abstract: Researchers who conduct longitudinal studies are inherently interested in studying individual and population changes over time (e.g., mathematics achievement, subjective well-being). To answer such research questions, models of change (e.g., growth models) make the assumption of longitudinal measurement invariance. In many applied situations, key constructs are measured by a collection of ordered-categorical indicators (e.g., Likert scale items). To evaluate longitudinal measurement invariance with ordered-categorical indicators, a set of hierarchical models can be sequentially tested and compared. If the statistical tests of measurement invariance fail to be supported for one of the models, it is useful to have a method with which to gauge the practical significance of the differences in measurement model parameters over time. Drawing on studies of latent growth models and second-order latent growth models with continuous indicators (e.g., Kim & Willson, 2014a; 2014b; Leite, 2007; Wirth, 2008), this study examined the performance of a potential sensitivity analysis to gauge the practical significance of violations of longitudinal measurement invariance for ordered-categorical indicators using second-order latent growth models. The change in the estimate of the second-order growth parameters following the addition of an incorrect level of measurement invariance constraints at the first-order level was used as an effect size for measurement non-invariance. This study investigated how sensitive the proposed sensitivity analysis was to different locations of non-invariance (i.e., non-invariance in the factor loadings, the thresholds, and the unique factor variances) given a sufficient sample size. This study also examined whether the sensitivity of the proposed sensitivity analysis depended on a number of other factors including the magnitude of non-invariance, the number of non-invariant indicators, the number of non-invariant occasions, and the number of response categories in the indicators. / Dissertation/Thesis / Doctoral Dissertation Psychology 2016

We introduce the historical context and motivation for the search for magnetic monopoles or monopole-like objects. Beginning the theoretical part we investigate the properties of groups as they relate to symmetries in physical theories. Using this as a basis we investigate the requirements for global and local gauge invariance for a scalar field, the latter giving the non-trivial connection to a gauge field. From this we present the Georgi-Glashow model and develop its particle spectrum using the connected Higgs field and its associated Higgs mechanism. We then present the electromagnetic duality by extending the Maxwell's equations toinclude magnetic sources. Using the assumption of magnetic sources we present the Dirac quantization condition, motivating the quantization of electric charge. Returning to our model we present the 't Hooft-Polyakov ansatz and investigate its defining properties as a finite energy soliton in our Higgs field. We show the magnetic properties and motivate its validity as a monopole like object. Continuing we define BPS-states on the lower bound for the mass of a monopole like object with magnetic and electric charge. Giving a BPS monopole as a solution in the vein of 't Hooft and Polyakov. Returning to the electromagnetic duality we propose the Montonen-Olive conjecture by exchanging massive vector bosons in our model with the BPS monopoles we developed. We shortly comment on evident problems and present supersymmetry as a possible solution. Finally we present the Witten Effect by allowing a CP violating term in our Lagrangian. From this we extend the Montonen-Olive conjecture to include invariance under the SL(2,Z) group.

abstract: Investigation of measurement invariance (MI) commonly assumes correct specification of dimensionality across multiple groups. Although research shows that violation of the dimensionality assumption can cause bias in model parameter estimation for single-group analyses, little research on this issue has been conducted for multiple-group analyses. This study explored the effects of mismatch in dimensionality between data and analysis models with multiple-group analyses at the population and sample levels. Datasets were generated using a bifactor model with different factor structures and were analyzed with bifactor and single-factor models to assess misspecification effects on assessments of MI and latent mean differences. As baseline models, the bifactor models fit data well and had minimal bias in latent mean estimation. However, the low convergence rates of fitting bifactor models to data with complex structures and small sample sizes caused concern. On the other hand, effects of fitting the misspecified single-factor models on the assessments of MI and latent means differed by the bifactor structures underlying data. For data following one general factor and one group factor affecting a small set of indicators, the effects of ignoring the group factor in analysis models on the tests of MI and latent mean differences were mild. In contrast, for data following one general factor and several group factors, oversimplifications of analysis models can lead to inaccurate conclusions regarding MI assessment and latent mean estimation. / Dissertation/Thesis / Doctoral Dissertation Educational Psychology 2018

