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The study of tactile illusions like visual illusions can reveal the brain's processing strategies. A famous tactile illusion is the cutaneous rabbit illusion. Fundamental to this illusion is the perceptual length contraction phenomenon: two taps that occur in rapid succession on the forearm are perceived as occurring closer together than they were physically placed. Our lab previously proposed a Bayesian probabilistic model that views perception as a compromise between expectation (prior experience) and sensation (likelihood of sensorineural data given hypothesized tap locations). The model proposes a low-speed prior, an expectation based on experience that objects tend to be stationary or to move slowly on the skin. When the sensation of space is unclear (e.g., taps are weak), the model predicts that expectation will strongly influence perception. Consistent with this prediction, our lab previously showed that the use of weaker taps causes more pronounced perceptual length contraction. Here we report psychophysical tests on 64 participants, which confirmed this finding. Our study also used stimulus sequences consisting of a weak and a strong tap, for which the Bayesian model predicts an asymmetric perceptual length contraction, such that the weaker tap location will be perceived to shift more than the stronger tap. The experimental results confirmed this prediction, providing further support for our Bayesian probabilistic model as an explanation for perceptual length contraction. However, our results revealed a discrepancy in the data at the smaller SOAs, which showed less length contraction than predicted. We hypothesized that participants might overestimate the smaller SOAs, an effect our lab defines as time dilation. Accordingly, in a second study we investigated the effects of varying SOA and lengths on perceived SOA. The model predicts more pronounced time dilation at smaller SOAs and larger lengths. The psychophysical data from 37 participants confirmed the trends predicted by the model. / Thesis / Master of Science (MSc)

This dissertation consists of four independent but related parts, each in a Chapter. The first part is an introductory. It serves as the background introduction and offer preparations for later parts. The second part discusses two population multivariate normal distributions with common covariance matrix. The goal for this part is to derive objective/non-informative priors for the parameterizations and use these priors to build up constructive random posteriors of the Kullback-Liebler (KL) divergence of the two multivariate normal populations, which is proportional to the distance between the two means, weighted by the common precision matrix. We use the Cholesky decomposition for re-parameterization of the precision matrix. The KL divergence is a true distance measurement for divergence between the two multivariate normal populations with common covariance matrix. Frequentist properties of the Bayesian procedure using these objective priors are studied through analytical and numerical tools. The third part considers the star-shape Gaussian graphical model, which is a special case of undirected Gaussian graphical models. It is a multivariate normal distribution where the variables are grouped into one "global" group of variable set and several "local" groups of variable set. When conditioned on the global variable set, the local variable sets are independent of each other. We adopt the Cholesky decomposition for re-parametrization of precision matrix and derive Jeffreys' prior, reference prior, and invariant priors for new parameterizations. The frequentist properties of the Bayesian procedure using these objective priors are also studied. The last part concentrates on the discussion of objective Bayesian analysis for partial correlation coefficient and its application to multivariate Gaussian models. / Ph. D.

High-dimensional data such as multi-modal neuroimaging data and large-scale networks carry excessive amount of information, and can be used to test various scientific hypotheses or discover important patterns in complicated systems. While considerable efforts have been made to analyze high-dimensional data, existing approaches often rely on simple summaries which could miss important information, and many challenges on modeling complex structures in data remain unaddressed. In this proposal, we focus on analyzing structured high-dimensional data, including functional data with important local regions and network data with community structures. The first part of this dissertation concerns the detection of ``important'' regions in functional data. We propose a novel Bayesian approach that enables region selection in the functional data regression framework. The selection of regions is achieved through encouraging sparse estimation of the regression coefficient, where nonzero regions correspond to regions that are selected. To achieve sparse estimation, we adopt compactly supported and potentially over-complete basis to capture local features of the regression coefficient function, and assume a spike-slab prior to the coefficients of the bases functions. To encourage continuous shrinkage of nearby regions, we assume an Ising hyper-prior which takes into account the neighboring structure of the bases functions. This neighboring structure is represented by an undirected graph. We perform posterior sampling through Markov chain Monte Carlo algorithms. The practical performance of the proposed approach is demonstrated through simulations as well as near-infrared and sonar data. The second part of this dissertation focuses on constructing diversified portfolios using stock return data in the Center for Research in Security Prices (CRSP) database maintained by the University of Chicago. Diversification is a risk management strategy that involves mixing a variety of financial assets in a portfolio. This strategy helps reduce the overall risk of the investment and improve performance of the portfolio. To construct portfolios that effectively diversify risks, we first construct a co-movement network using the correlations between stock returns over a training time period. Correlation characterizes the synchrony among stock returns thus helps us understand whether two or multiple stocks have common risk attributes. Based on the co-movement network, we apply multiple network community detection algorithms to detect groups of stocks with common co-movement patterns. Stocks within the same community tend to be highly correlated, while stocks across different communities tend to be less correlated. A portfolio is then constructed by selecting stocks from different communities. The average return of the constructed portfolio over a testing time period is finally compared with the SandP 500 market index. Our constructed portfolios demonstrate outstanding performance during a non-crisis period (2004-2006) and good performance during a financial crisis period (2008-2010). / PHD / High dimensional data, which are composed by data points with a tremendous number of features (a.k.a. attributes, independent variables, explanatory variables), brings challenges to statistical analysis due to their “high-dimensionality” and complicated structure. In this dissertation work, I consider two types of high-dimension data. The first type is functional data in which each observation is a function. The second type is network data whose internal structure can be described as a network. I aim to detect “important” regions in functional data by using a novel statistical model, and I treat stock market data as network data to construct quality portfolios efficiently

