Matrix models are formulated to study the dynamics of the structured populations. We consider closed populations, that is, without migration, and populations with migration. The effects of specific patterns of migration, whether with constant or time-dependent terms, are explored within the context of how they manifest in model output, such as population size. Time functions, commonly known as relative sensitivities, are employed to rank the parameters of the models from most to least influential in the population size or abundance of individuals per group

O entendimento de quebra espontânea de simetria é um problema importante para o estudo de fenômenos na evolução de sistemas abertos, tanto em física quanto em química, como também na biologia. Aqui estudamos um método a mais para este tipo de análise, usando conceitos de sistemas dinâmicos com simetria. O sistema dinâmico escolhido é discreto, isto é, realizado por iteração de um difeomorfismo equivariante sob a ação de um grupo compacto, neste caso um grupo finito do tipo Dm. Especificamente, investigamos o comportamento de atratores caóticos sob a variação dos parâmetros. / The understanding of spontaneous symmetry breaking is an important problem in the study of phenomena in the evolution of open systems, in physics and chemistry as well as in biology. Here we study another method for this kind of analysis, using concepts from dynamical systems with symmetry. The chosen dynamical system is discrete, that is, realized by iteration of an equivariant diffeomorphism under the action of a compact group, in this case one of the finite groups of type Dm. Specifically, we investigate the behavior of chaotic attractors under variation of the parameters.

Estômatos são poros responsáveis pela troca gasosa entre a folha e o meio externo. A partir da década de 80, experimentos revelaram um complexo padrão espaço temporal na abertura e fechamento dos estômatos. As experiências apontam para uma possível coordenação entre estômatos em algumas áreas da folha chamada de patches. Esse fenômeno é conhecido na literatura como patchy stomatal conductance. Frequentemente a coordenação dinâmica dos estômatos está associada à oscilações temporais na condutãncia estomática (média especial da abertura dos estômatos). Em 1997 Haefner, Buckley e Mott (HBM) publicaram uma análise numérica de um modelo dinâmico para explorar o comportamento complexo dos estômatos. O modelo é baseado em algumas características conhecidas dos estômatos e assume transporte hídrico em uma rede definida por uma geometria simples e bastante restritiva. De acordo com os autores, o modelo reproduz qualitativamente os dados experimentais. Recentemente, Ferraz e Prado mostraram que esse modelo não é capaz de reproduzir os resultados experimentais. Usando ingredientes do modelo sugerido por HBM, Ferraz e Prado sugeriram uma geometria realística de distribuição reservatórios hídricos. Embora essa configuração reproduza os patches, eles permanecem estáticos e nenhuma oscilação é observada. Sem explorar detalhes significativos, Ferraz e Prado afirmaram que a histerese na abertura estomatal poderia explicar vários aspectos dos resultados experimentais. No presente estudo comprovamos, através de uma abordagem computacional baseada em transdutores histeréticos, que a hipótese de histerese na abertura dos estômatos de fato reproduz qualitativamente os dados experimentais. Em nossa abordagem a histerese na abertura dos estômatos é emulada através de operadores chamados de histerons. A robustez da hipótese é testada usando diferentes tipos de histerons. Analisamos a correlação entre os estômatos na rede que simula a superfície da folha. Observamos que a correlação entre estômatos depende da geometria da veia. Uma análise detalhada dos parâmetros envolvidos revela uma dependência entre o período de oscilação na condutância estomática e o déficit de vapor d\'água entre a folha e o meio ambiente. Esta característica subjacente ao modelo pode inspirar novas experiências para testar a hipótese da histerese na abertura dos estômatos. / Stomata are pores on the surface of leaves responsible for controlling the exchange of gas between the plant and the environment. Experiments revealed a complex spatial-temporal pattern in the opening and closing mechanism of stomata. The main feature of the phenomenon is that stomata appear to be synchronized into clusters, known as patches. The dynamical coordination of stomata often involves oscillations in stomatal conductance. In 1997 Haefner, Buckley, and Mott (HBM) published a numerical analysis of a dynamic model to explore the complex behavior of stomata. The model is based on some known features of the stomata, and assumes that water diffuses within the leaves according to a simple geometric arrangement. According to the authors, the model reproduces qualitatively the experimental data. Recently, Ferraz and Prado showed that the computational approach of HBM is not able to reproduce the experimental results. Inspired by this model, Ferraz and Prado introduced a new geometric features that leads to static patches of stomata; however no oscillation was observed and the patches remained static. The authors suggested that hysteresis in stomatal aperture could explain several experimental aspects. We now report a further investigation of the changes suggested by Ferraz and Prado in the original model of HBM. The theoretical approach confirmed that hysteresis in the aperture mechanism of pores reproduces a variety of behaviors of stomatal conductance described in experiments. We explore the hysteresis feature through the formalism of hysteretic transducer. The robustness of the hysteretic assumption is tested by different kinds of hysteresis operators. We analyzed the correlation among stomata in the lattice. We observed that the correlation depends on the geometry of the veins. Finally, the analysis of the model reveals a dependence between the period of oscillation in the stomatal conductance time series and water vapor pressure deficits Δω - an external parameter. Further experiments might explore this underlying feature of the model.