Neste trabalho, discutem-se aspectos das transformações conformes na eletrodinâmica clássica com ênfase na invariância e nas leis de conservação. Inicialmente, abordaram-se aspectos gerais das transformações conformes e fez-se um resumo histórico da evolução dessas transformações. Procurou-se fazer uma apresentação didática, revisando-se a formulação Lagrangiana e o Teorema de Noether para campos aplicado à eletrodinâmica. Estudaram-se as transformações conformes no espaço plano, onde se mostrou que para dimensões maiores ou iguais a três o número de transformações é finito. A partir das equações de Maxwell em coordenadas curvilíneas, chegou-se à condição para que essas equações mantivessem sua forma cartesiana. Com essa condição, mostrou-se que a eletrodinâmica clássica é invariante para o grupo de transformações conformes. Foram discutidas as leis de conservação associadas à invariância conforme da eletrodinâmica clássica a partir do teorema de Noether. Das simetrias por translações no espaço-tempo, obtiveram-se as leis de conservação do momento linear e da energia. Das simetrias associadas às rotações, obtiveram-se seis quantidades conservadas: três delas ligadas à conservação do momento angular e, com relação às três restantes, observou-se, a partir de analogias com a mecânica, que estavam associadas ao movimento do centro de energia do campo. Para a interpretação da grandeza conservada por simetria de escala, verificou-se, também a partir de uma analogia mecânica, que essa simetria somente é verificada para partículas não massivas ou para partículas massivas a altas energias. Finalmente, para as transformações conformes especiais, verificou-se que as leis de conservação resultantes são consequências das leis anteriores de conservação para o campo eletromagnético, e neste caso, essa simetria também somente se manifesta para partículas de massa nula ou para altas energias. / In this work, aspects of conformal transformations in classical electrodynamics are discussed with emphasis on the invariance and conservation laws. Initially, a general view of conformal transformations was shown and a summary of the historical evolution of those transformations was presented. The work was approached didactically, and Noethers theorem based on the electrodynamics Lagrangian formulation was revised. The conformal transformations were studied in plane spaces and it was shown that, for dimensions greater than or equal to three, the number of transformations is finite. Starting from Maxwells equations in curvilinear coordinates, a condition for maintaining those equations in Cartesian form was established. With that condition, it was shown that the classical electrodynamics laws are invariant for the group of conformal transformations. The conservation laws associated with the conformal invariance of classical electrodynamics were discussed, based on Noethers theorem. From the space-time translation symmetry, the laws of conservation of linear momentum and of energy were obtained. From rotational symmetry, six conserved quantities were obtained: three of them associated with angular momentum and the remaining three, observed, starting from analogies with mechanics, were associated with the movement of the center of energy of the field. For the interpretation of the quantity conserved by scale symmetry, it was verified, also from a mechanical analogy, that that symmetry is only valid for null mass particles or for high energies. Finally, for the special conformal transformations, it was verified that the resultant laws of conservation are consequences of the previous laws, and in that case, symmetry is also valid only for particles of null mass or for high energies.

Nesta tese estudamos as propriedades críticas dos modelos anisotrópicos (isotrópicos) de Heisenberg com spin s arbitrário. O espectro das Hamiltonianas, com condições periódicas de contorno, foi calculado para redes finitas, resolvendo-se as equações do Bethe ansatz associadas. Nossos resultados indicam que a anomalia conforme destes modelos tem o valor c=3s/(1+s), independente da anisotropia, e os expoentes críticos variam continuamente com a anisotropia assim como no modelo de 8-vértices. O conteúdo de operadores destes modelos indica que a teoria de campos que governa a criticalidade destes modelos de spin é descrita por operadores formados pelo produto de um operador Gaussiano por outro com simetria Z(2s). Estudando estes modelos, com certas condições especiais de contorno, mostramos que eles são relacionados com uma nova classe de teorias unitárias recentemente propostas / This thesis is concerned with the critical properties of anisotropic (isotropic) Heisenberg chain,with arbitrary spin-s. The eigenspectrum of these Hamiltoniana, with periodic boundaries, are calculated for finite chains by solving numerically their associated Bethe ansatz equations. The results indicate that the conformal anomaly hás the value c=3s/1+s, independently of the anisotropy, and the exponentes vary continuously with the anisotropy like in the 8-vertex model. The operator content of these models indicate that the underlying field theory governing these critical spin-s models are described by composite fields formed by the product of Gaussian and Z(2s) fields. Studying these models, with some special boundary conditions, we show that they are related with a large class of unitary conformal field theories recntly introduced

