Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2017-02-16T11:16:03Z No. of bitstreams: 2 Dissertação - Mayk Joaquim dos Santos - 2017.pdf: 2151565 bytes, checksum: 0afafa6be7f2f9c3ee2a27ca9bf4bf24 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-02-16T11:16:36Z (GMT) No. of bitstreams: 2 Dissertação - Mayk Joaquim dos Santos - 2017.pdf: 2151565 bytes, checksum: 0afafa6be7f2f9c3ee2a27ca9bf4bf24 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-02-16T11:16:36Z (GMT). No. of bitstreams: 2 Dissertação - Mayk Joaquim dos Santos - 2017.pdf: 2151565 bytes, checksum: 0afafa6be7f2f9c3ee2a27ca9bf4bf24 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2017-01-16 / In this work we will show that, given a piecewise smooth vector field, we can apply the regularization method and, from it, via blow-up, turn it into a singular perturbation problem. By doing that, we can use the tools from singular perturbation theory to perform a qualitative study of piecewise smooth vector fields. Finally, we will show that, through successive changes of coordinates, a singularity of a discontinuous submanifold of codimension k, where k=1 or k=2, can be transformed into a singularity of codimension 0 in order to study the qualitative behavior in this submanifold, where the Filippov’s convention holds. / Neste trabalho mostraremos que, dado um campo de vetores suaves por partes, podemos aplicar o método de regularização e, a partir deste, via “blow-up”, o transformamos em um problema de perturbação singular. Podemos, dessa forma, fazer uso das ferramentas da teoria de perturbação singular para realizar um estudo qualitativo dos campos de vetores suaves por partes. Por último, mostraremos que através de sucessivas mudanças de coordenadas podemos transformar uma singularidade de uma subvariedade de descontinuidade de codimensão k, onde k=1 ou k=2, em uma uma singularidade de codimensão 0 e estudar o comportamento qualitativo ao longo desta subvariedade, onde é válida a convenção de Filippov.

Este trabalho apresenta um estudo qualitativo das equações diferenciais nãolineares que descrevem o sincronismo de fase nos PLLs de 3ª ordem que compõem redes OWMS de topologia mista, Estrela Simples e Cadeia Simples. O objetivo é determinar, através da Teoria de Bifurcações, os valores ou relações entre os parâmetros constitutivos da rede que permitam a existência e a estabilidade do estado síncrono, quando são aplicadas, no oscilador mestre, duas funções de excitação muito comuns na prática: o degrau e a rampa de fase. Na determinação da estabilidade dos pontos de equilíbrio, sob o ponto de vista de Lyapunov, a existência de pontos de equilíbrio não-hiperbólicos não permite uma aproximação linear e, nesses casos, é aplicado o Teorema da Variedade Central. Essa técnica de simplificação de sistemas dinâmicos permite fazer uma aproximação homeomórfica em torno desses pontos, preservando a orientação no espaço de fases e possibilitando determinar localmente suas estabilidades. / This work presents a qualitative study of the non-linear differential equations that describe the synchronous state in 3rd order PLLs that compose One-way masterslave time distribution networks with Single Star and Single Chain topologies. Using bifurcation theory, the dynamical behavior of third-order phase-locked loops employed to extract the syncronous state in each node is analyzed depending on constitutive node parameters when two usual inputs, the step and the ramp phase pertubations, are supposed to appear in the master node. When parameter combinations result in non hyperbolic synchronous states, from Lyapunov point of view, the linear approximation does not provide any information about the local behavior of the system. In this case, the center manifold theorem permits the construction of an equivalent vector field representing the asymptotic behavior of the original system in the neighborhood of these points. Thus, the local stability can be determined.

