Recent years have seen progress in the analysis of the heat kernel for certain reversible random walks in random environments. In particular the work of Barlow(2004) showed that the heat kernel for the random walk on the infinite component of supercritical bond percolation behaves in a Gaussian fashion. This heat kernel control was then used to prove a quenched functional central limit theorem. Following this work several examples have been analysed with anomalous heat kernel behaviour and, in some cases, anomalous scaling limits. We begin by generalizing the first result - looking for sufficient conditions on the geometry of the environment that ensure standard heat kernel upper bounds hold. We prove that these conditions are satisfied with probability one in the case of the random walk on continuum percolation and use the heat kernel bounds to prove an invariance principle. The random walk on dynamic environment is then considered. It is proven that if the environment evolves ergodically and is, in a certain sense, geometrically d-dimensional then standard on diagonal heat kernel bounds hold. Anomalous lower bounds on the heat kernel are also proven - in particular the random conductance model is shown to be "more anomalous" in the dynamic case than the static. Finally, the reflected random walk amongst random conductances is considered. It is shown in one dimension that under the usual scaling, this walk converges to reflected Brownian motion.

Neural responses in the primate ventral visual system become more complex in the later stages of the pathway. For example, not only do neurons in IT cortex respond to complete objects, they also learn to respond invariantly with respect to the viewing angle of an object and also with respect to the location of an object. These types of neural responses have helped guide past research with VisNet, a computational model of the primate ventral visual pathway that self-organises during learning. In particular, previous research has focussed on presenting to the model one object at a time during training, and has placed emphasis on the transform invariant response properties of the output neurons of the model that consequently develop. This doctoral thesis extends previous VisNet research and investigates the performance of the model with a range of more challenging and ecologically valid training paradigms. For example, when multiple objects are presented to the network during training, or when objects partially occlude one another during training. The different mechanisms that help output neurons to develop object selective, transform invariant responses during learning are proposed and explored. Such mechanisms include the statistical decoupling of objects through multiple object pairings, and the separation of object representations by independent motion. Consideration is also given to the heterogeneous response properties of neurons that develop during learning. For example, although IT neurons demonstrate a number of differing invariances, they also convey spatial information and view specific information about the objects presented on the retina. A updated, scaled-up version of the VisNet model, with a significantly larger retina, is introduced in order to explore these heterogeneous neural response properties.

This research outlines a conceptual framework and data analysis process to examine multisource feedback (MSF) rater group differences from a leadership assessment survey, after testing the measures for equivalence. MSF gathers and compares ratings from supervisors, peer, followers and self and is the predominant leadership assessment tool in the United States. The results of MSF determine significant professional outcomes such as leadership development opportunities, promotions and compensation. An underlying belief behind the extensive use of MSF is that each rater group has a different set of implicit leadership theories (ILTs) they use when assessing the leader, and therefore each group is able to contribute unique insight. If this is true, research findings would find rater group consistency in leadership assessment outcomes, but they do not. A review of group comparison research reveals that most empirical MSF studies fail to perform preliminary data exploration, employ consistent models or adequately test for measurement equivalence (ME); yet industry standards strongly suggest exploratory methods whenever data sets undergo changes, and misspecified models cause biased results. Finally, ME testing is critical to ascertain if rater groups have similar conceptualizations of the factors and items in an MSF survey. If conceptual ME is not established, substantive group comparisons cannot be made. This study draws on the extant MSF, ILT and ME literature and analyzes rater group data from a large, application-based MSF leadership database. After exploring the data and running the requisite MI tests, I found that the measures upheld measurement invariance and were suitable for group comparison. Additional MI tests for substantive hypotheses support found that significant mean differences did exist among certain rater groups and dimensions, but only direct report and peer groups were consistently significantly different in all four dimensions (analytical, interpersonal, courageous and leadership effectiveness). Additionally, the interpersonal dimension was the most highly correlated with leadership effectiveness in all five rater groups. The overall findings of this study address the importance of MSF data exploration, offer alternative explanations to the disparate leadership MSF research findings to date and question the application use of MSF tools in their current form.

