We present a mathematical model describing the dynamics occurring between two interacting populations, one of amoebae and one of virulent bacteria; it is meant to describe laboratory experiments with these two species in a mathematical framework and help understanding the role of the different mechanisms involved. In particular we aim to focus on how bacterial virulence may affect the dynamics of the system. The model is a modified reaction-diffusion-chemotaxis predator-prey one with a mechanism of redistribution of ingested biomass between amoeboid cells. The spatially homogeneous case is analyzed in detail; conditions for pattern formation are established; numerical simulations for the complete model are performed.

The thesis deals with the study of a natural extension of classical finite-dimensional time-optimal control problem to the space of positive Borel measures. This approach has two main motivations: to model real-life situations in which the knowledge of the initial state is only probabilistic, and to model the statistical distribution of a huge number of agents for applications in multi-agent systems. We deal with a deterministic dynamics and treat the problem first in a mass-preserving setting: we give a definition of generalized target, its properties, admissible trajectories and generalized minimum time function, we prove a Dynamic Programming Principle, attainability results, regularity results and an Hamilton-Jacobi-Bellman equation solved in a suitable viscosity sense by the generalized minimum time function, and finally we study the definition of an object intended to reflect the classical Lie bracket but in a measure-theoretic setting. We also treat a case with mass loss thought for modelling the situation in which we are interested in the study of an averaged cost functional and a strongly invariant target set. Also more general cost functionals are analysed which takes into account microscopical and macroscopical effects, and we prove sufficient conditions ensuring their lower semicontinuity and a dynamic programming principle in a general formulation.

The interplay between human behavior and the spreading of an epidemics represents a challenge in modeling the dynamics of infectious diseases. The technological revolution that we are experiencing nowadays gives access to new sources of digital data, capable of capturing behavioral patterns and social dynamics of our society and opening, in fact, the path to new opportunities for mathematical modelers. Provided by such tools, we discuss two different aspects of the dynamics of infectious diseases associated with human behavior. In the first part of the thesis, we focus on the mechanism driving the awareness of individuals during public health emergencies and describe epidemiological models especially tailored to better understand the underline features of the risk perception. The proposed framework is able to disentangle and characterize the contribution of media drivers and social contagion mechanisms in the building of awareness of individuals about infectious diseases. In the second part of the thesis, we present a data driven computational model aiming to assess the potential risk of experiencing measles re-emergence in Turkey. This study takes into consideration the recent massive migration of Syrian refugees in Turkey, which changed the social structure and focuses on the possible outbreak of an infectious disease, such as measles, as a consequence of the great concentration of Syrian refugees not adequately immunized against it. The model proposed is informed with mobility patterns inferred from mobile phone data and accounts for the different hypothetical policies adopted to integrate the refugees with the Turkish population.

The thesis deals with various problems arising in deterministic control, jumping processes and control for locomotion in fluids. It is divided in three parts. The first part is focused on some optimal control problems on network and stratified domains with junctions, where each edge/hyper-plane has its own controlled dynamics and cost. We consider some possible approximations for such a problems given by the use of a switching rule of delayed-relay type and study the passage to the limit when the parameter of the approximation goes to zero. First, we take into account some problems on network: a twofold junction problem, a threefold junction one and an extension of the last one. For each of these problems we characterize the limit functions as viscosity solution and maximal subsolution of a suitable Hamilton-Jacobi problem. Secondly, we consider a bi-dimensional multi-domain problem and as done for the problems on network we characterize the limit function as viscosity solution of a suitable Hamilton-Jacobi problem. The second part studies a decentralized routing problem over a network, using the paradigm of mean-field games with large number of players. Building on a state-space extension technique, we turn the problem into an optimal control one for each single player. The main contribution is an explicit expression of the optimal decentralized control which guarantees the convergence both to local and to global equilibrium points. Furthermore, we study the stability of the system also in the presence of a delay which we model using an hysteresis operator. As a result of the hysteresis, we prove existence of multiple equilibrium points and analyze convergence conditions. In the last part of the thesis we investigate different strategies to overcome the so-called scallop paradox concerning periodic locomotion in fluid. We show how to obtain a net motion exploiting the fluid's type change during a periodic deformation. We consider two different models: in the first one that change is linked to the magnitude of the opening and closing velocity of the scallop's valves. Instead, in the second one it is related to the sign of the above velocity. In both cases we prove that the mechanical system is controllable, i.e. the scallop is able to move both forward and backward using cyclical deformations.