Made available in DSpace on 2016-03-15T19:38:51Z (GMT). No. of bitstreams: 1 Pericles do Prado Turnes Junior.pdf: 1375255 bytes, checksum: 24dc630ef135368b840995d533e161e8 (MD5) Previous issue date: 2014-07-29 / Instituto Presbiteriano Mackenzie / There are many epidemiological models written in terms of ordinary differential equations (ODE). This approach is based on the homogeneous mixing assumption; that is, the topological structure of the network of social contacts, established by the individuals in the population, is not relevant to forecast the propagation of the studied pathogen. In this work, an epidemiological model formulated in terms of ODE and probabilistic cellular automata (PCA) is proposed to study the spread of contagious diseases that do not conferimmunity. The state variables of this model are the percentages of susceptible individuals, infected individuals and empty space. It is shown that this dynamical system can experience Hopf and transcritical bifurcations. Then, this model is used to evaluate the validity of the homogeneous mixing assumption, by using real data related to the transmission of gonorrhea, hepatitis C virus, human immunodeficiency virus and obesity. / Muitos modelos epidemiológicos são escritos em termos de equações diferenciais ordinárias (EDO). Essa abordagem baseia-se no pressuposto de mistura homogênea; ou seja, a estrutura topológica da rede de contatos sociais, estabelecida pelos indivíduos da população, não é relevante para prever o avanço do patógeno em estudo. Neste trabalho, é proposto um modelo epidemiológico formulado em termos de EDO e de autômato celular probabilista (ACP) para estudar a propagação de doenças contagiosas que não conferem imunidade. As variáveis de estado desse modelo são as porcentagens de indivíduos suscetíveis, de indivíduos infectados e de espaço vazio. Mostra-se que esse sistema dinâmico pode apresentar bifurcações de Hopf e transcrítica. O modelo é , então, usado para avaliar a validade da hipótese de mistura homogênea, usando dados relacionados à transmissão de gonorreia, vírus da hepatite C, vírus da imunodeficiência humana e obesidade.

Inicialmente, consideramos o mapa Logístico com os vários fenômenos nele presentes, para depois, ao perturbarmos esse mapa, adicionando periodicamente um termo de amplitude constante, identificarmos os novos fenômenos e as alterações que a introdução da perturbação faz aparecer. Apresentamos o circuito eletrônico de Matsumoto e, em seguida, o consideramos em um regime caótico perturbado por uma tensão elétrica senoidal externa. A introdução desta perturbação faz o circuito permanecer caótico, tornar-se periódico ou quasi-periódico no toro de duas frequências. Aplicamos diversos métodos de controle de caos a três sistemas (mapa Logístico, mapa de Hénon e circuito de Matsumoto). Para a estabilização de uma órbita periódica, consideramos os métodos de Ott-Grebogi-Yorke (OGY), de Romeiras, de Pyragas, de Sinha, de Singer e de H¨ubbler. Para o direcionamento da trajetória para um ponto de equilíbrio, usamos o método de Sinha. Para a transferência da trajetória para um dos atratores coexistentes no sistema de Matsumoto, usamos o método de Jackson-H¨ubbler (OPCL). Usando um conjunto de pertubações constantes em um parâmetro previamente escolhido, mostramos como é possével dirigir rapidamente uma trajetória, de qualquer um dos três sistemas considerados nesta tese, para um determinado alvo. Além disso, é mostrado como esse método pode ser aplicado experimentalmente. / Initially, we consider the Logistic map with its many non-linear phenomena. Then, we use this knowledge to discern new phenomena that shall appear when the map is perturbed, that is the Logistic map perturbed by a periodic and constant term. The Matsumoto\'s circuit is presented and, after we set this circuit to behave chaotically, we perturb it with a sinoidal wave, characterized by its frequency and amplitude. This perturbation is responsible for the appearence of a quasi-periodic and periodic oscillations, or the maintenance of chaos. We presented and applied many methods for controlling chaotic oscillations in three systems (the Logistic and Henon maps, and the Matsumoto\'s circuit), showing many ways for stabilizing a periodic orbit, using the methods of Ott-Grebogi-York (OGY), Romeiras, Singer, Sinhas and Huebbler. For targeting the trajectory to a equilibrium point, the Sinha\'s method was used. To transfer the system trajectory from one to another of the coexisting attractors presented in the Matsumoto\'s circuit, we use the Jackson-Huebbler (OPCL) method. Using a set of constant perturbations, in a previously chosen parameter, we showed how we can rapidly direct a trajectory of any of the considered three systems to a aimed target. Besides, it is shown how this method can be experimentally applied.

