Neste trabalho é abordado o exemplo proposto por Nicolai Haydn, no qual é dado um exemplo de um deslocamento onde é possível construir in nitas medidas de máxima entropia, além de in nitos estados de equilíbrio. / In this work, we present the example shown by Nicolai Haydn, which is given by subshift where is possible to show in nity measures of maximal entropy, besides in nitely many distinct equilibrium states.

Made available in DSpace on 2014-06-11T19:26:15Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-09-11Bitstream added on 2014-06-13T20:47:15Z : No. of bitstreams: 1 lenarduzzi_fn_me_sjrp.pdf: 432607 bytes, checksum: 6e0e82d0a71ba0e530e2f097612c9be5 (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / O objetivo principal deste trabalho e estudar os resultados apresentados por R. Zeimuller em Poisson Suspensions of Compactly Regenerative Transformations[Z0]. Neste artigo, partindo de um espaço de medida σ-finito (X;A;μ) com uma transformação ergódica T, o autor consideração de T em poeiras enumeráveis de pontos, o que define uma transformação T num espaço de probabilidade ~ X. Será mostrado que ~ T e invariante e ergódica para uma medida ~μ em ~ X, que est a relacionada com estes conjuntos enumer aveis de pontos. Apesar de não valer o teorema de Birkhoff para o espaço inicial (X;A;μ ) que tem medida infinita, vale a convergência das médias ergódicas neste novo espaço, o que permite recuperar a medida de um conjunto A em termos do número de visitas a A se forem consideradas órbitas de conjuntos enumeráveis ~ μ-típicos ao invés de olhar para a órbita de um só ponto. São estabelecidas ainda condições suficientes para obter um Teorema Central do Limite que acompanha o teorema ergódico de Birkhoff para ~Sn . Também em faremos um breve estudo sobre conservatividade de aplicações em espa ços σ-nito com medida total infinita, taxa de errância de conjuntos de medida positiva e medida aleatória de Poisson / The main purpose of this work is to understand the results presented by R. Zeimuller on his paper Poisson Suspensions of Compactly Regenerative Transformati-ons[Z0]. In this paper, considering σ- nite space (X;A;μ) and a ergodic transformation T, the author considers the action of T on a countable ensemble of points, which de nes a transformation ~ acting on another probability space ~ X. It will be proved that ~ T is invariant and ergodic for a measure ~μ on ~ X, which is related to this countable set of points. We know that Birkhoff's ergodic theorem is not valid on its classical formulation to a in nite measure space (X;A;μ), however we have the convergence of the ergodic means on this new space. This allows us to, somehow, recover the measure of a given set A just looking at the number of its visits considering the orbits of a ~ μ-typical coun-table set instead of looking at the orbit of one single point. It is also established some su cient conditions in order to get a Central Limit Theorem for ~ Sn . We'll also make a brief discussion on conservativity of maps on σ-finite spaces with full measure in nity, wandering rate of positive measure and Poisson random measure. We'll also make a brief discussion on conservativity of maps on σ-finite spaces with full measure in nity, wandering rate of positive measure and Poisson random measure

Efficient uncertainty propagation schemes for dynamical systems are investigated here within the framework of stochastic finite element analysis. Uncertainty in the mathematical models arises from the incomplete knowledge or inherent variability of the various parametric and geometric properties of the physical system. These input uncertainties necessitate the use of stochastic mathematical models to accurately capture their behavior. The resolution of such stochastic models is computationally quite expensive. This work is concerned with development of model order reduction techniques for obtaining the dynamical response statistics of stochastic finite element systems. Efficient numerical methods have been proposed to propagate the input uncertainty of dynamical systems to the response variables. Response statistics of randomly parametrized structural dynamic systems have been investigated with a reduced spectral function approach. The frequency domain response and the transient evolution of the response of randomly parametrized structural dynamic systems have been studied with this approach. An efficient discrete representation of the input random field in a finite dimensional stochastic space is proposed here which has been integrated into the generic framework of the stochastic finite element weak formulation. This framework has been utilized to study the problem of random perturbation of the boundary surface of physical domains. Truncated reduced order representation of the complex mathematical quantities which are associated with the stochastic isoparametric mapping of the random domain to a deterministic master domain within the stochastic Galerkin framework have been provided. Lastly, an a-priori model reduction scheme for the resolution of the response statistics of stochastic dynamical systems has also been studied here which is based on the concept of balanced truncation. The performance and numerical accuracy of the methods proposed in this work have been exemplified with numerical simulations of stochastic dynamical systems and the convergence behavior of various error indicators.

abstract: The three-dimensional flow contained in a rapidly rotating circular split cylinder is studied numerically solving the Navier--Stokes equations. The cylinder is completely filled with fluid and is split at the midplane. Three different types of boundary conditions were imposed, leading to a variety of instabilities and complex flow dynamics. The first configuration has a strong background rotation and a small differential rotation between the two halves. The axisymmetric flow was first studied identifying boundary layer instabilities which produce inertial waves under some conditions. Limit cycle states and quasiperiodic states were found, including some period doubling bifurcations. Then, a three-dimensional study was conducted identifying low and high azimuthal wavenumber rotating waves due to G\"ortler and Tollmien–-Schlichting type instabilities. Over most of the parameter space considered, quasiperiodic states were found where both types of instabilities were present. In the second configuration, both cylinder halves are in exact counter-rotation, producing an O(2) symmetry in the system. The basic state flow dynamic is dominated by the shear layer created in the midplane. By changing the speed rotation and the aspect ratio of the cylinder, the flow loses symmetries in a variety of ways creating static waves, rotating waves, direction reversing waves and slow-fast pulsing waves. The bifurcations, including infinite-period bifurcations, were characterized and the flow dynamics was elucidated. Additionally, preliminary experimental results for this case are presented. In the third set up, with oscillatory boundary conditions, inertial wave beams were forced imposing a range of frequencies. These beams emanate from the corner of the cylinder and from the split at the midplane, leading to destructive/constructive interactions which produce peaks in vorticity for some specific frequencies. These frequencies are shown to be associated with the resonant Kelvin modes. Furthermore, a study of the influence of imposing a phase difference between the oscillations of the two halves of the cylinder led to the interesting result that different Kelvin modes can be excited depending on the phase difference. / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics 2017