Made available in DSpace on 2016-04-27T16:57:56Z (GMT). No. of bitstreams: 1 dissertacao_rosana_lima.pdf: 743608 bytes, checksum: f0e3154b93715613f934ccac523facf4 (MD5) Previous issue date: 1999-04-29 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Este trabalho teve por objetivo estudar métodos geométricos e algébricos de resolução de equações de terceiro grau, observando as vantagens e desvantagens de cada um. Para isso, construímos uma seqüência didática, enfatizando o método geométrico de Omar Khayyam, matemático árabe do século XII. Foi feita uma pesquisa histórica, e este método foi escolhido por utilizar o quadro geométrico, quadro este pouco explorado em sala de aula. Utilizamos, também, na seqüência, a fórmula de Cardano e o dispositivo de Briot-Ruffini para resolver equações cúbicas. Aplicamos nossa seqüência a dois grupos. O primeiro, formado por quatro alunos do curso de Ciência da Computação da PUC-SP. O segundo, formado por alunos da terceira série do Ensino Médio, do Colégio Vera Cruz; no início, contávamos com 32 alunos, ao final, eles eram em número de 6. A abstenção, ao final da aplicação, se deve, principalmente, à época em que a seqüência foi aplicada. Com resultados obtidos, vemos que o quadro geométrico dificilmente é usado pelos alunos ao tentar resolver um problema. O método de Omar Khayyam foi considerado o mais prático deles, pois pode ser usado para qualquer equação cúbica. A fórmula de Cardano causa problemas aos alunos que não conhecem números complexos e o dispositivo de Briot-Ruffini só pode ser usado quando a equação que se quer resolver tem uma raiz inteira. Os alunos perceberam, também, que podem escolher que caminho seguir, para resolver uma equação de terceiro grau, dependendo de seus coeficientes. Além disso, o quadro geométrico, agora, é levado em consideração

Made available in DSpace on 2016-04-27T16:58:09Z (GMT). No. of bitstreams: 1 dissertacao_marly_nardi_ferraz_nunes.pdf: 523449 bytes, checksum: 60d6904ff936356079c395ae72c8d18a (MD5) Previous issue date: 2001-05-11 / This study discribes research performed with the help of activities that place great emphasis upon the student s actions. Teaching and learning the concepts connected with limits and infinite has proved a hard task, often with unsatisfactory results. In France, Aline Robert has done research with over 1.300 students on the acquisition of the concept of convergence of numerical sequences. The same researcher has concluded that the learning process would be more effective if this concept was taught by means of activities conducted by the students themselves. Inspired by her investigations and also based on Piaget s constructivist theory, we carried out activity work with students from a Faculty of Mathematics, who had still not been introduced to the studies of limits and infinitesimal calculus. The aim of our work was to enable the students to better assimilate concepts related to the convergence of sequences. Based on principles of Didactical Engineering, we prepared and applied a sequence composed of ten activities and one post-test. During these activities we utilized problems to work on the concepts related to numerical sequences and convergence. From analysis of the results we concluded that the procedure described here promoted, in general, an increase in knowledge of the students and, in particular, the acquisition, by most students, of notions related to the concept of convergence of numerical sequences. This experience represented a rupture of our traditional pedagogical practices in favor of a new dynamics, which required of ourselves and of the students a change in posture. Among the conclusions are issues that can be the object of further studies / Este trabalho relata uma pesquisa realizada por meio de atividades que privilegiam a ação dos estudantes. O ensino e a aprendizagem dos conceitos relacionados com limites e infinito têm se mostrado árduos e, muitas vezes, com resultados insatisfatórios. Aline Robert realizou, na França, uma pesquisa com mais de 1.300 estudantes sobre a aquisição do conceito de convergência de seqüências numéricas. A pesquisadora concluiu que a aprendizagem seria mais efetiva se o ensino desse conceito fosse conduzido através de atividades realizadas pelos alunos. Inspirados nessa pesquisa, e baseados na teoria construtivista de Piaget, desenvolvemos um trabalho de atividades com alunos de um curso de licenciatura em matemática, que não haviam ainda sido introduzidos no estudo dos limites e do cálculo infinitesimal. O objetivo desse trabalho é propiciar aos alunos a apropriação de conceitos relacionados com a convergência de seqüências. Utilizando-nos dos princípios da Engenharia Didática, elaboramos e aplicamos uma seqüência composta de 10 atividades e um pós-teste. Nessas atividades foram trabalhados, através de problemas, os conceitos relacionados com seqüências numéricas e convergência. A análise dos resultados nos permitiu concluir que o procedimento empregado possibilitou, em geral, o progresso do conhecimento dos alunos, e em particular a aquisição, pela maioria dos estudantes, de noções articuladas ao conceito de convergência de seqüências numéricas. Essa experiência representou uma ruptura de nossa prática pedagógica tradicional, em favor de uma nova dinâmica, que exigiu de nós e dos alunos uma mudança de postura. Dentre as conclusões, foram levantadas questões que poderão ser objeto de futuras pesquisas

