterior e o modelo não estruturado, por sua vez, foi desenvolvido na tentativa de simplificar a descrição do processo ao considerar menos variáveis e possuir menor número de parâmetros ajustáveis. Nos modelos, as variáveis consideradas no ajuste foram as concentrações de biomassa, de glicose, de retamicina e de oxigênio dissolvido no meio. Os resultados das simulações foram avaliados estatisticamente por comparação com os dados experimentais. Os modelos também foram comparados entre si através de uma análise estatística. Observou-se que, dentre os modelos estudados, o modelo híbrido apresentou sensibilidade pronunciada às condições iniciais e qualidade de representação dos dados experimentais inferior à dos demais modelos. Os modelos morfologicamente estruturado e não estruturado apresentaram capacidade similar de representação do comportamento dos dados experimentais dos ensaios descontínuos, descontínuo-alimentados e contínuos com baixas taxas de alimentação. / The mathematical modeling of retamycin production during batch, fed-batch and continuous cultivations of Streptomyces olindensis was studied. Through the mathematical modeling, it is possible to identify the best conditions to conduct the process. Different models considered were: a morphologically structured model, an unstructured model and a hybrid model that combines artificial neural networks with mass balances. The morphologically structured model included an enhancement in a model previously described. The unstructured model was developed as an attempt to simplify the description of the process by considering fewer variables and fewer parameters to be adjusted. The variables considered in the models were the concentrations of biomass, glucose, retamycin and dissolved oxygen. Simulation results were submitted to statistical analysis such as model discrimination and test of adequacy to verify which of the models were suitable to describe the process and whether the results of the simulations fit the experimental data or not. Results show that the hybrid model presented high sensitivity to the initial conditions and its capability of representing the experimental data was worse than that of the other developed models. Both the morphologically structured model and the unstructured model show similar suitability to represent the experimental data behavior for batch, fed-batch and low-dilution rate continuous runs.

No contexto de refino de petróleo, alquilação é o processo pelo qual se produz uma corrente de hidrocarbonetos chamada de alquilado, na faixa da gasolina, a partir de olefinas leves (propeno, butenos) e isobutano. A demanda por alquilado como corrente integrante do pool de gasolinas de uma refinaria tem aumentado ao longo das duas últimas décadas devido a diversos fatores, sendo o principal a adoção de normas mais restritivas para a qualidade de combustíveis automotivos. No presente trabalho foi desenvolvido e validado um modelo matemático fenomenológico capaz de representar adequadamente as reações químicas envolvidas no processo de alquilação catalítica que utiliza ácido fluorídrico como catalisador, bem como estimar o rendimento de produto e subprodutos da reação e a qualidade do alquilado, representada pelo teor de tri-metil-pentanos (TMP) e di-metil-hexanos (DMH) no alquilado. A construção do modelo foi baseada em balanços de massa e energia no conjunto reacional, utilizando mecanismos cinéticos disponíveis na literatura, sendo os seus parâmetros cinéticos estimados por regressão não linear a partir de literatura. O modelo foi validado com dados obtidos em uma unidade industrial de propriedade da Petrobrás, localizada em Cubatão. Os resultados obtidos permitem afirmar que o modelo apresentou boa resposta para a identificação do consumo de reagentes e rendimento de produtos. Sua resposta tendeu a subestimar a quantidade de frações pesadas do alquilado. / Alkylation is the process which light hydrocarbons (like butenes and iso-bute) are transformed into heavier hydrocarbons, called alkylate. The alkylate demand as a gasoline component has been growing since the middle 90s, mostly due to more severe quality requirements for gasoline. This work proposes a mathematical model that accounts for the main chemical reactions for a HF Alkylation Unit. The alkylate yield and quality, described by its composition, are also represented as well. This model as based on mass and energy balances for the alkylation reactor, using the most accepted kinetic mechanism available at literature. The model constants were estimated by non-linear regression with available data from literature. The model validation was performed comparing the simulation results with data collected at an industrial Alkylation unit at Cubatão, Brazil, without further parameter adjustment. The results show a good model response for the consumption of reagents and alky yield. The model, however, underpredicts the yield of heavier fractions.

