Orientador: Sônia Cristina Poltroniere Silva / Resumo: A Matemática está constantemente presente em nosso cotidiano, sendo ferramenta importante para uma melhor compreensão do mundo e facilitadora dos processos de tomada de decisão. Neste sentido, o trabalho com resolução de problemas ao longo da formação escolar básica faz-se extremamente necessário. Inserida neste contexto, a modelagem matemática é uma ferramenta que permite uma melhor leitura e um tratamento mais adequado do problema. Essa dissertação aborda, inicialmente, conceitos básicos relativos ao Problema de Corte de Estoque e a sua modelagem matemática, com ênfase na definição dos padrões de corte. Posteriormente, é discutido o método branch-and-bound, utilizado na resolução de problemas de otimização linear inteira, como é o caso do problema de corte. Por m, são propostas duas situações-problema, que consideram aplicações do Problema de Corte, para serem trabalhados com alunos do Ensino Médio, considerando os conceitos matemáticos assimilados previamente. / Abstract: Mathematics is constantly present in our daily lives, being an important tool for a bet ter understanding of the world and facilitating decision making processes. In this sense, problem-solving work throughout basic school education is extremely necessary. In this context, mathematical modeling is a tool that allows a better reading and a better treat ment of the problem. This dissertation initially addresses the basic concepts related to the Cutting Stock Problem and the mathematical modeling for the one-dimensional case, with emphasis on the de nition of the cutting patterns. Subsequently, the Branch-and-bound method, used in solving Integer Linear Programming Problems, such as the cutting pro blem, is discussed. Finally, problem situations are proposed, which consider applications of the Cutting Stock Problem, to be worked with high school students, emphasizing the previously assimilated mathematical concepts. / Mestre

abstract: Neglected tropical diseases (NTDs) comprise of diverse communicable diseases that affect mostly the developing economies of the world, the “neglected” populations. The NTDs Visceral Leishmaniasis (VL) and Soil-transmitted Helminthiasis (STH) are among the top contributors of global mortality and/or morbidity. They affect resource-limited regions (poor health-care literacy, infrastructure, etc.) and patients’ treatment behavior is irregular due to the social constraints. Through two case studies, VL in India and STH in Ghana, this work aims to: (i) identify the additional and potential hidden high-risk population and its behaviors critical for improving interventions and surveillance; (ii) develop models with those behaviors to study the role of improved control programs on diseases’ dynamics; (iii) optimize resources for treatment-related interventions. Treatment non-adherence is a less focused (so far) but crucial factor for the hindrance in WHO’s past VL elimination goals. Moreover, treatment non-adherers, hidden from surveillance, lead to high case-underreporting. Dynamical models are developed capturing the role of treatment-related human behaviors (patients’ infectivity, treatment access and non-adherence) on VL dynamics. The results suggest that the average duration of treatment adherence must be increased from currently 10 days to 17 days for a 28-day Miltefosine treatment to eliminate VL. For STH, children are considered as a high-risk group due to their hygiene behaviors leading to higher exposure to contamination. Hence, Ghana, a resource-limited country, currently implements a school-based Mass Drug Administration (sMDA) program only among children. School staff (adults), equally exposed to this high environmental contamination of STH, are largely ignored under the current MDA program. Cost-effective MDA policies were modeled and compared using alternative definitions of “high-risk population”. This work optimized and evaluated how MDA along with the treatment for high-risk adults makes a significant improvement in STH control under the same budget. The criticality of risk-structured modeling depends on the infectivity coefficient being substantially different for the two adult risk groups. This dissertation pioneers in highlighting the cruciality of treatment-related risk groups for NTD-control. It provides novel approaches to quantify relevant metrics and impact of population factors. Compliance with the principles and strategies from this study would require a change in political thinking in the neglected regions in order to achieve persistent NTD-control. / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics for the Life and Social Sciences 2020