A proposta deste trabalho é apresentar resultados para o estudo sistemático de sistemas dinâmicos reversíveis-equivariantes, ou seja, em presença simultânea de simetrias e antisimetrias. Este é o caso em que o domínio e as equações que regem o sistema são invariantes pela ação de um grupo de Lie compacto Γ formado pelas simetrias e anti-simetrias do problema. Apresentamos métodos de teoria de Singularidades e teoria de invariantes para classificar bifurcações a um parâmetro de pontos de equilíbrio destes sistemas. Para isso, separamos o estudo de aplicações Γ-reversíveis-equivariantes em dois casos: auto-dual e não auto-dual. No primeiro caso, a existência de um isomorfismo linear Γ-reversível-equivariante estabelece uma correspondência entre a classificação de problemas Γ-reversíveis-equivariantes e a classificação de problemas Γ-equivariantes associados, para os quais todos os elementos de Γ agem como simetria. Os resultados obtidos para o caso não auto-dual se baseiam em teoria de invariantes e envolvem técnicas algébricas que reduzem a análise ao caso polinomial invariante. Dois algoritmos simbólicos são estabelecidos para o cálculo de geradores para o módulo das funções anti-invariantes e para o módulo das aplicações reversíveis-equivariantes. / The purpose of this work is to present results for the sistematic study of reversible-equivariant dynamical systems, namely in simultaneous presence of symmetries and reversing simmetries. This is the case when the domain and the equations modeling the system are invariant under the action of a compact Lie group Γ formed by the symmetries and reversing symmetries of the problem. We present methods in Singularities and Invariant theory to classify oneparameter steady-state bifurcations of these systems. For that, we split the study of the ¡¡reversible-equivariant mapping into two cases: self-dual and non self-dual. In the first case, the existence of a Γ-reversible-equivariant linear isomorphism establishes a one-toone correspondence between the classification of Γ-reversible-equivariant problems and the classification of the associated Γ-equivariant problems, for which all elements in Γ act as symmetries. The results obtained for the non self-dual case are based on Invariant theory and involve algebraic techniques that reduce the analysis to the invariant polynomial case. Two symbolic algorithms are established for the computation of generators for the module of anti-invariant functions and for the module of reversible-equivariant mappings.

Philosophiae Doctor - PhD / There is a growing interest in the dynamics of the co-infection of these two diseases. In this thesis, firstly we focus on studying the effect of a distributed delay representing the incubation period for the malaria parasite in the mosquito vector to possibly reduce the initial transmission and prevalence of malaria. This model can be regarded as a generalization of SEI models (with a class for the latently infected mosquitoes) and SI models with a discrete delay for the incubation period in mosquitoes. We study the possibility of occurrence of backward bifurcation. We then extend these ideas to study a full model of HIV and malaria co-infection. To get further inside into the dynamics of the model, we use the geometric singular perturbation theory to couple the fast and slow models from the full model. Finally, since the governing models are very complex, they cannot be solved analytically and hence we develop and analyze a special class of numerical methods to solve them. / South Africa

Voluntary coughs are used as a diagnostic tool to detect lung diseases. Understanding the mechanics of a cough is therefore crucial to accurately interpreting the test results. A cough is characterised by a dynamic compression of the airways, resulting in large flow velocities and producing transient peak expiratory flows. Existing models for pulmonary flow have one or more of the following limitations: 1) they assume quasi-steady flows, 2) they assume low speed flows, 3) they assume a symmetrical branching airway system. The main objective of this thesis is to develop a model for a cough in the branching pulmonary airway system. First, the time-dependent one-dimensional equations for flow in a compliant tube is used to simulate a cough in a single airway. Using anatomical and physiological data, the tube law coupling the fluid and airway mechanics is constructed to accurately mimic the airway behaviour in its inflated and collapsed states. Next, a novel model for air flow in an airway bifurcation is constructed. The model is the first to capture successfully subcritical and supercritical flows across the bifurcation and allows for free time evolution from one case to another. The model is investigated by simulating a cough in both symmetric and asymmetric airway bifurcations. Finally, a cough model for the complete branching airway system is developed. The model takes into account the key factors involved in a cough; namely, the compliance of the lungs and the airways, the coughing effort and the sudden opening of the glottis. The reliability of the model is assessed by comparing the model predictions with previous experimental results. The model captures the main characteristics of forced expiatory flows; namely, the flow limitation phenomenon (the flow out of the lungs becomes independent of the applied expiratory effort) and the negative effort dependence phenomenon (the flow out of the lungs decreases with increasing expiratory effort). The model also gives a good qualitative agreement with the measured values of airway resistance. The location of the collapsed airway segment during forced expiration is, however, inconsistent with previous experimental results. The effect of changing the model parameters on the model predictions is therefore discussed.