O presente estudo se propôs a responder à questão de investigação: como a Modelagem Matemática pode contribuir como um meio do educando ser protagonista da sua aprendizagem, aspirando a sua autonomia? A pesquisa apresenta uma proposta de sequência de tarefas em um ambiente de aprendizagem de Modelagem Matemática, dividida em três partes, que são: o convite para realizar modelagem, uma experiência com a temática água e uma experiência com um tema de livre escolha. O estudo foi desenvolvido durante o segundo semestre de 2016, com uma turma de terceiro ano do Ensino Médio de uma escola municipal de Sapucaia do Sul, no horário regular de aula. Apoiada na teoria da Modelagem Matemática em uma perspectiva Sócio-crítica de Barbosa (2001), elaboração de perguntas em um ambiente de Modelagem Matemática de Sant’Ana e Sant’Ana (2009) e na Pedagogia da Autonomia de Paulo Freire (1996), e utilizando o estudo de caso como metodologia, o presente trabalho evidenciou que os estudantes podem ser ativos na construção dos seus conhecimentos. Além disso, percebeu-se, como resultados, que quando lhes é oportunizado um ambiente de liberdade e consideração, que respeita as suas escolhas, os alunos vão assumindo sua responsabilidade pela sua aprendizagem, construindo, aos poucos, suas preferências, suas opções e sua autonomia. / The present study aims to answer the research question: how can Mathematical Modeling contribute as a way for the learner to be the protagonist of their learning by aspiring to their autonomy? The research presents a task sequence proposal in a mathematical modeling-learning environment, divided into three parts. Such parts are the invitation to perform modeling, an experience with water theme, and an experiment with a theme of free student’s choice. The study was developed during the second semester of 2016, with a third year High School class from a municipal school in Sapucaia do Sul, at regular school hours. Based on the theory of Mathematical Modeling in a Socio-critical perspective of Barbosa (2001), elaboration of questions in an environment of Mathematical Modeling of Sant'Ana and Sant'Ana (2009) and in the pedagogy of autonomy of Paulo Freire (1996), and using the case study as a methodology, the present study showed that students can be active in the construction of their knowledge. In addition, it was noticed that, when it is offered an environment of freedom and consideration, respecting their choices, students will assume their responsibility for their learning, gradually building their preferences, their choices and their autonomy.

Mathematical modeling is a thinking process that applies various sets of cognitive attributes – one component of intellectual resources (i.e., cognitive resources). Students are able to develop cognitive attributes when they engage in mathematical modeling activities. Furthermore, using many of the cognitive attributes developed during the mathematical modeling process, students solve mathematics problems, for example, in assessments. Examining students’ mastery of these cognitive attributes, we can investigate relationships between students’ cognitive development through mathematical modeling practices in classrooms and their performance on mathematics assessments. The purpose of this research is to quantitatively and empirically investigate the relationships between students’ development of mathematics cognitive attributes and their achievement. For the current study, we selected the four cognitive attributes representing different stages of the mathematical modeling practices – select, analyze, compute, and represent. The generalized DINA (deterministic inputs, noisy “and” gate) is applied to generate students’ mastery profiles of the cognitive attributes from their responses to test items. Using students’ mastery profiles as datasets, three secondary analysis studies are conducted with linear regression analysis and multivariate approach to repeated measure ANOVA. The findings show that development of the four cognitive attributes in mathematical modeling is positively related to mathematics achievement. In addition, students, who developed select and compute throughout 4th to 8th grades, scored higher in mathematics assessment with large degrees of effects. The findings suggest important implications to teachers: Students need to have opportunities develop a wide range of cognitive attributes of mathematical modeling, which would result in higher achievement. Teachers need to have instructional emphases on different stages of mathematical modeling depending on grade levels: students’ representing a solution at elementary-school levels; and analyzing a problem situation and selecting strategies at middle-school levels. The study also suggests teachers shift an instructional emphasis from learning mathematics contents to high-order thinking like mathematical modeling to accomplish higher mathematics achievement.

