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In this thesis, assuming that higher spatial dimensions existed only during the inflationary prematter phases of the universe, we construct a (1+D)-dimensional (D&gt / 3), nonsingular, homogeneous and isotropic Friedmann model for dimensional reduction. In this model, dimensional reduction occurs in the form of a phase transition that follows from a purely thermodynamical consideration that the universe heats up during the inflationary prematter phases. When the temperature reaches its Planck value Tpl,D, which is taken as the maximum attainable physical temperature, the phase of the universe changes from one prematter era with D space dimensions to another prematter era with ( D-1) space dimensions where T_pl,D is higher. In this way, inflation gets another chance to continue in the lower dimension and the reduction process stops when we reach D=3 ordinary space dimensions. As a specific model, we investigate the evolution of a (1+4)-dimensional universe and see that dimensional reduction occurs when a critical length parameter l_4,3 reaches the Planck length of the lower dimension. Although the predictions of our model for the cosmological parameters are beyond the ranges accepted by recent measurements for closed geometry, for a broad range of initial conditions they are within the acceptable ranges for open geometry

Fault detection and diagnosis presents a big challenge within the petrochemical industry. The annual economic impact of unexpected shutdowns is estimated to be $20 billion. Assistive technologies will help with the effective detection and classification of the faults causing these shutdowns. Clustering analysis presents a form of unsupervised learning which identifies data with similar properties. Various algorithms were used and included hard-partitioning algorithms (K-means and K-medoid) and fuzzy algorithms (Fuzzy C-means, Gustafson-Kessel and Gath-Geva). A novel approach to the clustering problem of time-series data is proposed. It exploits the time dependency of variables (time delays) within a process engineering environment. Before clustering, process lags are identified via signal cross-correlations. From this, a least-squares optimal signal time shift is calculated. Dimensional reduction techniques are used to visualise the data. Various nonlinear dimensional reduction techniques have been proposed in recent years. These techniques have been shown to outperform their linear counterparts on various artificial data sets including the Swiss roll and helix data sets but have not been widely implemented in a process engineering environment. The algorithms that were used included linear PCA and standard Sammon and fuzzy Sammon mappings. Time shifting resulted in better clustering accuracy on a synthetic data set based on than traditional clustering techniques based on quantitative criteria (including Partition Coefficient, Classification Entropy, Partition Index, Separation Index, Dunn’s Index and Alternative Dunn Index). However, the time shifted clustering results of the Tennessee Eastman process were not as good as the non-shifted data. Copyright / Dissertation (MEng)--University of Pretoria, 2009. / Chemical Engineering / unrestricted

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No / This paper describes a novel approach to the fusion of multidimensional images for colour displays. The goal of the method is to generate an output image whose gradient matches that of the input as closely as possible. It achieves this using a constrained contrast mapping paradigm in the gradient domain, where the structure tensor of a high-dimensional gradient representation is mapped exactly to that of a low-dimensional gradient field which is subsequently reintegrated to generate an output. Constraints on the output colours are provided by an initial RGB rendering to produce ‘naturalistic’ colours: we provide a theorem for projecting higher-D contrast onto the initial colour gradients such that they remain close to the original gradients whilst maintaining exact high-D contrast. The solution to this constrained optimisation is closed-form, allowing for a very simple and hence fast and efficient algorithm. Our approach is generic in that it can map any N-D image data to any M-D output, and can be used in a variety of applications using the same basic algorithm. In this paper we focus on the problem of mapping N-D inputs to 3-D colour outputs. We present results in three applications: hyperspectral remote sensing, fusion of colour and near-infrared images, and colour visualisation of MRI Diffusion-Tensor imaging.

Compressive sensing (CS) is a novel imaging technology based on the inherent redundancy of natural scenes. The minimum number of required measurements which defines the maximum image compression rate is lower-bounded by the sparsity of the image but is dependent on the type of acquisition patterns employed. Increased measurements by the Rice single pixel camera (SPC) slows down the acquisition process, which may cause the image recovery to be more susceptible to background noise and thus limit CS's application in imaging, detection, or classifying moving targets. In this study, two methods (hybrid-subspace sparse sampling (HSS) for imaging and secant projection on a manifold for classification are applied to solving this problem. For the HSS method, new image pattern are designed via robust principle component analysis (rPCA) on prior knowledge from a library of images to sense a common structure. After measuring coarse scale commonalities, the residual image becomes sparser, and then fewer measurements are needed. For the secant projection case, patterns that can preserve the pairwise distance between data points based on manifold learning are designed via semi-definite programming. These secant patterns turn out to be better in object classification over those learned from PCA. Both methods considerably decrease the number of required measurements for each task when compared with the purely random patterns of a more universal CS imaging system.

The standard Kaluza-Klein theory is reviewed and its basic equations are rewritten in an anholonomic basis. A five dimensional Yang-Mills type quadratic and cubic curvature gravity model is introduced. By employing the Palatini variational principle, the field equations and the stress-energy tensors of these models are presented. Unification of gravity with electromagnetism is achieved through the Kaluza-Klein reduction mechanism. Reduced curvature invariants,field equations and stress-energy tensors in four dimensional space-time are obtained. The structure of interactions among the gravitational, electromagnetic and massless scalar fields are demonstrated in detail. It is shown that in addition to a set of generalized Maxwell and Yang-Mills type gravity equations the Lorentz force also emerges from this theory. Solutions of the standard Kaluza-Klein theory are explicitly demonstrated to be intrinsically contained in the quadratic model.