Orientador: Marco Antonio Teixeira / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-26T09:33:59Z (GMT). No. of bitstreams: 1 Souza_WenderJosede_D.pdf: 1230622 bytes, checksum: 578f86e5fe4ff35247fcfb0fb04975b8 (MD5) Previous issue date: 2014 / Resumo: Neste trabalho consideramos alguns aspectos da teoria qualitativa de sistemas dinâmicos suaves por partes. Nosso principal objetivo é estudar uma classe de tais sistemas, onde o conjunto de descontinuidade é dado por uma hipersuperfície ? e além disso, assumimos que em cada região determinada por ? o campo de vetores definido é um sistema Hamiltoniano. Apresentamos estudos relacionados à regularização de campos de vetores suaves por partes em Rn que preservam volume nas componentes suaves. Abordamos também singularidades de funções suaves por partes, onde formas normais e seus desdobramentos são apresentados. Por fim estudamos bifurcações de campos de vetores Hamiltonianos refrativos / Abstract: In this work, we consider some aspects of the qualitative theory of non smooth dynamical systems in Rn. Our main goal is to study a class of such systems where the discontinuity set is concentrated in a hypersurface ? and moreover, we assume that in each region determined by ? the vector field is a Hamiltonian system. We present studies related to the regularization of piecewise vector fields in Rn that are volume preserving on each smooth components. We also analyze singularities of piecewise smooth functions where normal forms and their unfolding are presented. Finally, we study bifurcations of refractive Hamiltonian vector fields / Doutorado / Matematica / Doutor em Matemática

O presente estudo teve por objetivo avaliar as características anatômicas das bifurcações radiculares, e compará-las às dimensões das pontas ativas das curetas de Gracey e Pádua-Lima. Foram utilizados 198 dentes, distribuídos entre primeiros e segundos molares superiores e inferiores, provenientes do Banco de Dentes da Universidade de Taubaté. Depois de codificados, os dentes foram fotografados por meio de uma câmera acoplada a um aparelho estereoscópio. As imagens foram digitalizadas por meio de um programa de captação de imagens (Pixel View) e avaliadas por meio de um programa de leitura (Image Tool). Nos dentes foram avaliados: a altura dos troncos radiculares, o ângulo de divergência e a distância interradiculares. Nos instrumentais foram avaliados o comprimento, a largura e a espessura das lâminas. Após análise estatística dos dados, os resultados obtidos mostraram que as bifurcações vestibulares de 2MS foram as que menos permitiram o acesso dos instrumentais avaliados, sendo as curetas Gracey acessíveis à maioria das bifurcações. As bifurcações mesiais e distais de molares superiores, por apresentarem maior distância interradicular e ângulos mais divergentes, são as que mais permitem acesso aos instrumentais avaliados. Baseados nestes resultados podemos concluir que as características anatômicas radiculares podem ser um fator de restrição à instrumentação periodontal. / The present study aimed to evaluate the anatomic characteristics of the root bifurcations and compare them with the active tips of the curettes of Gracey and Pádua-Lima. One hundred ninety eight teeth were used, distributed among first and second upper and lower molars, from the Teeth Bank of the University of Taubaté. After received a numerical code, the teeth were photographed by a camera attached to a stereomicroscope. The images were scanned through a capture image program (Pixel View) and evaluated through a software program (Image Tool for Windows 2.0). The length of the root trunk, the divergence angle between the roots and the inter-root dimensions in the bifurcation region were evaluated. In the instruments, characteristics as width, thickness and length of the curettes blade were analyzed. After the statistics analysis, the results obtained showed that the 2MS buccal bifurcations are those least allow access by the instruments evaluated, and the Gracey curettes had access of the majority of the bifurcations. The mesiais and distal bifurcations of upper molars, to have greater inter-root dimensions distance and divergent angles, are those that allow access to more instrumental evaluated. Based in those results, we can conclude that the roots anatomic characteristics can be a factor to restriction the periodontal instrumentation.