Gene regulatory networks (GRNs) are crucial for understanding complex biological processes and disease mechanisms, particularly in cancer. However, GRN inference remains challenging due to the intricate nature of gene interactions and limitations of existing methods. Traditionally, prior knowledge in GRN inference simplifies the problem by reducing the search space, but its full potential is unrealized. This research aims to develop a method that uses prior knowledge to guide the GRN inference process, enhancing accuracy and biological plausibility of the resulting networks. We extended the Fused Sparse Structural Equation Models (FSSEM) framework to create the Fused Lasso Adaptive Prior (FLAP) method. FSSEM incorporates gene expression data and genetic variants in the form of expression quantitative trait loci (eQTLs) perturbations. FLAP enhances FSSEM by integrating prior knowledge of gene-gene interactions into the initial network estimate, guiding the selection of relevant gene interactions in the final inferred network. We evaluated FLAP using synthetic data to assess the impact of incorrect prior knowledge and real lung cancer data, using prior knowledge from various gene network databases (GIANT, TissueNexus, STRING, ENCODE, hTFtarget). Our findings demonstrate that integrating prior knowledge improves the accuracy of inferred networks, with FLAP showing tolerance for incorrect prior knowledge. Using real lung cancer data, functional enrichment analysis and literature validation confirmed the biological plausibility of the networks inferred by FLAP. Different sources of prior knowledge impacted the results, with GIANT providing the most biologically relevant networks, while other sources showed less consistent performance. FLAP improves GRN inference by effectively integrating prior knowledge, demonstrating robustness against incorrect prior knowledge. The method’s application to lung cancer data indicates that high-quality prior knowledge sources enhance the biological relevance of inferred networks. Future research should focus on improving the quality and integration of prior knowledge, possibly by developing consensus methods that combine multiple sources. This approach has potential applications in cancer research and drug sensitivity studies, offering a more accurate understanding of gene regulatory mechanisms and potential therapeutic targets.

The purpose of this study was to explore and describe the experiences of Recognition of Prior Learning (RPL) nursing candidates related to the four-year comprehensive nursing training programme at a Nursing Education Institution in Gauteng. To this end an exploratory descriptive qualitative research design was undertaken. The research sample comprised of 13 purposefully selected participants. Face-to-face individual interviews, using open-ended questions (Grand tour), were used to collect data, which was analysed using Tesch’s approach. Findings from the study highlighted the challenges faced by nursing RPL candidates as adult students. These included challenges related to their theoretical learning as well as their clinical facility experiences. Based on the study results, recommendations were formulated in assisting them to successfully and timeously complete their nursing programme / Health Studies / M.A. (Nursing Science)