State estimation and tracking (also known as filtering) is an integral part of any system performing inference in a partially observable environment, whether it is a robot that is gauging an environment through noisy sensors or a natural language processing system that is trying to model a sequence of characters without full knowledge of the syntactic or semantic state of the text. In this work, we develop a framework for constructing state estimators. The framework consists of a model class, referred to as predictive state models, and a learning algorithm, referred to as two-stage regression. Our framework is based on two key concepts: (1) predictive state: where our belief about the latent state of the environment is represented as a prediction of future observation features and (2) instrumental regression: where features of previous observations are used to remove sampling noise from future observation statistics, allowing for unbiased estimation of system dynamics. These two concepts allow us to develop efficient and tractable learning methods that reduce the unsupervised problem of learning an environment model to a supervised regression problem: first, a regressor is used to remove noise from future observation statistics. Then another regressor uses the denoised observation features to estimate the dynamics of the environment. We show that our proposed framework enjoys a number of theoretical and practical advantages over existing methods, and we demonstrate its efficacy in a prediction setting, where the task is to predict future observations, as well as a control setting, where the task is to optimize a control policy via reinforcement learning.

Orientador: Ali Messaoudi / Coorientador: Patricia Romano Cirilo / Banca: Carlos Gustavo Tamm de Araujo Moreira / Banca: Claudio Aguinaldo Buzzi / Resumo: O objetivo principal deste trabalho e estudar os resultados apresentados por R. Zeimuller em Poisson Suspensions of Compactly Regenerative Transformations[Z0]. Neste artigo, partindo de um espaço de medida σ-finito (X;A;μ) com uma transformação ergódica T, o autor consideração de T em "poeiras" enumeráveis de pontos, o que define uma transformação T num espaço de probabilidade ~ X. Será mostrado que ~ T e invariante e ergódica para uma medida ~μ em ~ X, que est a relacionada com estes conjuntos enumer aveis de pontos. Apesar de não valer o teorema de Birkhoff para o espaço inicial (X;A;μ ) que tem medida infinita, vale a convergência das médias ergódicas neste novo espaço, o que permite recuperar a medida de um conjunto A em termos do número de visitas a A se forem consideradas órbitas de conjuntos enumeráveis ~ μ-típicos ao invés de olhar para a órbita de um só ponto. São estabelecidas ainda condições suficientes para obter um Teorema Central do Limite que acompanha o teorema ergódico de Birkhoff para ~Sn . Também em faremos um breve estudo sobre conservatividade de aplicações em espa ços σ-nito com medida total infinita, taxa de errância de conjuntos de medida positiva e medida aleatória de Poisson / Abstract: The main purpose of this work is to understand the results presented by R. Zeimuller on his paper Poisson Suspensions of Compactly Regenerative Transformati-ons[Z0]. In this paper, considering σ- nite space (X;A;μ) and a ergodic transformation T, the author considers the action of T on a countable "ensemble" of points, which de nes a transformation ~ acting on another probability space ~ X. It will be proved that ~ T is invariant and ergodic for a measure ~μ on ~ X, which is related to this countable set of points. We know that Birkhoff's ergodic theorem is not valid on its classical formulation to a in nite measure space (X;A;μ), however we have the convergence of the ergodic means on this new space. This allows us to, somehow, recover the measure of a given set A just looking at the number of its visits considering the orbits of a ~ μ-typical coun-table set instead of looking at the orbit of one single point. It is also established some su cient conditions in order to get a Central Limit Theorem for ~ Sn . We'll also make a brief discussion on conservativity of maps on σ-finite spaces with full measure in nity, wandering rate of positive measure and Poisson random measure. We'll also make a brief discussion on conservativity of maps on σ-finite spaces with full measure in nity, wandering rate of positive measure and Poisson random measure / Mestre

Neste trabalho é abordado o exemplo proposto por Nicolai Haydn, no qual é dado um exemplo de um deslocamento onde é possível construir in nitas medidas de máxima entropia, além de in nitos estados de equilíbrio. / In this work, we present the example shown by Nicolai Haydn, which is given by subshift where is possible to show in nity measures of maximal entropy, besides in nitely many distinct equilibrium states.

abstract: The current paper presents two studies that examine how asymmetries during interpersonal coordination are compensated for. It was predicted that destabilizing effects of asymmetries are stabilized through the recruitment and suppression of motor degrees-of-freedom (df). Experiment 1 examined this effect by having participants coordinate line movements of different orientations. Greater differences in asymmetries between participants yielded greater spatial deviation, resulting in the recruitment of df. Experiment 2 examined whether coordination of movements asymmetrical in shape (circle and line) yield simultaneous recruitment and suppression of df. This experiment also tested whether the initial stability of the performed movement alters the amount of change in df. Results showed that changes in df were exhibited as circles decreasing in circularity and lines increasing in circularity. Further, more changes in df were found circular (suppression) compared to line (recruitment) movements. / Dissertation/Thesis / M.A. Psychology 2013

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.

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.