This thesis studies the Reach Control Problem (RCP) for affine systems defined on simplices. The thesis focuses on cases when it is known that the problem is not solvable by continuous state feedback. Previous work has proposed (discontinuous) piecewise affine feedback to resolve the gap between solvability by open-loop controls and solvability by feedbacks. The first results on solvability by time-varying feedback are presented. Time-varying feedback has the advantage to be more robust to measurement errors circumventing problems of discontinuous controllers. The results are theoretically appealing in light of the strong analogies with the theory of stabilization for linear control systems. The method is shown to solve RCP for all cases in the literature where continuous state feedback fails, provided it is solvable by open loop control. Textbook examples are provided. The motivation for studying RCP and its relevance to complex control specifications is illustrated using a material transfer system.

This thesis investigates the computation of invariance kernels for planar nonlinear systems with one input, with application to wind turbine stability. Given a known bound on the absolute value of the input variations (possibly around a fixed non-zero value), it is of interest to determine if the system's state can be guaranteed to stay within a desired region K of the state space irrespective of the input variations. The collection of all initial conditions for which trajectories will never exit K irrespective of input variations is called the invariance kernel. This thesis develops theory to characterize the boundary of the invariance kernel and develops an algorithm to compute the exact boundary of the invariance kernel. The algorithm is applied to two simplified wind turbine systems that tap kinetic energy of the turbine to support the frequency of the grid. One system provides power smoothing, and the other provides inertial response. For these models, limits on speed and torque specify a desired region of operation K in the state space, while the wind is represented as a bounded input. The theory developed in the thesis makes it possible to define a measure called the wind disturbance margin. This measure quantifies the largest range of wind variations under which the specified type of grid support may be provided. The wind disturbance margin quantifies how the exploitation of kinetic energy reduces a turbine's tolerance to wind disturbances. The improvement in power smoothing and inertial response made available by the increased speed range of a full converter-interfaced turbine is quantified as an example.

Thesis (Ph.D.)--Boston University. University Professors Program. / This is a study of the relationship between persistent Bantu traditional values and social, political and economic institutions, using the premises of the Convergence Theory and the Invariance Hypothesis to determine what that relationship should be. Traditional values like the concept of man as a life force, the principle of communalism and the belief in the interaction between the dead, the living and those to be born have remained invariant throughout the history of the Bantu. This, contrary to the prescriptions of the dominant modernization theory which calls for the dismantling of these values once the society faces the so called "universal forces of change," like the introduction of modern industries, the development of means of communications, the growth of urban centers and above all, the development of modern science and technology. We used a descriptive analysis approach to examine the relationship between values and patterns of authority on the one hand and patterns of solidarity on the other. We did this first in the traditional setting. Then we did an analytical content criticism of those values in the colonial and post colonial periods which most people link to the introduction of modernization in Africa. We found out that, despite change in the environment, traditional values stay the same. Change will occur at the structural level but in order for the new institutions to be legitimate, they must reflect the traditional values of the people. This in a way explains the failure of some imposed political and social institutions to function in Africa.