<p>In this thesis we apply mathematics and formal modeling to study culture from an evolutionary standpoint. Cultural evolution theory is based on the belief that we can increase our understanding of human behavior by studying how culture is created and spread. Together with my co-authors I use mathematical modeling to investigate why we need a theory for cultural evolution, what it can tell us, and how we can test such a theory.</p><p>The thesis consists of an introduction and five papers. The first paper is an empirical test of whether we need to know the history of a population to be able to determine what culture they will have. The second paper looks at the circumstances under which a genetic predisposition for imitating parents could evolve. The third paper looks at the accumulation of neutral traits, that is, cultural variants that flow between people at random without affecting their fitness; neutrality provides an important null hypothesis to other explanations of why we have the culture that we do. The fourth paper makes an attempt at defining what makes a cultural variant successful, and thereby reveals some important differences between genetic and cultural evolution. Finally, the fifth paper investigates a model that can be used to study mechanisms of cultural evolution in laboratory experiments.</p>

In this thesis we apply mathematics and formal modeling to study culture from an evolutionary standpoint. Cultural evolution theory is based on the belief that we can increase our understanding of human behavior by studying how culture is created and spread. Together with my co-authors I use mathematical modeling to investigate why we need a theory for cultural evolution, what it can tell us, and how we can test such a theory. The thesis consists of an introduction and five papers. The first paper is an empirical test of whether we need to know the history of a population to be able to determine what culture they will have. The second paper looks at the circumstances under which a genetic predisposition for imitating parents could evolve. The third paper looks at the accumulation of neutral traits, that is, cultural variants that flow between people at random without affecting their fitness; neutrality provides an important null hypothesis to other explanations of why we have the culture that we do. The fourth paper makes an attempt at defining what makes a cultural variant successful, and thereby reveals some important differences between genetic and cultural evolution. Finally, the fifth paper investigates a model that can be used to study mechanisms of cultural evolution in laboratory experiments.

Trunk instability is a major problem for people with spinal cord injury (SCI); it not only limits their independence, but also leads to secondary health complications such as kyphosis, pressure sores, and respiratory dysfunction. In exploring mechanisms that may facilitate or compromise postural stability, dynamic models are very useful because the spine dynamics are difficult to study in vivo compared to other structures of the body. Therefore, one objective of this work was to develop a detailed three-dimensional dynamic model of the human trunk as a tool for investigating the neural-mechanical control strategy that healthy people apply to maintain trunk stability during various tasks. Since trunk control is fairly complex, however, another objective of this work was to provide insights into the balance control strategy of a simpler neuro-musculo-skeletal system that may facilitate future studies on trunk control. For this purpose, the control of the ankle joint complex during quiet standing (anterior-posterior degree of freedom) was studied in place of the trunk. The obtained results reveal that a neural-mechanical control scheme using a proportional-derivative controller as the neural control strategy can overcome a large sensory-motor (feedback) time delay and stabilize the ankle joint during quiet standing. Moreover, a detailed dynamic model of the trunk has been developed that is: (1) based on highly accurate geometric models; and (2) universally applicable. Thus, this work also responds to the postulation that structurally more complex models are needed to better characterize the biomechanics of multifaceted systems. Combining the developed biomechanical tools for the trunk with the postural control insights for the ankle joint during standing will be beneficial for: (1) understanding the neural-mechanical control strategy that facilitates trunk stability in healthy people; and for (2) developing neuroprostheses for trunk stability after SCI and other neurological disorders.