Este trabalho calcula analítica e numericamente a densidade espectral para o modelo de Anderson de duas impurezas sem correlação eletrônica (U=0). Nossos resultados servem como passo inicial para se entender o modelo com a correlação eletrônica. O modelo estudado descreve a interação entre elétrons de um metal e impurezas magnéticas localizadas, e a simplificação, U = 0, torna o Hamiltoniano quadrático permitindo assim que se divida o mesmo em dois termos: um envolvendo apenas operadores pares (canal par) e outro envolvendo apenas operadores ímpares (canal ímpar). Cada termo encontrado difere pouco do Hamiltoniano de Nível Ressonante. Nossos resultados abrangem tanto a diagonalização analítica como a numérica pelo método do Grupo de Renormalização, adaptado para o caso de duas impurezas. A simplicidade do Hamiltoniano permite que (1) se identifique características do modelo que afetam adversamente a precisão do cálculo numeríco e (2) se encontre uma maneira de circundar tais dificuldades. Os resultados aqui encontrados ajudaram o desenvolvimento do cálculo da densidade espectral do modelo correlacionado, desenvolvido paralelamente em nosso grupo de pesquisa. / This work calculates analytically and numerically the spectral density for the two impurity uncorrelated Anderson model (U = O). Our results serve as an initial step towards understanding models with electronic correlation. The studied model describes the interaction between conduction-band electrons of a metal and localized magnetic impurities. The simplification U = O turns the Hamiltonian quadratic, allowing us to split it into two parts: one involving only even operators (even channel), the other involving odd operators (odd channel). Each term has a form differing a little from that for the Resonant Level Hamiltonian. Our results include analytic diagonalization as well as numerical calculations using the method of the Renormalization Group, adapted for the two impurity case. The traditional tridiagonalization method imposes particle-hole symmetry, while our treatment preserves the energy dependence of the coupling, between the impurities and the conduction-band, and consequently, the natural asymmetry of the model. The simplicity of the Hamiltonian allowed us to (1) identify characteristics of the model that affect adversely the acuracy of the numeric calculation and (2) find a way to surround such difficulties. The results here found helped the development of the calculation of the spectral density of the correlated model, developed simultaneously in our research group.

Esta dissertação visa estudar a aplicabilidade e a importância prognóstica de métodos matemáticos não lineares no estudo das variações da freqüência cardíaca bem como no das mudanças morfológicas em sinais de eletrocardiograma. Apresentaremos uma revisão geral desse assunto focando em técnicas de análise não linear para o estudo de sinais de eletrocardiograma (ECG) visando construir uma base de conhecimentos que permita, no futuro, a abordagem de novos aspectos dessas metodologias. Como resultado do aprendizado, é gerado um programa que utiliza algumas das técnicas descritas ao longo da dissertação. Ao final da dissertação, abordaremos as vantagens e desvantagens dos métodos não lineares, concluindo que são ferramentas promissoras para a análise de sinais de ECG. / This dissertation presents a study about the applicability and the prognostic importance of nonlinear mathematical methods in the variations of heart frequency as well as in the morphological changes in the electrocardiogram signs. We will present a general revision of this subject focusing on application of nonlinear analysis for the study of electrocardiogram (ECG) signs in order to provide a base of knowledge that allows, in the future, the approach of new aspects of these methodologies. As a result this work, it was built a program that uses nonlinear analysis described along the dissertation. At the end of this document, we describe the advantages and disadvantages of the nonlinear methods, concluding that they are promising tools in the analysis of ECG signs.