This thesis addresses chemotherapy-induced peripheral neuropathy (CIPN)- a form of pain sensation and a prevalent dose-limiting side-effect of several chemotherapy agents such as vincristine, paclitaxel, and oxaliplatin. These agents are used for treating various cancers such as leukemia, brain tumor, lung cancer. Peripheral neuropathy is a numbing, tingling, and burning sensation felt in the palms and feet, which occurs due to damage to neurons (nerve cells). Prolonged CIPN can impact the quality of life of cancer patients. Occasionally, severe CIPN can result in termination of chemotherapy treatment altogether. Currently, there are no established strategies for treating CIPN due to a lack of understanding of its mechanisms. Moreover, different patients react differently to the same treatment; a subgroup of patient population may never experience CIPN, while another may experience severe CIPN for the same dose. In addition, there are no established strategies for predicting CIPN either. This thesis addresses both prediction and mechanisms of CIPN.<br><br>The following paragraphs reflect the organization of this thesis. Each paragraph introduces a research problem, the approaches taken to investigate it, and states the key results.<br><br>First, a metabolomics-based approach was used to investigate CIPN prediction. Blood samples of pediatric leukemic cancer patients who underwent treatment with a chemotherapy agent - vincristine were provided. These blood samples were analyzed at different treatment time points using mass spectrometry to obtain the metabolite profiles. Machine learning was then employed to identify specific metabolites that can predict overall susceptibility to peripheral neuropathy in those patients at specific treatment time points. Subsequently, selected metabolites were used to train machine learning models to predict neuropathy susceptibility. Finally, the models were deployed into an open-source interactive tool- <i>VIPNp</i>- that can be used by researchers to predict CIPN in new pediatric leukemic cancer patients.<br><br>Second, the focus was shifted to the pathophysiology of pain and the pain-sensing neuron; specifically: (i) investigating pain sensation mutations and the dynamics of the pain-sensing neuron, and (ii) exploring chemotherapy-induced peripheral neuropathy mechanisms. <br><br>While pain is a common experience, genetic mutations in individuals can alter their experience of pain, if any at all (certain mutations yield individuals insensitive to pain). Despite its ubiquity, we do not have a complete understanding of the onset and/or mechanisms of pain sensation. Pain sensation can be broadly classified into three types: (i) nociceptive, (ii) neuropathic, and (iii) inflammatory. Nociceptive pain arises due to a noxious external stimulus (e.g., upon touching a hot object). Neuropathic pain (which is felt as a side-effect of the aforementioned chemotherapy agents) is the numbing and tingling sensation due to nerve damage. Inflammatory pain occurs due to damage to internal tissues. Pain in any form can be characterized in terms of electrical signaling by the pain-sensing neuron. Signal transmission regarding pain occurs through generation of an electrical signal called the action potential- a peak in neuron membrane potential. Excessive firing of action potentials by a pain-sensing neuron indicates pain of a specific form and intensity. In order to investigate this electrical signaling, a mathematical modeling approach was employed. The neuron membrane was assumed to be an electrical circuit and the potential across the membrane was modeled in terms of the sodium and potassium ions flowing across it via voltage-gated sodium and potassium channels, respectively. Generation of a single action potential followed by a resting state corresponds to a normal state, whereas periodic firing of action potentials (an oscillatory state) corresponds to pain of some form and intensity <i>in vitro</i>. Therefore, an investigation into the switch from a resting state to an oscillatory state was proposed. A bifurcation theory approach (generally useful in exploring changes in qualitative behavior of a model) was used to explore possible bifurcations to explain this switch. Firstly, genetic mutations that can shift the pain sensation threshold in the pain-sensing neuron were explored. The detected bifurcation points were found to be sensitive to specific sodium channels’ model parameters, implying sodium channels’ sensitivity towards the pain sensation threshold. This was corroborated by experimental evidence in existing literature. Secondly, a theoretical analysis was performed to explore all possible bifurcations that can explain the dynamics of this pain-sensing neuron model. The mathematical modeling simulations revealed a mixture of small amplitude and large amplitude membrane potential oscillations (mixed-mode oscillations) for specific parameter values. The onset and disappearance of the oscillations were investigated. Model simulations further demonstrated that the mixed-mode oscillations solutions belonged to Farey sequences. Furthermore, regions of bistability- where stable steady state and periodic solutions coexisted- were explored. Additionally, chaotic behavior was observed for specific model parameters.<br><br>Finally, this thesis investigated the role of voltage-gated ion channels in inducing CIPN using the same mathematical model. Repetitive firing of action potentials in the absence of any external stimulus was used as an indicator of peripheral neuropathy. Bifurcation analysis revealed that specific sodium and potassium conductances can induce repetitive firing without any external stimulus. The findings were supplemented by recording the firing rate of a sensory neuron culture. Next, a chemotherapy agent - paclitaxel, was introduced in the model to investigate its potential effects on the firing behavior. It was seen that a medium dose of paclitaxel increased repetitive firing. This was supported by the firing rate recordings of the sensory neuron culture.<br><br>In summary, this thesis presents a prediction strategy for CIPN. Moreover, it presents a bifurcation theory-based framework that can be used to investigate pain sensation, in particular, genetic mutations related to pain sensation and chemotherapy-induced peripheral neuropathy. This framework can be used to find potential voltage-gated ion channels that can be targeted to control the pain sensation threshold in individuals, and can be extended to investigate various degeneracies in CIPN mechanisms to find therapeutic cures for it.