Aim Satisfaction with life is a measure of protection in older adults. There lies the importance of providing quality instruments. The aim of the study was to evaluate the invariance of the life satisfaction scale (SWLS) in two samples of older adults in Spain and Peru. Method The participants were 857 older adults in Spain (mean age = 68.23 years, SD = 5.93) and 336 older adults in Peru (average age = 72.42, SD = 7.07). All multi-group confirmatory factor analyzes were estimated in Mplus 8.0. Results The results indicate the presence of a strict invariance of the one-dimensional structure of the SWLS in samples of older adults in Spain and Peru, which allows for meaningful comparisons of latent means and covariances. Comparison of latent means showed small differences in the construct between the cultural groups. Conclusions The SWLS is a valid instrument for intercultural comparisons between Spanish and Peruvian population. The measurement invariance assessment contributes to a better understanding of life satisfaction in populations from different cultural contexts. / Objetivo La satisfacción con la vida es una medida de protección en los adultos mayores. Aquí radica la importancia de tener instrumentos de calidad para medirla. El objetivo de este estudio fue evaluar la invarianza de la Escala de Satisfacción con la Vida (SWLS) en 2 muestras de adultos mayores de España y Perú. Método Los participantes fueron 857 adultos mayores españoles (edad media: 68,23 años y DT: 5,93) y 336 adultos mayores peruanos (edad media: 72,42 años y DT: 7,07). Todos los análisis factoriales multi-muestra se estimaron en Mplus 8.0. Resultados Los resultados indican la presencia de una invarianza estricta de la estructura unifactorial de la SWLS en muestras de adultos mayores de España y Perú, lo que permite realizar comparaciones adecuadas, tanto de medias latentes como de relaciones con otras variables. La comparación de las medias latentes mostró pequeñas diferencias en el constructo entre las 2 culturas. Conclusiones La SWLS es una escala válida para realizar comparaciones transculturales entre poblaciones peruanas y españolas. La evaluación de la invarianza de medida contribuye a entender mejor la satisfacción vital desde contextos culturales diferentes.

<p>The power of positive attitudes toward science is that they influence science achievement by reinforcing higher performance. Interestingly, there continue to be gender disparities in attitudes toward science across many countries. Males generally have more positive attitudes toward science than females. Although most research related to attitudes toward science have been based on the Trends in International Mathematics and Science Study (TIMSS) Student Questionnaire, there remains a dearth of evidence validating the TIMSS science attitudes items and measurement equivalence across genders. </p><p>The goals of this research were as follows: (1) to build support for the structural validity of the TIMSS items, and (2) to investigate whether the instrument measures the same latent construct (attitudes toward science) across genders. The present study followed two steps of statistical analyses. As a first step, two modeling methods (confirmatory factor analysis and exploratory structural equation modeling) were conducted to identify the best-fitting model for the instrument. Second, after determining the model of choice, we tested several nested invariance models progressively. </p><p>This study found (1) the latent factor structure of the TIMSS items and (2) strong measurement invariance across genders. This result indicated that the instrument is well designed by the <i>a priori</i>specification and measures the same latent variable for both female and male students. This study provides support for the multidimensional approach to measuring science attitudes and shows the flexibility of ESEM over CFA by demonstrating that the ESEM approach provided better representation of the underlying factor structure. </p>

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.

Estudamos nesta dissertação o conteúdo de operadores da cadeia quântica do modelo XY anisotrópico com interações de três spins (XY triplete anisotrópico). Verificamos que, como no caso de interações de dois spins, este modelo pode ser visto como uma superposição de duas cadeias quânticas Ising, que neste caso apresentam interações de três spins (Ising triplete). Como conseqüência, todo o conteúdo de operadores do modelo XY triplete é obtido através de um estudo sistemático do conteúdo de operadores do Ising triplete o que é feito numericamente explorando-se as relações entre as lacunas de massa e as dimensões anômalas dos operadores do modelo, previstas pela invariância conforme. / We study in this work the operator content of the staggered XY model quantum chain with three-spin interactions (staggered XY triplet). We verified that, as quantum Ising chains, but in this case with three-spin interactions (Ising triplet). It is possible therefore to obtain all the operator content of the XY triplet model by a systematic numerical analysis of the Ising triplet´s operator content, which follows by exploiting the relations between the mass gap amplitudes and the anomalous dimension of the operators of the model, predicted by conformal invariance.

O conceito de indistinguibilidade em uma estrutura, entendido como invariância sob os automorfismos dessa estrutura, é apresentado, analisado e aplicado ao exa me do problema filosófico dos objetos indistinguíveis. Especialmente considerada é a versão desse problema que aparece na teoria quântica. / The concept of indistinguishability in a structure, understood as invariance under the automorphisms of that structure, is presented, analysed and applied to the examination of the philosophical problem of indistinguishable objects. Specially considered is the version of this problem that appears in the quantum theory.