Made available in DSpace on 2016-04-27T16:58:12Z (GMT). No. of bitstreams: 1 dissertacao_maria_regina_pereira.pdf: 561764 bytes, checksum: cdeb9d4b1f5af7487783ab6c2c5e4cd9 (MD5) Previous issue date: 2001-10-18 / The objective of this work is to offer the possibility of better understand and also to recover the Geometry condition in the Ensino Fundamental and Ensino Médio (Primary and Secondary Teaching System) curricula. I have focused my research looking for justification for its abandon and from the existing literature inventory I describe some researches which give ideas about its situation. Such examples result in a repertoire composition in order to relate the focused works on n this subject and to be useful as a level for further researches / O objetivo deste trabalho é oferecer a possibilidade de melhor compreender e resgatar a condição da Geometria nos currículos do Ensino Fundamental e Ensino Médio. Centrando-me na procura de justificativas para o seu abandono, a partir de um inventário da literatura existente, descrevo algumas pesquisas a título de ilustração. Tais exemplos convergem para a composição de um repertório, cujo fim é relacionar trabalhos centrados neste tema e servir de patamar para futuras investigações

Made available in DSpace on 2016-04-27T16:58:13Z (GMT). No. of bitstreams: 1 dissertacao_ismael_araujo_silva.pdf: 615518 bytes, checksum: f211a91228074c46cec931700518ea40 (MD5) Previous issue date: 2002-05-17 / From her origin, the concept of probabilities grew in multiple perspectives: concretely, the probability of an event or phenomenon has been conceived in a classic slope or laplaciana (based on the "Law of Laplace"), in a slope based on the relative frequency of the event in study (based on the "Law of the Great Numbers" of Jacques Bernoulli) and in a slope personal or subjective. This master's degree dissertation had for objective the study and application of a didactic sequence in the which the concepts or notions that lead to the definition of probabilities were approached starting from activities or situation-problem and the conceptions of relative frequency of an event and classic of probability they could be integrated in the teaching tends in view a deeper and signifcant learning in understanding terms and application of the probabilities. Starting from the establishment of the theoretical foundations and of a research methodology, of the studies of the History, of the Origins of the Knowledge and of the Didactic Transposition, we established our problem, hypotheses and research objectives then. We applied a didactic sequence then with the intention of we reach our research objectives. Soon afterwards, we elaborated our conclusions and we presented a bibliography of our work following by the applied questionnaire in the pilost test / Desde a sua origem, o conceito de probabilidades desenvolveu-se em múltiplas perspectivas: concretamente, a probabilidade de um acontecimento ou de um fenômeno tem sido concebida numa vertente clássica ou laplaciana (baseada na "Lei de Laplace"), numa vertente freqüentista (baseada na "Lei dos Grandes Números" de Jacques Bernoulli) e numa vertente pessoal ou subjetiva. Esta dissertação de mestrado teve por objetivo o estudo e aplicação de uma seqüência didática na qual os conceitos ou noções que conduzem à definição de probabilidades fossem abordados a partir de atividades ou situações-problema e as concepções freqüentista e clássica de probabilidade pudessem ser integradas no ensino tendo em vista uma aprendizagem mais profunda e significativa em termos de compreensão e aplicação das probabilidades. A partir do estabelecimento de uma fundamentação teórica e de uma metodologia de pesquisa, dos estudos da História, da Epistemologia e da Transposição Didática, estabelecemos nossa problemática, hipóteses e objetivos de pesquisa. Aplicamos, então, uma seqüência didática com o intuito de atingirmos nossos objetivos de pesquisa. Em seguida, elaboramos nossas conclusões e apresentamos uma bibliografia de nossa pesquisa seguida do questionário aplicado no teste piloto