Wo, Weifeng. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 99-102). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

The purpose of this work is to illuminate some of the non-smooth phenomena found in piecewise-smooth continuous and discrete dynamical systems, which do not occur in smooth systems. We will explain how such non-smooth phenomena arise in applications which experience impact, such as impact oscillators, and a type of rotating machine, called magnetic bearing systems. The study of their dynamics and sensitivity to parameter variation gives not just insights into the critical motion found in these applications, but also into the complexity and beauty in their own right. This work comprises two parts. The first part studies a general one-dimensional discontinuous power law map which can arise from impact oscillators with a repelling wall. Parameter variation and the influence of the exponent on the existence and stability of periodic orbits is presented. In the second part we analyse two coupled oscillators that model rotating machines colliding with a circular boundary under friction. The study of the dynamics of rigid bodies impacting with and without friction is approached in two ways. On the one hand existence and stability conditions for non-impacting and impacting invariant sets are derived using local and global methods. On the other hand the analysis of parameter variation reveals new non-smooth bifurcations. Extensive numerical studies confirm these results and reveal further phenomena not attainable otherwise.

Orientador: Edson Denis Leonel / Banca: Juliano Antônio de Oliveira / Banca: Renê Orlando Medrado Torricos / Resumo: Neste trabalho consideramos o modelo do poço de potencial dependente do tempo e construimos de forma detalhada o mapeamento discreto bidimensional nas variáveis energia e fase que descreve a dinâmica do sistema. Mostramos que o espaço de fases é do tipo misto, contendo mares de caos, curvas invariantes e ilhas de estabilidade. Encontramos a matriz Jacobiana para o mapeamento assim como seu determinante, confirmando a propriedade de preservação de área. Estudamos a evolução no tempo da energia quadrática média e discutimos leis de escala para o comportamento dessa evolução. Por fim demos início à resolução da equação da difusão a fim de encontrarmos uma equação analitíca para energia quadrática média / Abstract: In this work we consider the model of the time-dependent potential well and we construct in detail the two-dimensional discrete mapping in the energy and phase variables that describes the dynamics of the system. We show that the phase space is of the mixed type, containing chaotic seas, invariant curves and stability islands. We obtain the Jacobian matrix for the mapping as well as its determinant, confirming the area preservation property. We study the evolution in time of the average squared energy and discuss scaling laws for the behavior of this evolution. Finally we started the resolution of the diffusion equation in order to find an analytical equation for mean quadratic energy / Mestre

Goal-directed behavior requires flexible selection among action plans and updating behavioral strategies when they fail to achieve desired goals. Lateral prefrontal cortex (LPFC) is implicated in the execution of behavior-guiding rule-based cognitive control while anterior cingulate cortex (ACC) is implicated in monitoring processes and updating rules. Rule-based cognitive control requires selective processing while process monitoring benefits from combinatorial processing. I used a combination of computational and experimental methods to investigate how network oscillations and neuronal heterogeneity contribute to cognitive control through their effects on selective versus combinatorial processing modes in LPFC and ACC. First, I adapted an existing LPFC model to explore input frequency- and coherence-based output selection mechanisms for flexible routing of rate-coded signals. I show that the oscillatory states of input encoding populations can exhibit a stronger influence over downstream competition than their activity levels. This enables an output driven by a weaker resonant input signal to suppress lower-frequency competing responses to stronger, less resonant (though possibly higher-frequency) input signals. While signals are encoded in population firing rates, output selection and signal routing can be governed independently by the frequency and coherence of oscillatory inputs and their correspondence with output resonant properties. Flexible response selection and gating can be achieved by oscillatory state control mechanisms operating on input encoding populations. These dynamic mechanisms enable experimentally-observed LPFC beta and gamma oscillations to flexibly govern the selection and gating of rate-coded signals for downstream read-out. Furthermore, I demonstrate how differential drives to distinct interneuron populations can switch working memory representations between asynchronous and oscillatory states that support rule-based selection. Next, I analyzed physiological data from the LeBeau laboratory and built a de novo model constrained by the biological data. Experimental data demonstrated that fast network oscillations at both the beta- and gamma frequency bands could be elicited in vitro in ACC and neurons exhibited a wide range of intrinsic properties. Computational modeling of the ACC network revealed that the frequency of network oscillation generated was dependent upon the time course of inhibition. Principal cell heterogeneity broadened the range of frequencies generated by the model network. In addition, with different frequency inputs to two neuronal assemblies, heterogeneity decreased competition and increased spike coherence between the networks thus conferring a combinatorial advantage to the network. These findings suggest that oscillating neuronal populations can support either response selection (routing), or combination, depending on the interplay between the kinetics of synaptic inhibition and the degree of heterogeneity of principal cell intrinsic conductances. Such differences may support functional differences between the roles of LPFC and ACC in cognitive control.

by Guan-xin Li. / "January 1999." / Thesis (Ph.D.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (p. 223-225). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.