Orientador: Helenice de Oliveira Florentino Silva / Resumo: Esta pesquisa teve por objetivo propor um modelo matemático para auxílio no planejamento da aplicação de agentes maturadores e da colheita da cana-de-açúcar, visando obter uma matéria-prima para o setor sucroenergético com máxima qualidade tecnológica relacionada ao teor de sacarose presente no caldo da cana-de-açúcar. Para tanto, inicialmente, foi realizada a revisão teórica acerca da temática relacionada ao ciclo produtivo da cana-de-açúcar, e, ainda, foram pesquisados os resultados de investigações científicas voltadas para essa atividade e que contemplam o uso de agentes químicos de maturação. Na sequência, buscou-se identificar o conjunto de variáveis e processos que ocorrem na fase de maturação da cana, e, também, foi analisada a temática relacionada à utilização de modelos matemáticos aplicados à otimização de processos envolvidos na cultura em questão. Foi formulado um modelo matemático de programação linear inteira a partir de técnicas de Programação por Metas Ponderadas. A avaliação do modelo proposto foi realizada mediante testes computacionais, utilizando quatro cenários baseados em instâncias compostas por 18, 50, 100 e 500 talhões, nos quais foi simulado o cultivo de 18 variedades de cana-de-açúcar adaptáveis à região centro-sul do Brasil. O modelo proposto neste trabalho foi validado e sua utilidade pôde ser evidenciada pela sua aplicabilidade na identificação do momento ideal para realizar a aplicação do maturador, pela identificação do momento ótimo para real... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: This research aimed to propose a mathematical model to support the planning of the application of ripening agents and sugarcane harvesting, aiming to obtain raw material for the sugarcane industry with maximum technological quality related to the sucrose content present in the sugarcane juice. Initially, the theoretical review was carried out on the theme related to the sugarcane production stages. Then, a research was conducted in order to identify the results of scientific investigations focused on that activity approaching the use of chemical maturation agents. Next, it was sought to identify the set of variables and processes that occurred during the sugarcane maturation phase, and it was also analyzed the theme related to the use of optimization mathematical modeling applied to the crop in question. Finally, an integer linear programming mathematical modeling based on Weighted Goal Programming techniques was formulated. The evaluation of the proposed model was performed through computational tests using four scenarios based on 18, 50, 100 and 500 fields, in which the cultivation of 18 sugarcane varieties adaptable to the south-central region of Brazil was simulated. The model proposed in this research was validated and its usefulness could be evidenced not only by its applicability in the identification of the ideal moment for the application of the ripener, as well as in the identification of the optimum moment for the sugarcane harvest, but, also for the possibility of... (Complete abstract click electronic access below) / Doutor

Title: Quantifying aspects of orthosis in relation to ankle sprain Objectives: To detect whether various types of ankle bracing affect dynamic postural stability. Investigation of attenuation of vertical forces in different conditions. To determine range of motion for each orthosis. Methods: Monitoring of dynamic variables by piezoelectric measuring device - Kistler recording of dynamic changes. Mathematical modeling of damping characteristics and detected variables. Measuring of range of motion by goniometer with and without orthosis. Results: Results suggest, that bracing conditions have an effect on dynamic postural stability and orthosis limit range of motion. Attenuation of vertical forces is affected by using orthosis. Keywords: ankle instability, orthosis, mathematical modeling, stabilization

How can we model global phenomenon based on local interactions? Agent-Based (AB) models are local rule-based discrete method that can be used to simulate complex interactions of many agents. Unfortunately, the relative ease of implementing the computational model is often counter-balanced by the difficulty of performing rigorous analysis to determine emergent behaviors. Calculating existence of fixed points and their stability is not tractable from an analytical perspective and can become computationally expensive, involving potentially millions of simulations. To construct meaningful analysis, we need to create a framework to approximate the emergent, global behavior. Our research has been devoted to developing a framework for approximating AB models that move via random walks and undergo state transitions. First, we developed a general method to estimate the density of agents in each state for AB models whose state transitions are caused by neighborhood interactions between agents. Second, we extended previous random walk models of instantaneous state changes by adding a cumulative memory effect. In this way, our research seeks to answer how memory properties can also be incorporated into continuum models, especially when the memory properties effect state changes on the agents. The state transitions in this type of AB model is primarily from the agents’ interaction with their environment. These modeling frameworks will be generally applicable to many areas and can be easily extended.

This dissertation presents my efforts to use viologens to improve the performance of glucose fuel cells and aqueous redox flow batteries. These two electrochemical systems have the potential to efficiently exploit renewable sources of energy. The contributions and significance of this work are briefly described below. Glucose Fuel cells. For glucose fuel cells, viologens were adopted as an electron mediator to facilitate the transfer of electrons from glucose to electrodes for power generation. Use of a mediator circumvents the need for precious metal electrodes to catalyze glucose oxidation. Both the oxidation efficiency and rate of glucose oxidation are important to the viability of glucose fuel cells. Oxidation efficiency is defined as the extent to which the carbons of a carbohydrate (glucose for instance) are oxidized relative to full oxidation to carbon dioxide. The efficiency measured in this study depended on the initial molar ratio of viologen to glucose and also on the rate of the regeneration of the mediator. The maximum conversion efficiency observed was ~22%, which is about three times larger than the values observed for precious-metal-based fuel cells. Rate performance is another important aspect of a glucose fuel cell. Detailed simulations demonstrated that rate performance of viologen-mediated cells was limited principally by mass transfer. The maximum obtainable current density was ~200 mA/cm2, which is significantly higher than the rates available from biological fuel cells and comparable to the values observed for precious-metal-based fuel cells. Viologen-mediated fuel cells offer the potential for higher oxidation efficiency and high current densities at a significantly lower cost. This makes viologen-mediated cells an appealing option for future development of glucose fuel cells. Redox Flow Battery. An asymmetric viologen called MMV was assessed for potential use in aqueous flow batteries to improve performance. With an asymmetric structure, MMV demonstrated one of the most negative redox potentials reported to date for organic electroactive compounds. MMV also showed a relatively high solubility in neutral electrolytes. The electrochemical reaction of MMV involved a reversible single electron transfer with fast kinetics. These characteristics support MMV as a promising anolyte for flow battery applications to improve capacity, energy density, and cell potential. MMV, however, exhibited poor cycling performance at elevated concentrations since it underwent irreversible or partially reversible side reactions. Signs of dimerization and precipitation were observed during cycling. These undesired reactions can be potentially mitigated by synthesizing asymmetric MMV derivatives that possess a higher charge than that possessed by MMV (+1). This modification can reduce the extent of dimerization by increasing repulsive forces between the monomers, and it also has the potential to reduce precipitation by increasing the solubility limit of the compounds.