Made available in DSpace on 2016-04-27T16:58:13Z (GMT). No. of bitstreams: 1 dissertacao_elizabeth_soares.pdf: 607526 bytes, checksum: 962068a5a7e0968574b6eb6c0789b9cb (MD5) Previous issue date: 2002-05-27 / The purpose of this study was to investigate the evolution that could be reached by students of 5th-8th grades in their knowledge of the broad sense of the order relationship arriving before or at the same time as during the delivery of a didactic intervention designed in the light of the theoretical framework of Brousseau. Students were challenged with problems dealing with the arrangement of characters in order of arrival, thus requiring non-numerical order relationships to be handled. For analyzing the answers, elements of Brousseau s Theory of Didactical Situations were employed, along with elements of Machado s investigations on the mechanisms of mother-tongue imbuement and of Polanyi s reflections on the structure of tacit knowing. With the help of these referentials, the answers were grouped into categories, which enabled problem-solving procedures to be observed, in addition to factors that were found to have facilitated or hindered the students search for all the range of solutions. These factors were related to the didactical contract, to mechanisms borrowed from the mother tongue, and to influences derived from other fields of knowledge. Results revealed that despite their lack of previous practice with problems having multiple solutions or with those involving non-numerical ordering, students were able to evolve in their knowledge by experiencing the teaching sequence delivered to them / Esta pesquisa teve por objetivo estudar a evolução de conhecimentos alcançada por alunos de 5ª a 8ª séries do ensino fundamental a respeito do sentido amplo da relação de ordem chegar antes ou ao mesmo tempo que , ao se aplicar uma seqüência didática elaborada à luz do quadro teórico de Brousseau. Foram propostos aos alunos problemas envolvendo ordenações de personagens, de modo a levá-los a manipular relações de ordem não-numéricas. A análise das respostas contou não só com elementos da Teoria das Situações Didáticas, de Brousseau, mas também com elementos da impregnação da Língua Materna, de Machado, e do conhecimento tácito, de Polanyi. Com o auxílio desses referenciais, as respostas puderam ser agrupadas em categorias, nas quais se evidenciam não apenas procedimentos para a busca de soluções, mas também fatores que facilitaram e outros que dificultaram o alcance de todas as soluções possíveis fatores esses relacionados com o contrato didático, com a impregnação da Língua Materna e com influências de outras áreas de conhecimento. Os resultados obtidos permitiram concluir que os alunos não tinham familiaridade com problemas com múltiplas soluções, nem com problemas envolvendo ordenações não-numéricas, mas que puderam progredir ao vivenciarem a aplicação da seqüência didática proposta

Made available in DSpace on 2016-04-29T14:32:24Z (GMT). No. of bitstreams: 1 dissertacao_francisco_bezerra.pdf: 2850257 bytes, checksum: d6a64322b6b117ca8141a066cef945ea (MD5) Previous issue date: 2001-11-21 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The aim of this work was to investigate the approaching to the fraction teaching, in which was intended to introduce the representation of fraction based on problem-solving that result in significative and challenge situation for students. The research was carried out into two groups, both coursing the third grade of a public school in São Paulo. One of them was taught by a teaching sequence elaborated by the author of this research and involving the use of symbolic and pictorial representation based on the presupposed of their participation, the result coming up from situations involving problems, the team work and their life experience. This was the experimental group (EG). The pupil from the another group did not received any teaching of fraction. This was called reference group (RG). Both groups were submitted to two independent tests: the pre test, held before the fraction introduction and the other, and the post test, after having the experimental group being contact with this subject. The analysis of the results involved two points of view: the quantitative and qualitative approaches. Finally, concerning the general perform of the groups, the experimental group presented a superior performance if compared with the reference group that stayed at same level as beginning. The study offered us significant leads about the building up process of these contents. The most valuable one was that the building up process of the basic concepts in the rational field as an example of the historic way, gathers strength when it comes from solving the concrete problem from the life problems / O objetivo deste trabalho foi investigar uma abordagem para o ensino dos números fracionários, em que se pretendeu estudar a aquisição do conceito deste e de suas representações com base em situações-problema que fossem significativas e desafiadoras para o aluno. Trabalhou-se com duas turmas de 3ª série, uma que serviu de grupo experimental (GE) e outra de mesmo nível que representou o grupo controle (GC), ambas do Ensino Fundamental, de uma Escola Pública da cidade de São Paulo. No GE foram estudadas as questões da aprendizagem relacionadas à aquisição do conceito de fração, tomando-se por base uma seqüência de ensino elaborada, pelo autor desta pesquisa, utilizando-se das representações simbólicas e pictóricas, com base nos pressupostos da participação, da resolução de situações-problema, do trabalho em grupo e de vivências relacionadas ao dia-a-dia da criança. O GC não teve qualquer contato formal com esse conteúdo. Os dois grupos foram submetidos a dois testes individuais: um antes (pré-teste) da aquisição dos conceitos de fração e outro (pós-teste), depois de ter tido contato com esse conteúdo. A análise dos resultados envolveu duas etapas: a análise quantitativa e a qualitativa dos instrumentos diagnósticos. Em síntese, quanto ao desempenho geral dos grupos nos testes, pode-se citar que o GE apresentou um desempenho satisfatório, ao passo que o GC manteve-se no mesmo patamar. O estudo ofereceu pistas significativas sobre o processo de aquisição desse conteúdo. A mais valiosa delas foi a de que o processo de construção dos conceitos de fração, a exemplo da história, ganha força quando se inicia baseando-se na resolução de problemas concretos, advindos da realidade