Nous montrons ici, en utilisant les méthodes de l'analyse stochastique, le principe d'invariance pour des diffusion sur $\mathbb{R} ^{d},d\geq 2$, en milieu périodique au delà des hypothèses d'uniforme ellipticité et au delà des hypothèses de régularité sur le potentiel. La théorie du calcul stochastique pour les processus associés aux formes de Dirichlet est largement utilisée pour justifier l'existence du processus de Markov à temps continus, défini pour presque tout point de départ sur $\mathbb{R} ^{d}$. Pour la preuve du principe d'invariance, nous montrons une nouvelle inégalité de type Sobolev avec des poids différents, qui nous permet de déduire l'existence et la bornitude d'une densité de la probabilité de transition associée au processus de Markov. Cette inégalité, est l'outil principal de ce travail. La preuve fera appel à des techniques d'analyse harmonique. Enfin, le chapitre 3 contient le résultat principal du travail de la thèse : le principe d'invariance qui veut dire que la suite de processus $(_{\varepsilon }X_{t\varepsilon ^{-2}})$ converge en loi quand $\varepsilon$ tend vers zéro vers un mouvement Brownien. Notre stratégie suit quelques étapes classiques : nous nous appuyons sur la construction de ce qu'on appelle ici correcteur. Afin de contrôler le correcteur, et aussi pour montrer son existence, nous nous appuyons sur l'inégalité de Sobolev. Le resultat est obenu seulement avec les hypothèses, le potentiel $V$ est périodique et satisfait: $e^{V}+e^{-V}$ locallement dans $L^{1}\left( \mathbb{R} ^{d};dx\right)$ ou $dx$ est la mesure de Lebesgue. / We prove here, using stochastic analysis methods, the invariance principle for a $\mathbb{R} ^{d}$ diffusions $d\geq 2$, in a periodic potential beyond uniform boundedness assumptions of potential. The potential is not assumed to have any regularity. So the stochastic calculus theory for processes associated to Dirichlet forms is used to justify the existence of a continuous Markov process starting from almost all $x\in \mathbb{R} ^{d}$ and denoted by $\left( X_{t},t>0\right)$ (cf chapter 1). In chapter 2, we prove a new Sobolev inequality with different weights by using some materials in harmonic analysis. In chapter 3, we prove the main result (Theorem 1) of this work: the invariance principle. Our strategy for proving Theorem 1 follows some classical steps: we rely on the construction of the so-called corrector. In order to control the corrector, and actually also in order to show its existence, we rely on the Sobolev inequality. All the work is done under the following hypothesis: the potential $V$ is periodic and satisfies $e^{V}+e^{-V}$ are locally in $L^{1}\left( \mathbb{R} ^{d};dx\right)$ where $dx$ is the Lebesgue measure.

PIRES, Rilder de Sousa. Difusão singular em um sistema confinado. 2013. 64 f. Dissertação (Mestrado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2013. / Submitted by Edvander Pires (edvanderpires@gmail.com) on 2015-10-23T19:14:37Z No. of bitstreams: 1 2013_dis_rspires.pdf: 2524951 bytes, checksum: 2a38032e0c2de28e051d588ecd2b47f3 (MD5) / Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2015-10-23T19:38:52Z (GMT) No. of bitstreams: 1 2013_dis_rspires.pdf: 2524951 bytes, checksum: 2a38032e0c2de28e051d588ecd2b47f3 (MD5) / Made available in DSpace on 2015-10-23T19:38:52Z (GMT). No. of bitstreams: 1 2013_dis_rspires.pdf: 2524951 bytes, checksum: 2a38032e0c2de28e051d588ecd2b47f3 (MD5) Previous issue date: 2013 / Patterns of scale invariance, associated with power laws, are often found in nature, for instance, in the fluctuations of prices of items in stock markets and in the energy spectrum of turbulent systems. These two systems and many others that exhibit scale invariance present some common properties: they are comprised of several elements that interact in a non-linear way, are not in equilibrium, and exhibit self-organization. Scale invariance is also found in the correlations observed in the critical state of systems that present phase transitions. The concept of self-organized criticality suggests that the properties of invariance spontaneously arise in complex systems. Several models exhibit properties of self-organized critically, including invasion percolation, sand-piles and the trough model, however it is not clear what are the necessary ingredients for criticality to arise. It is known that this property appears in some non-linear diffusive systems. In this work, we introduce a confining potential in a one-dimensional diffusion model with a singular non-linearity on diffusion coefficient, and analyze how this affects in the steady state of the system. We then derive a diffusion equation and obtain a solution for stationary density profile. Our analytical solution is in good agreement with the numerical results. We also present a statistical study of the distribution of avalanches sizes in this model, and obtain profiles following power laws, what is not usually observed in other one-dimensional systems. We also investigated how these profiles vary when the confinement increases, and using finite size scaling we found a universal curve for the distribution of avalanche sizes. Our results show that the action of confinement in a one-dimensional system can yield scale invariance. / Padrões de invariância de escala, associados à leis de potência, são frequentemente observados na natureza. Alguns exemplos são: flutuações em preços de itens de bolsa de valores e outros investimentos, além do espectro de energia em sistemas turbulentos. Esses dois sistemas e vários outros que exibem invariância de escala têm propriedades em comum: compõem-se de vários elementos que interagem de forma não linear, estão fora do equilíbrio e exibem auto-organização. Invariância de escala também é encontrada nas correlações observadas no ponto crítico de sistemas que apresentam transições de fase. O conceito de criticalidade auto-organizada sugere que as propriedades de invariância emergem espontaneamente em sistema complexos. Vários modelos exibem propriedades criticamente auto-organizadas, entre eles percolação invasiva, pilhas de areia e o modelo de desníveis, no entanto, não se sabe ao certo quais os ingredientes necessários para criticalidade emergir. Sabe-se que essa propriedade se manifesta em alguns sistemas difusivos não lineares. Nesse trabalho, introduzimos um potencial confinante em um modelo de difusão unidimensional com uma não linearidade singular no coeficiente de difusão e analisamos a influência dessa mudança no estado estacionário do sistema. Conseguimos, então, derivar uma equação de difusão do modelo e obtemos uma solução para o perfil de densidade. Nossa solução analítica concorda perfeitamente com os resultados numéricos. Fizemos, ainda, um estudo estatístico do perfil de avalanches do modelo, e obtemos perfis de avalanche em leis de potência, o que normalmente não é observado em outros sistemas unidimensionais. Analisamos, ainda, como esses perfis variam na medida que se aumenta o confinamento, e usando transformações de escala encontramos uma curva universal para os perfis de distribuição de tamanhos de avalanche. Nossos resultados demonstram que a ação do confinamento em um sistema unidimensional pode levar ao surgimento da invariância de escala.