As técnicas de análise de estabilidade transitória em sistemas elétricos de potência desenvolveram-se significativamente nas últimas duas décadas. Atualmente, o principal desafio dos pesquisadores é a obtenção de técnicas que sejam adequadasa análises em tempo real. Neste sentido, as idéias de Liapunov associadas ao Princípio de Invariância de LaSalle têm sido utilizadas para estimar a bacia de atraçãoo dos sistemas de potência. Embora esta filosofia seja bastante adequada a análises de estabilidade em tempo real, existem alguns obstáculos que impedem a aplicação da mesma à análise de sistemas reais. Dentre estes obstáculos poder-se-ia destacar a impossibilidade de utilização de modelos mais realísticos e a limitação da análise ao primeiro "swing". Em verdade, estes obstáculos estão intimamente relacionados com as limitações do Princípio de Invariância de LaSalle. Para superar estes problemas, propõe-se, neste trabalho, uma extensão deste princípio que é mais geral e portanto mais flexível do que o original. Aproveitando esta maior flexibilidade, duas aplicações em análise de estabilidade transitória são abordadas, ambas com o objetivo de reduzir os obstáculos anteriormente mencionados. Na primeira, propõe-se uma nova função energia para sistemas de potência com perdas nas linhas de transmissão. Mostra-se que esta é uma função de Liapunov no sentido mais geral da extensão do Princípio de Invariância de LaSalle, podendo portanto ser empregada para estudos de estabilidade. Na segunda, uma metodologia de análise de estabilidade multi-"swing" é proposta com base em uma análise de coerência de geradores.

Muitos sistemas físicos são modelados por sistemas dinâmicos discretos. Com o advento da tecnologia digital os sistemas discretos tornaram-se ainda mais importantes, sendo assim, o desenvolvimento de ferramentas analíticas para este tipo de sistema é de grande importância. Neste trabalho, estudam-se alguns dos principais resultados relacionados à estabilidade de sistemas dinâmicos discretos, e alguns novos são propostos. É bem conhecido na literatura que a estabilidade de um ponto de equilíbrio pode ser caracterizada pelo Método Direto de Lyapunov, via uma função auxiliar denominada função de Lyapunov. LaSalle, ao estudar a teoria de Lyapunov, estabeleceu uma importante relação entre função de Lyapunov e conjuntos limites de Birkhoff, que deu origem ao Princípio de Invariância de LaSalle. Este, entre outras coisas, permite a análise de estabilidade assintótica. Tanto o Método Direto de Lyapunov quanto o Princípio de Invariância requerem que a variação da função de Lyapunov seja não positiva ao longo das trajetórias do sistema. Em sistemas com comportamentos mais complexos, dificilmente encontra-se uma função com esta propriedade. Neste trabalho, propõe-se uma versão mais geral do Princípio de Invariância para sistemas discretos, a qual não exige que a variação da função de Lyapunov seja sempre não positiva. Com isto, a obtenção de funções deste tipo torna-se mais simples e muitos problemas, que antes não poderiam ser tratados com a teoria convencional, passam a ser tratados através deste novo resultado. Os resultados desenvolvi- dos, neste trabalho, são úteis para encontrar estimativas de atratores de sistemas não-lineares discretos. / Many physical systems are modeled by discrete dynamic systems. With the evolution digital technology, the discrete systems became still more important, so the development of analytic tools for this type of system has high importance nowadays. ln this work, some of the main results in stability of discrete dynamic systems are studied and some new ones are proposed. lt is well known in the literature that the stability of an equilibrium point may be characterized by the Lyapunov\'s Direct Method, with a function known as Lyapunov auxiliary function. LaSalle, when studying the Lyapunov theory, established an important relationship between Lyapunov function and Birkhoff limit sets. Then, he created the Lasalle\'s lnvariance Principle. This, among other features, allows the analysis of asymptotically stability. Both the Lyapunov\'s Direct Method and the lnvariance Principle request the variation of the Lyapunov function to be negative semidefinite along the system trajectory. In systems with more complex behaviors, a function is hardly found with this property. This work developed a more general version of the lnvariance Principle for discrete systems, which does not require the variation of the Lyapunov function to be always negative semidefinite. This new theory enables to find these functions easily and many insoluble problems, which could not be treated with the conventional theory before, become treatable by this new result. The results of this work are useful to find estimates of discrete nonlinear systems atractors.

Along with continuously increasing computerization, our expectations on software and hardware reliability increase considerably. Therefore, software reliability has become one of the most important software quality attributes. Software reliability modeling based on test data is done to estimate whether the current reliability level meets the requirements for the product. Software reliability modeling also provides possibilities to predict reliability. Costs of software developing and tests together with profit issues in relation to software reliability are one of the main objectives to software reliability prediction. Software reliability prediction currently uses different models for this purpose. Parameters have to be set in order to tune the model to fit the test data. A slightly different prediction model, Time Invariance Estimation, TIE is developed to challenge the models used today. An experiment is set up to investigate whether TIE could be found useful in a software reliability prediction context. The experiment is based on a comparison between the ordinary reliability prediction models and TIE.