Submitted by Rafael Silva Santos (rafael.silva.sts@gmail.com) on 2018-04-19T01:03:05Z No. of bitstreams: 1 Dissertacao - Rafael Silva Santos - vDeposito.pdf: 42155755 bytes, checksum: fb36b8d70ad22da512d7f23dc3a13691 (MD5) / Approved for entry into archive by Elza Mitiko Sato null (elzasato@ibilce.unesp.br) on 2018-04-19T14:25:43Z (GMT) No. of bitstreams: 1 santos_rs_me_sjrp.pdf: 42155755 bytes, checksum: fb36b8d70ad22da512d7f23dc3a13691 (MD5) / Made available in DSpace on 2018-04-19T14:25:44Z (GMT). No. of bitstreams: 1 santos_rs_me_sjrp.pdf: 42155755 bytes, checksum: fb36b8d70ad22da512d7f23dc3a13691 (MD5) Previous issue date: 2018-03-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Funções de transferência (FTs) são uma parte crucial do processo de exploração volumétrica em Visualização Direta de Volumes. Nesse processo, FTs desempenham duas tarefas principais: a classificação de materiais e o mapeamento de informações presentes nos dados para propriedades visuais. A busca por uma solução que lide com ambas as tarefas envolve uma série de fatores que, em conjunto, são um dos maiores desafios de visualização volumétrica. Neste trabalho, propomos uma abordagem de exploração que tem por objetivo envolver todo escopo e simplificar tanto a definição de FTs multidimensionais quanto a manipulação de datasets. A abordagem se organiza em três componentes: uma heurística baseada em entropia e correlação que guia a seleção de atributos para formação do espaço de entrada; um método de classificação que emprega a técnica de redução de dimensionalidade FastMap e a técnica de agrupamento DBSCAN para proporcionar a descoberta semiautomática de características volumétricas; e uma interface simplificada que, atrelada ao método de classificação, produz um gráfico de dispersão 2D de características para a exploração do volume. Inicialmente, o usuário deve analisar o ranking de atributos para formar um espaço multidimensional. Depois, deve escolher parâmetros para gerar o gráfico de características. Finalmente, deve navegar por esse gráfico a fim de identificar materiais ou estruturas relevantes. Nos experimentos realizados para avaliar a abordagem, os mecanismos disponibilizados permitiram encontrar e isolar de forma efetiva características inseridas em todos os datasets investigados. Aponta-se ainda como contribuição o baixo custo computacional, na prática, a complexidade de tempo do método de classificação é de O (n log n). O tempo de execução foi inferior a 11 segundos, mesmo quando datasets formados por cerca de 10 milhões de instâncias e com mais de 10 dimensões são utilizados. / Transfer functions (TFs) are a crucial part of the volume exploration process in Direct Volume Rendering. In this process, TFs perform two main tasks: material classification and mapping of information to visual properties. The search for a solution that copes with both tasks involves a number of factors that, together, is one of the greatest challenges of volume visualization. In this work, we propose an exploration approach that aims to involve the entire scope and a simplify both the definition of multidimensional TFs and the manipulation of datasets. The approach is organized into three components: a heuristic based on entropy and correlation that guides the selection of attributes to conceive the input space; a classification method, which uses the dimensionality reduction technique FastMap and the clustering technique DBSCAN to provide a semiautomatic features finding; and a simplified interface that, linked to the previous method, provide a 2D scatter plot of features for volume exploration. Initially, the user must analyze at the ranking of attributes to form a multidimensional space. Afterwards, it must choice parameters to generate the scatter plot. Finally, it must navigate through this chart in order to reveal relevant materials and features. In the experiments performed to evaluate the approach, the available mechanisms allow to effectively find and isolate features inserted in all investigated datasets. It is also pointed out as contribution a low computational cost, in practice the time complexity of the classification method is O(n log n). The runtime was less than 11 seconds, even when datasets formed by about 10 million instances and with more than 10 dimensions are used.

We present the supersymmetry and localization of an N=2 theory on S3b along with that of an N=(2,2) theory on S2. Performing the dimensional reduction of the theory on S3b produces a theory on S2 with no flux-sectors. A re-evaluated version of twisted reduction is applied on the level of the S3b partition function, arguing for a splitting of the partition function into pieces. The splitting produces flux-like sectors correspondent to the S2 theory but holds the potential for superfluous sectors. An argument interpreting these sectors as true flux is given and utilized to remove superfluous sectors due to topological restrictions on S2. The final result is a method which gives a bijective mapping ZS3b to ZS2 . / Vi utför konstruktionen av två supersymmetriska teorier på en deformerad 3-sfär samt en 2-sfär. Den utökade symmetrin tillåter oss att använda en lokaliseringsmetod för att reducera partitionsfunktionerna till ändligt-dimensionella integraler. På 2-sfären finner vi diskreta konfigurationer vars tolkning vi vill finna i konstruktionen på 3-sfären. Vi utför en dimensionell reduktion ifrån 3-sfären till 2-sfären och finner en ekvivalens som saknar dessa konfigurationer. Som substitut presenteras en metod där integralen delas upp i delar som kan tolkas att vara ekvivalenta med de avsaknade diskreta konfigurationerna. Slutligen framförs ett argument för vilka delar av integralen som kan existera på 2-sfären och resterande delar avfärdas. Resultatet är en exakt avbilding mellan partitionsfunktionerna.

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