Orientador: Prof. Dr. Alysson Fábio Ferrari / Tese (doutorado) - Universidade Federal do ABC, Programa de Pós-Graduação em Física, 2017. / As deformações do espaço-tempo têm sido bastante estudadas desde diferentes abordagens tais como a não comutatividade canônica e deformações via álgebras de Hopf, com a motivação de que estas deformações podem aparecer a escalas de altas energias, como por exemplo a escala de Planck. De igual forma, pode-se buscar estender deformações para a estrutura do superespaço e a supersimetria, e assim estudar o comportamento clássico e quântico, como a invariância supersimétrica e renormalizabilidade, em modelos definidos sobre estas estruturas. Dois tipos de deformações possíveis da supersimetria foram estudadas neste trabalho. O primeiro deles envolve a introdução de um produto não comutativo em (3+1) dimensões, que embora seja um produto não associativo e que quebra a álgebra da supersimetria, permite construir um modelo de Wess-Zumino com correções de derivadas de ordem superior do tipo Lee-wick, e que resultam ser invariante sob as transformações da SUSY usual. O segundo tipo de deformação estudado utiliza o conceito de álgebras de Hopf, através de um twist de Drinfel¿d. No caso do modelo de Wess-Zumino em (2 + 1) dimensões, veremos que apesar de que as estruturas sejam construídas de forma consistente e seja possível preservar a álgebra da SUSY usando geradores deformados, o modelo resulta não ser invariante sob esta última e não renormalizável. Também foi usado o formalismo de twist para um modelo de Chern-simons com SUSY N = 2 em (2 + 1) dimensões, que permite construir um modelo invariante de calibre, no entanto a invariância da SUSY não seja evidente. Neste modelo, embora em principio a álgebra da SUSY pode ser preservada pelo uso de geradores deformados, estes tornam-se bastante complicados, dificultando a prova da invariância supersimétrica. Pode-se concluir que existem diferentes formas de deformar as estruturas algébricas da supersimetria e que devido aos vínculos de cada modelo em específico torna-se difícil a construção de modelos que preservem algumas das propriedades importantes de modelos supersimétricos que se estudam, tais como a invariância e renormalização. / The space-time deformations have been well studied using different approaches, like as canonical commutativity and deformations via Hopf algebras, with the motivation of such deformations can appear in high scale energies, for example, planck scales. The same way, they can extend deformations to superspace and supersymmetry structures, and thus, study the quantum and classical behavior, like as the supersymmetry invariance and renormalizability, in models defined on these structures. Two classes of possible transformation of supersymmetry were studied in this work. The first one involves the introduction of one non commutative product in (3 + 1) dimensions, although it is not associative and breaks the supersymmetry algebra. It allows the construction of a Wess- Zumino model with higher order derivatives corrections like as Lee-Wick models, and it is invariant under usual SUSY transformations. The second deformation class studied utilizes the Hopf algebra concept, through Drinfel¿d twist. In the Wess-Zumino case in (2 + 1) dimensions, we can observe, although, the construction of the algebraic structure is consistent and it is possible preserve the SUSY algebra using deformed generators, the model is not invariant under this last and non renormalizable, also the twist formalism was used to Chern-Simons model N = 2 in (2 + 1) dimensions, it allows to construct an invariant gauge model, however the SUSY invariance is not evident. In this model, although the SUSY algebra can be preserved using the deformed generators, they become complicated, making it difficult to prove the supersymmetric invariance. It is possible to conclude that there are different ways to deform the algebraic structures of supersymmetry and because of the constraints of each specific model, it is difficult the construction of models which preserve some important properties of supersymmetry models studies, like as invariance and renormalizability.