[pt] O tema da presente dissertação é o problema da demarcação entre os termos lógicos e extralógicos no âmbito das ciências formais, anunciado primeiramente por Alfred Tarski em seu artigo de 1936, On the Concept of Logical Consequence. Depois de expor e discutir o problema em questão, mostrando seu surgimento a partir da necessidade de uma definição materialmente adequada do conceito de conseqüência lógica, analisamos a solução formulada por Tarski em um artigo publicado postumamente, intitulado What Are Logical Notions? Algumas discussões subsidiárias, igualmente importantes para o trabalho como um todo, dizem respeito à concepção dos conceitos de modelo e interpretação que se podem depreender dos artigos supracitados, e de como ela difere da assim chamada concepção standard em teoria de modelos. Nosso objetivo principal é mostrar o lugar ocupado pelo conceito de forma lógica na obra de Tarski, e de como sua concepção acerca deste conceito implica uma visão ampliada do conceito de conseqüência lógica, cuja caracterização correta torna necessária a estratificação das formas lógicas numa hierarquia de tipos. / [en] The subject of this paper is the problem of demarcation between logical and extra-logical terms of formal languages, as formulated for the first time by Tarski in his 1936 paper On the Concept of Logical Consequence. After presenting and discussing the demarcation problem, pointing out how it arises from the need for a materially adequate definition of the concept of logical consequence, we analyze the solution presented by Tarski in his posthumously published paper, entitled What Are Logical Notions? Some subsidiary issues, that are also important for the work as a whole, concern the conception of model and interpretation that springs from the two papers mentioned, and how this conception differs from the standard conception in model theory. Our main goal is to show the place occupied by the concept of logical form in Tarski`s work, and how his conception of this concept implies a broader view about the related concept of logical consequence whose correct characterization makes necessary the stratification of logical forms into a hierarchy of types.

Le cinquième télescope (CT5) du réseau H.E.S.S. (High Energy Stereoscopic System) a été inauguré en 2012. H.E.S.S. est destiné à l’observation du ciel austral dans le domaine des rayons γ et CT5, dont le seuil est d’environ 30 GeV, a permis la détection du pulsar de Vela après 24 heures d’observations. Certains scénarios de gravitation quantique (QG) prédisent une violation d’invariance de Lorentz (LIV). Celle-ci se manifeste par l’ajout de termes ∝(E/EQG)n aux relations de dispersion du photon, où E est l’énergie du quanta de lumière, EQG l’énergie caractéristique des processus de QG et n l’ordre de la correction. Cette dépendance en énergie peut être testée par des mesures de temps de vol entre photons reçus de sources astrophysiques variables (noyaux actifs de galaxies), transitoires (sursauts γ) ou encore périodiques (pulsars). Cette thèse présente l’analyse des données recueillies par CT5 sur le pulsar de Vela. Une méthode de maximum de vraisemblance ayant déjà montré sa robustesse sur d’autres types de sources a été adaptée au cas du pulsar de Vela. Aucune déviation des relations de dispersion standard n’est observée, par conséquent des limites sont placées sur EQG. La plus contraignante est obtenue pour une correction linéaire superluminique aux relations de dispersion EQG > 7.0×1015 GeV. / The fifth telescope (CT5) of the H.E.S.S. array (High Energy Stereoscopic System) was inaugurated in 2012. H.E.S.S. is designed to scrutinize the southern γ ray sky and CT5, whose threshold is about 30 GeV, allowed the Vela pulsar detection in 24 hours observation time. Some quantum gravity (QG) scenarios predict a violation of Lorentz invariance (LIV). This could manifest by additional terms ∝(E/EQG)n to the photon dispersion relations, where E is the light quantum energy, EQG the typical scale at which QG processes are expected to occur and n the order of the correction. This energy dependence could be tested by time of flight measurements between photons emitted from variable (active galactic nuclei), transient (gamma ray bursts) or periodical (pulsars) astrophysical sources. This thesis presents the analysis of the CT5 collected data from the Vela pulsar. A maximum likelihood method already successfully applied to other source species has been adapted here to the Vela pulsar. No deviation from standard photon dispersion relations is observed, therefore limits have been placed on EQG. The most restrictive result has been obtained for a superluminal linear correction to the dispersion relations EQG > 7.0×1015 GeV.