Aglomerados de galáxias são as maiores estruturas no Universo. Sua distribuição mapeia os halos de matéria escura formados nos potenciais profundos do campo de matéria escura. Consequentemente, a abundância de aglomerados é altamente sensível a expansão do Universo, assim como ao crescimento das perturbações de matéria escura, constituindo uma poderosa ferramenta para fins cosmológicos. Na era atual de grandes levantamentos observacionais que produzem uma quantidade gigantesca de dados, as propriedades estatísticas dos objetos observados (galáxias, aglomerados, supernovas, quasares, etc) podem ser usadas para extrair informações cosmológicas. Para isso, é necessária o estudo da formação de halos de matéria escura, da detecção dos halos e aglomerados, das ferramentas estatísticas usadas para o vínculos de parâmetros, e finalmente, dos efeitos da detecções ópticas. No contexto da formulação da predição teórica da contagem de halos, foi analisada a influência de cada parâmetro cosmológico na abundância dos halos, a importância do uso da covariância dos halos, e a eficácia da utilização dos halos para vincular cosmologia. Também foi analisado em detalhes os intervalos de redshift e o uso de conhecimento prévio dos parâmetros ({\\it priors}). A predição teórica foi testada um uma simulação de matéria escura, onde a cosmologia era conhecida e os halos de matéria escura já haviam sido detectados. Nessa análise, foi atestado que é possível obter bons vínculos cosmológicos para alguns parâmetros (Omega_m,w,sigma_8,n_s), enquanto outros parâmetros (h,Omega_b) necessitavam de conhecimento prévio de outros testes cosmológicos. Na seção dos métodos estatísticos, foram discutidos os conceitos de {\\it likelihood}, {\\it priors} e {\\it posterior distribution}. O formalismo da Matriz de Fisher, bem como sua aplicação em aglomerados de galáxias, foi apresentado e usado para a realização de predições dos vínculos em levantamentos atuais e futuros. Para a análise de dados, foram apresentados métodos de Cadeias de Markov de Monte Carlo (MCMC), que diferentemente da Matriz de Fisher não assumem Gaussianidade entre os parâmetros vinculados, porém possuem um custo computacional muito mais alto. Os efeitos observacionais também foram estudados em detalhes. Usando uma abordagem com a Matriz de Fisher, os efeitos de completeza e pureza foram extensivamente explorados. Como resultado, foi determinado em quais casos é vantajoso incluir uma modelagem adicional para que o limite mínimo de massa possa ser diminuído. Um dos principais resultados foi o fato que a inclusão dos efeitos de completeza e pureza na modelagem não degradam os vínculos de energia escura, se alguns outros efeitos já estão sendo incluídos. Também foi verificados que o uso de priors nos parâmetros não cosmológicos só afetam os vínculos de energia escura se forem melhores que 1\\%. O cluster finder(código para detecção de aglomerados) WaZp foi usado na simulação, produzindo um catálogo de aglomerados. Comparando-se esse catálogo com os halos de matéria escura da simulação, foi possível investigar e medir os efeitos observacionais. A partir dessas medidas, pôde-se incluir correções para a predição da abundância de aglomerados, que resultou em boa concordância com os aglomerados detectados. Os resultados a as ferramentas desenvolvidos ao longo desta tese podem fornecer um a estrutura para a análise de aglomerados com fins cosmológicos. Durante esse trabalho, diversos códigos foram desenvolvidos, dentre eles, estão um código eficiente para computar a predição teórica da abundância e covariância de halos de matéria escura, um código para estimar a abundância e covariância dos aglomerados de galáxias incluindo os efeitos observacionais, e um código para comparar diferentes catálogos de halos e aglomerados. Esse último foi integrado ao portal científico do Laboratório Interinstitucional de e-Astronomia (LIneA) e está sendo usado para avaliar a qualidade de catálogos de aglomerados produzidos pela colaboração do Dark Energy Survey (DES), assim como também será usado em levantamentos futuros. / Abstract Galaxy clusters are the largest bound structures of the Universe. Their distribution maps the dark matter halos formed in the deep potential wells of the dark matter field. As a result, the abundance of galaxy clusters is highly sensitive to the expansion of the universe as well as the growth of dark matter perturbations, representing a powerful tool for cosmological purposes. In the current era of large scale surveys with enormous volumes of data, the statistical quantities from the objects surveyed (galaxies, clusters, supernovae, quasars, etc) can be used to extract cosmological information. The main goal of this thesis is to explore the potential use of galaxy clusters for constraining cosmology. To that end, we study the halo formation theory, the detection of halos and clusters, the statistical tools required to quarry cosmological information from detected clusters and finally the effects of optical detection. In the composition of the theoretical prediction for the halo number counts, we analyze how each cosmological parameter of interest affects the halo abundance, the importance of the use of the halo covariance, and the effectiveness of halos on cosmological constraints. The redshift range and the use of prior knowledge of parameters are also investigated in detail. The theoretical prediction is tested on a dark matter simulation, where the cosmology is known and a dark matter halo catalog is available. In the analysis of the simulation we find that it is possible to obtain good constraints for some parameters such as (Omega_m,w,sigma_8,n_s) while other parameters (h,Omega_b) require external priors from different cosmological probes. In the statistical methods, we discuss the concept of likelihood, priors and the posterior distribution. The Fisher Matrix formalism and its application on galaxy clusters is presented, and used for making forecasts of ongoing and future surveys. For the real analysis of data we introduce Monte Carlo Markov Chain (MCMC) methods, which do not assume Gaussianity of the parameters distribution, but have a much higher computational cost relative to the Fisher Matrix. The observational effects are studied in detail. Using the Fisher Matrix approach, we carefully explore the effects of completeness and purity. We find in which cases it is worth to include extra parameters in order to lower the mass threshold. An interesting finding is the fact that including completeness and purity parameters along with cosmological parameters does not degrade dark energy constraints if other observational effects are already being considered. The use of priors on nuisance parameters does not seem to affect the dark energy constraints, unless these priors are better than 1\\%.The WaZp cluster finder was run on a cosmological simulation, producing a cluster catalog. Comparing the detected galaxy clusters to the dark matter halos, the observational effects were investigated and measured. Using these measurements, we were able to include corrections for the prediction of cluster counts, resulting in a good agreement with the detected cluster abundance. The results and tools developed in this thesis can provide a framework for the analysis of galaxy clusters for cosmological purposes. Several codes were created and tested along this work, among them are an efficient code to compute theoretical predictions of halo abundance and covariance, a code to estimate the abundance and covariance of galaxy clusters including multiple observational effects and a pipeline to match and compare halo/cluster catalogs. This pipeline has been integrated to the Science Portal of the Laboratório Interinstitucional de e-Astronomia (LIneA) and is being used to automatically assess the quality of cluster catalogs produced by the Dark Energy Survey (DES) collaboration and will be used in other future surveys.