In this thesis, we first review the current development of optimal regression designs under the second-order least squares estimator in the literature. The criteria include A- and D-optimality. We then introduce a new formulation of A-optimality criterion so the result can be extended to c-optimality which has not been studied before. Following Kiefer's equivalence results, we derive the optimality conditions for A-, c- and D-optimal designs under the second-order least squares estimator. In addition, we study the number of support points for various regression models including Peleg models, trigonometric models, regular and fractional polynomial models. A generalized scale invariance property for D-optimal designs is also explored. Furthermore, we discuss one computing algorithm to find optimal designs numerically. Several interesting applications are presented and related MATLAB code are provided in the thesis. / Graduate

abstract: Measurement invariance exists when a scale functions equivalently across people and is therefore essential for making meaningful group comparisons. Often, measurement invariance is examined with independent and identically distributed data; however, there are times when the participants are clustered within units, creating dependency in the data. Researchers have taken different approaches to address this dependency when studying measurement invariance (e.g., Kim, Kwok, & Yoon, 2012; Ryu, 2014; Kim, Yoon, Wen, Luo, & Kwok, 2015), but there are no comparisons of the various approaches. The purpose of this master's thesis was to investigate measurement invariance in multilevel data when the grouping variable was a level-1 variable using five different approaches. Publicly available data from the Early Childhood Longitudinal Study-Kindergarten Cohort (ECLS-K) was used as an illustrative example. The construct of early behavior, which was made up of four teacher-rated behavior scales, was evaluated for measurement invariance in relation to gender. In the specific case of this illustrative example, the statistical conclusions of the five approaches were in agreement (i.e., the loading of the externalizing item and the intercept of the approaches to learning item were not invariant). Simulation work should be done to investigate in which situations the conclusions of these approaches diverge. / Dissertation/Thesis / Masters Thesis Psychology 2016