Classificação de imagens de textura, especialmente aquelas com mudanças significativas de rotação, iluminação, escala e ponto de vista, é um problema fundamental e desafiador na área de visão computacional. Esta tese propõe dois descritores de imagem simples, porém eficientes, chamados de Sampled Local Mapped Pattern Magnitude (SLMP_M) e Completed Local Mapped Pattern (CLMP) aplicados na classificação de textura. Os descritores propostos são parte de um aprimoramento do descritor Local Mapped Pattern (LMP) para trabalhar de maneira eficiente com imagens de textura rotacionadas. Os métodos propostos necessitam de um pré-ajuste de parâmetros que utiliza o método de otimização por enxame de partículas, e são discriminativos e robustos para a descrição de texturas rotacionadas em ângulos arbitrários. Para a validação dos descritores propostos duas bases de imagens são utilizadas, Kylberg Sintorn Rotation Dataset e Brodatz Texture Rotation Dataset, uma nova base de dados desenvolvida pela autora, formada por imagens de texturas rotacionadas do Álbum de Brodatz. As duas bases contêm imagens de texturas naturais que foram rotacionadas fisicamente no momento da captura e rotacionadas por processos computacionais. É feita também uma avaliação da influência de métodos de interpolação no processo de rotação das imagens e são comparados com diferentes descritores presentes na literatura. Cinco métodos de interpolação são investigados: Lanczos, B-spline, Cúbica, Linear e Nearest Neighbor. Os resultados experimentais demonstram que os descritores propostos nesta tese superam o desempenho dos descritores Completed Local Binary Pattern (CLBP), e dos descritores que combinam a versão generalizada das características de Fourier com variações do descritor Local Binary Pattern (LBP), LBPDFT, ILBPDFT, LTPDFT e ILTPDFT. Os resultados também demonstram que a escolha do método de interpolação no processo de rotação das imagens influencia na capacidade de reconhecimento. / Texture image classification, especially those with significant changes of rotation, illumination, scale and point of view, is a fundamental and challenging problem in the field of computer vision. This thesis proposes two simple, but efficient, image descriptors called Sampled Local Mapped Pattern Magnitude (SLMP_M) and Completed Local Mapped Pattern (CLMP) applied in texture classification. The proposed descriptors are part of an enhancement to the Local Mapped Pattern (LMP) descriptor to work efficiently with rotated texture images. The descriptors proposed requires a parameter preset by the particle swarm optimization method, they are discriminating and robust for the description of rotated textures at arbitrary angles. For the validation of the proposed descriptors two image datasets are used: Kylberg Sintorn Rotation Dataset and Brodatz Texture Rotation Dataset, a new texture dataset introduced, which contains rotated texture images from Brodatzs Album. Both databases contain images of natural textures that have been rotated by Hardware and computational procedures. An evaluation of the influence of interpolation methods on the image rotation process is also presented and compared with different descriptors in the literature. Five interpolation methods are investigated: Lanczos, B-spline, Cubic, Linear and Nearest Neighbor. The experimental results show that the descriptors proposed in this thesis outperform the performance of the Completed Local Binary Pattern (CLBP) descriptors, and the descriptors that combine the generalized version of the Fourier characteristics with variations of the descriptor Local Binary Pattern (LBP), LBPDFT, ILBDFT, LTPDFT e ILTPDFT compared. The results also prove that the selection of the interpolation method in the image rotation process influences the recognition capability.

Data from rating scale assessments have rank-invariant properties only, which means that the data represent an ordering, but lack of standardized magnitude, inter-categorical distances, and linearity. Even though the judgments often are coded by natural numbers they are not really metric. The aim of this thesis is to further develop the nonparametric rank-based Svensson methods for paired ordinal data that are based on the rank-invariant properties only. The thesis consists of five papers. In Paper I the asymptotic properties of the measure of systematic disagreement in paired ordinal data, the Relative Position (RP), and the difference in RP between groups were studied. Based on the findings of asymptotic normality, two tests for analyses of change within group and between groups were proposed. In Paper II the asymptotic properties of rank-based measures, e.g. the Svensson’s measures of systematic disagreement and of additional individual variability were discussed, and a numerical method for approximation was suggested. In Paper III the asymptotic properties of the measures for paired ordinal data, discussed in Paper II, were verified by simulations. Furthermore, the Spearman rank-order correlation coefficient (rs) and the Svensson’s augmented rank-order agreement coefficient (ra) were compared. By demonstrating how they differ and why they differ, it is emphasized that they measure different things. In Paper IV the proposed test in Paper I for comparing two groups of systematic changes in paired ordinal data was compared with other nonparametric tests for group changes, both regarding different approaches of categorising changes. The simulation reveals that the proposed test works better for small and unbalanced samples. Paper V demonstrates that rank invariant approaches can also be used in analysis of ordinal data from multi-item scales, which is an appealing and appropriate alternative to calculating sum scores.