The use of pre-hardened mold steels has increased appreciably over the years; more than 80% of the plastic mold steels are used in pre-hardened condition. These steels are delivered to the customer in finished state i.e. there is no need of any post treatment. With hardness around ~40HRC, they have properties such as good polishability, good weldability, corrosion resistance and thermal conductivity. Machinability is a very important parameter in pre-hardened mold steels as it has a direct impact on the cost of the mold. In normal machining operations involving intricate or near net shapes, machining constitutes around 60% of the total mold cost. Efforts are underway to explore every possible way to reduce costs associated with machining and to make production more economical. All the possible parameters which are considered to affect the machinability are being investigated by the researchers. This thesis work focuses on the effect of prior austenite grain size on the machinability of pre-hardened mold steel (Uddeholm Nimax).  Austenitizing temperatures and holding times were varied to obtain varying grain sized microstructures in different samples of the same material. As it was difficult to delineate prior-austenite grain boundaries, experimental and empirical methods were employed to obtain reference values. These different grain sized samples were thereafter subjected to machining tests, using two sets of cutting parameters. Maximum flank wear depth=0.2mm was defined for one series of test which were more akin to rough machining, and machining length of 43200mm or maximum wear depth=0.2mm were defined for second series of tests which were similar to finishing machining. The results were obtained after careful quantative and qualitative analysis of cutting tools. The results obtained for Uddeholm Nimax seemed to indicate that larger grain sized material was easier to machine. However, factors such as retained austenite content and work hardening on machined surface, which lead to degradation of machining operations were also taken into consideration. Uddeholm Nimax showed better machinability in large grained samples as retained austenite(less than 2%) content was minimal in the large grained sample. Small grained sample in Uddeholm Nimax had a higher retained austenite (7+2%) which resulted in degradation of machining operation and a lesser cutting tool life.

The purpose of this study was to explore and describe the experiences of Recognition of Prior Learning (RPL) nursing candidates related to the four-year comprehensive nursing training programme at a Nursing Education Institution in Gauteng. To this end an exploratory descriptive qualitative research design was undertaken. The research sample comprised of 13 purposefully selected participants. Face-to-face individual interviews, using open-ended questions (Grand tour), were used to collect data, which was analysed using Tesch’s approach. Findings from the study highlighted the challenges faced by nursing RPL candidates as adult students. These included challenges related to their theoretical learning as well as their clinical facility experiences. Based on the study results, recommendations were formulated in assisting them to successfully and timeously complete their nursing programme / Health Studies / M.A. (Nursing Science)