<p>Embryonic development is a complicated phenomenon influenced by genetic regulation and biomechanical cellular behaviors. However, the relative influence of these factors on spatiotemporal morphogen distributions is not well understood. Bone Morphogenetic Proteins (BMPs) are the primary morphogen guiding the dorsal-ventral (DV) patterning of the early zebrafish embryo, and BMP signaling is regulated by a network of extracellular and intracellular factors that impact the range and signaling of BMP ligands.  Recent advances in understanding the mechanism of pattern formation support a source-sink mechanism, however, it is not clear how the source-sink mechanism shapes patterns in 3D, nor how sensitive the pattern is to biophysical rates and boundary conditions along both the anteroposterior (AP) and DV axes of the embryo.</p><p> Throughout blastulation and gastrulation, major cell movement, known as epiboly, happens along with the BMP mediated DV patterning. The layer of epithelial cells begins to thin as it spreads toward the vegetal pole of the embryo until it has completely engulfed the yolk cell. This dynamic domain may influence the distributions of BMP network members. This project aims to investigate the multiscale regulatory network of the BMP signaling dynamics along with the biophysical deformation of the embryo tissue during epiboly. </p><p> In this study, we present a three-dimensional (3D) growing domain mathematical modeling framework to simulate the BMP patterning and epiboly process during the blastula to gastrula stage zebrafish embryo, with both finite difference and finite element approaching. These models provide a starting point to elucidate how different mechanisms and components work together in 3D to create and maintain the BMP gradient in the zebrafish embryo. We are interested in how the cellular movements impact the formation of gradients by contributing an advective term whereby the morphogens are swept with the moving cells as they move vegetally. Dynamic cell imaging data are used to quantify the cell movement during the epiboly. We evaluated the accuracy of the mesh updating compared to the advection caused by cell movement and its role in embryonic patterning. Quantitative whole-mount RNA scope data of BMP2b, Chordin, Noggin, Sizzled, and phosphorylated-SMAD data are collected and analyzed precisely to test the hypotheses of the gradient formation mechanism in our model. We also present a novel approach of Neuro Network model to accelerate the computationally intensive PDE simulations. Our goal is to develop a complete advection-diffusion-reaction model that incorporates all stages of zebrafish embryonic development data. By combining the biophysics of epiboly with the regulatory dynamics of the BMP network, we can test complex models to investigate the consistent spatiotemporal DV patterning in the early zebrafish embryo.</p>

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A dynamical system's state evolves over time, and when the system stays near a particular state this state is known as a stable state of the system. Through control methods, dynamical systems can be manipulated such that virtually any state can be made stable. Although most real systems evolve continuously in time the application of digital control methods to these systems is inherently discrete. States are sampled (with sensors) and fed back into the system in discrete-time to determine the input needed to control the continuous system. Additionally, dynamical systems often experience time delays. Some examples of time delays are delays due to transmission distances, processing software, sampling information, and many more. Such delays are often a cause of poor performance and, at times, instability in these systems. Recently a criterion referred to as intrinsic stability has been developed that ensures that a dynamic system cannot be destabilized by delays. The goal of this thesis is to broaden the definition of intrinsic stability to closed-loop systems, which are systems in which the control depends on the state of the system, and to determine control parameters that optimize this resilience to time delays. Here, we give criteria describing when a closed-loop system is intrinsically stable. This allows us to give examples in which systems controlled using Linear Quadratic Regulator (LQR) control can be made intrinsically stable.

In this paper, we develop a model for predation movements of a subsocial spider species, Anelosimus studiosus. We expand on a previous model to include multiple spider interaction on the web as well as a latency period during predation. We then use the model to test different spatial configurations to determine the optimal spacing of spiders within a colony for successful capture during predation. The model simulations indicate that spiders uniformly spacing out along the edge of the web results in the most successful predation strategy. This is similar to the behavior observed by Ross (2013) in which it was determined to be statistically significant that during certain times of the day, spiders were positioned along the edge more than expected under complete spatial randomness.