abstract: A simulation study was conducted to explore the influence of partial loading invariance and partial intercept invariance on the latent mean comparison of the second-order factor within a higher-order confirmatory factor analysis (CFA) model. Noninvariant loadings or intercepts were generated to be at one of the two levels or both levels for a second-order CFA model. The numbers and directions of differences in noninvariant loadings or intercepts were also manipulated, along with total sample size and effect size of the second-order factor mean difference. Data were analyzed using correct and incorrect specifications of noninvariant loadings and intercepts. Results summarized across the 5,000 replications in each condition included Type I error rates and powers for the chi-square difference test and the Wald test of the second-order factor mean difference, estimation bias and efficiency for this latent mean difference, and means of the standardized root mean square residual (SRMR) and the root mean square error of approximation (RMSEA). When the model was correctly specified, no obvious estimation bias was observed; when the model was misspecified by constraining noninvariant loadings or intercepts to be equal, the latent mean difference was overestimated if the direction of the difference in loadings or intercepts of was consistent with the direction of the latent mean difference, and vice versa. Increasing the number of noninvariant loadings or intercepts resulted in larger estimation bias if these noninvariant loadings or intercepts were constrained to be equal. Power to detect the latent mean difference was influenced by estimation bias and the estimated variance of the difference in the second-order factor mean, in addition to sample size and effect size. Constraining more parameters to be equal between groups—even when unequal in the population—led to a decrease in the variance of the estimated latent mean difference, which increased power somewhat. Finally, RMSEA was very sensitive for detecting misspecification due to improper equality constraints in all conditions in the current scenario, including the nonzero latent mean difference, but SRMR did not increase as expected when noninvariant parameters were constrained. / Dissertation/Thesis / Masters Thesis Educational Psychology 2016

O objetivo deste trabalho é apresentar algoritmos aplicados para extração de características invariantes à rotação em imagens de impressões digitais. No pré-processamento da imagem utiliza-se detecção de bordas pelo detector de Canny tendo como resultado uma imagem binarizada e afinada. Na extração das minúcias a metodologia adotada é o número de cruzamentos (CN), que extrai os aspectos locais, tais como, as minúcias fim de linha e bifurcações. A direção das cristas locais não é utilizada porque nas imagens rotacionadas a condição de permanência das propriedades biométricas não são satisfeitas. A comparação das impressões digitais utiliza os vetores gerados pela extração de minúcias considerando a posição (x,y) da minúcia armazenada em um vetor por tipo de minúcia (um vetor para crista final e outro vetor para crista bifurcada) e calculando a distância Euclidiana dessa posição (x,y) ao centro de massa da distribuição de minúcias para cada tipo de minúcia. Assim, as duas imagens são similares quando a distância Euclidiana entre os vetores de cada imagem e por tipo de minúcia forem mínimas. São discutidas as limitações de outros trabalhos existentes envolvendo rotação, translação e distorção da imagem de impressão digital, mostrando que os poucos trabalhos que tratam o problema possuem resultados não satisfatórios. Os maiores problemas ocorridos foram a extração de minúcias espúrias, mas foram resolvidos com os métodos sugeridos por Dixon (1979), tendo resultados satisfatórios em duas metodologias. No método média, a precisão para encontrar uma imagem foi de 100%, duas imagens 97,32%, três imagens 92,35%, quatro imagens 86,41% e cinco imagens 71,86%. E no método normal, a precisão para encontrar uma imagem foi de 100%, duas imagens 99,20%, três imagens 96,95%, quatro imagens 94,00% e cinco imagens 76,43%. / The objective of this research is to present algorithms that can be applied in fingerprints images in order to extract certain features, which are invariant to an likely rotation in the given image. In the preprocessing stage, the Canny border detector is used, resulting in a binary, fine tuned image. For the minutiae extraction, the crossing number method is used, which extracts local aspects such as minutiae endings and bifurcations. The direction of local ridges is ignored because, in rotated images, the permanence conditions of the biometric attributes are not fulfilled. The process of matching fingerprints uses two arrays (one for ridge endings and the other for bifurcations), which are generated by the extraction of the minutiae, considering the (x,y) coordinate of the given minutiae stored in the arrays, and calculating its Euclidian distance relating to the center of mass of the minutiae distribution, for each of its types (ending or bifurcation). Thus, both images are similar when the Euclidian distance between the arrays of each image, distinct by the type of each minutiae, is minimal. The limitations of other pieces of research works concerning fingerprint image rotation, translation and distortion are discussed, indicating that the only few ones that deal with these kinds of problems give unsatisfactory results.