This thesis provides novel methodology for statistical analysis of paired high-dimensional genomic data, with the aimto identify gene interactions specific to each group of samples as well as the gene connections that change between the two classes of observations. An example of such groups can be patients under two medical conditions, in which the estimation of gene interaction networks is relevant to biologists as part of discerning gene regulatory mechanisms that control a disease process like, for instance, cancer. We construct these interaction networks fromdata by considering the non-zero structure of correlationmatrices, which measure linear dependence between random variables, and their inversematrices, which are commonly known as precision matrices and determine linear conditional dependence instead. In this regard, we study three statistical problems related to the testing, single estimation and joint estimation of (conditional) dependence structures. Firstly, we develop hypothesis testingmethods to assess the equality of two correlation matrices, and also two correlation sub-matrices, corresponding to two classes of samples, and hence the equality of the underlying gene interaction networks. We consider statistics based on the average of squares, maximum and sum of exceedances of sample correlations, which are suitable for both independent and paired observations. We derive the limiting distributions for the test statistics where possible and, for practical needs, we present a permuted samples based approach to find their corresponding non-parametric distributions. Cases where such hypothesis testing presents enough evidence against the null hypothesis of equality of two correlation matrices give rise to the problem of estimating two correlation (or precision) matrices. However, before that we address the statistical problem of estimating conditional dependence between random variables in a single class of samples when data are high-dimensional, which is the second topic of the thesis. We study the graphical lasso method which employs an L1 penalized likelihood expression to estimate the precision matrix and its underlying non-zero graph structure. The lasso penalization termis given by the L1 normof the precisionmatrix elements scaled by a regularization parameter, which determines the trade-off between sparsity of the graph and fit to the data, and its selection is our main focus of investigation. We propose several procedures to select the regularization parameter in the graphical lasso optimization problem that rely on network characteristics such as clustering or connectivity of the graph. Thirdly, we address the more general problem of estimating two precision matrices that are expected to be similar, when datasets are dependent, focusing on the particular case of paired observations. We propose a new method to estimate these precision matrices simultaneously, a weighted fused graphical lasso estimator. The analogous joint estimation method concerning two regression coefficient matrices, which we call weighted fused regression lasso, is also developed in this thesis under the same paired and high-dimensional setting. The two joint estimators maximize penalized marginal log likelihood functions, which encourage both sparsity and similarity in the estimated matrices, and that are solved using an alternating direction method of multipliers (ADMM) algorithm. Sparsity and similarity of thematrices are determined by two tuning parameters and we propose to choose them by controlling the corresponding average error rates related to the expected number of false positive edges in the estimated conditional dependence networks. These testing and estimation methods are implemented within the R package ldstatsHD, and are applied to a comprehensive range of simulated data sets as well as to high-dimensional real case studies of genomic data. We employ testing approaches with the purpose of discovering pathway lists of genes that present significantly different correlation matrices on healthy and unhealthy (e.g., tumor) samples. Besides, we use hypothesis testing problems on correlation sub-matrices to reduce the number of genes for estimation. The proposed joint estimation methods are then considered to find gene interactions that are common between medical conditions as well as interactions that vary in the presence of unhealthy tissues.

In this work, a method to choose the best run order for a given experimental design is proposed, for the simple linear regression model with MA errors. More specifically we investigate the best run order of an uniform design when errors follow a MA(1) or a subset MA(k) process where k is a positive integer. The correlation matrix P resulting from the errors is usually difficult to obtain a good estimate. Using the change of variance function(CVF) to see the relation of the uncorrelated and the serially correlated errors. Criterion proposed by Zhou (2001), we find the best run order of the uniform design on [-1,1] to minimize the robust criterion, |CVF|. We will display the permutation of a run order after rearrangement by our method and show how the structure is decomposed into three categories to solve the problem.

Molecular dynamics simulations were performed on the influenza A non-structural protein 1 (NS1) RNA binding domain (RBD), a homodimer. Fourteen simulations were performed at 298K, nine ionized with 0.1M KCl and five with no ions. Several analysis techniques were employed to study RBD residue flexibility. The focus of the study was the RNA binding cavity formed by side chains of helix 2 (chain A) and helix 2’ (chain B) and cavity intermonomeric salt bridges. Opening of the salt bridges D29–R46’ and D29’–R46 was observed in several of the trajectories. The RNA binding cavity has large flexibility, where the dimension and shape change during the dynamics. One pair of residues surrounding the cavity and necessary for RNA binding, residues R38 and R38’, have motions during the simulations which cover the top of the cavity. There is correlation between the salt bridge breaking, flexibility of R38 and R38’, and the cavity size and shape changes. Possible RBD small molecule drug targets are these two salt bridges and the pair R38 and R38’. Disrupting the events that occur around these areas could possibly inactivate RNA binding function of the domain. These results could have implications in searching for potential molecules that effectively treat influenza A.

Abstract This thesis project is divided in two parts. The first part examines the possibility that correlation matrix estimates based on an outlier sample would contain information about extreme events. According to my findings, such methods do not perform better than simple shrinkage methods where robust shrinkage targets are used. The method tested is especially outperformed when it comes to the extreme events, where a shrinkage of the correlation matrix towards the identity matrix seems to give the best result. The second part is about valuation of skewness in marginal distributions and the penalizing of heavy tails. I argue that it is reasonable to use a degrees of freedom parameter instead of kurtosis and a certain regression parameter, that I develop, instead of skewness due to robustness issues. When minimizing the one period draw-down is our target, the "value" of skewness seems to have a linear relationship with expected returns. Re-valuing of expected returns, in terms of skewness, in the standard Markowitz framework will tend to lower expected shortfall (ES), increase skewness and lower the realized portfolio variance. Penalizing of heavy tails will most times in the same way lower ES, lower kurtosis and realized portfolio variance. The results indicate that the parameters representing higher order moments in some way characterize the assets and also reflect their future behavior. These properties can be used in a simple optimization framework and seem to have a positive impact even on portfolio level

The purpose of this thesis is to test the Q method applied in discursive analysis in public policy. The author will carry out research using available scientific literature dealing with the method and prepare a case study whose purpose will be to test the reliability of the method Q in a practical case. Promoters of the Q method argue that the uniqueness of the method rests in its resistance to the subjective influence of the researcher. The purpose of this work is therefore a practical verification of to what extent may the researcher's subjective stance at the selection of the default set of statements reflect on the overall result of the analysis.

No description available.

Correlated stocks should, in equilibrium, have correlated momenta, but in practice momenta do not always correlate. We use short-term inconsistencies between correlations and momenta to predict price corrections, produce more meaningful investment indicators, and improve upon accepted investing strategies. In particular, our approaches integrate inconsistencies within an entire security class rather than relying only on individual or pairwise security data. We use this theory to improve upon not only the standard momentum portfolio but also Pair Trading and Momentum Reversion methods. This results in three strategies for portfolio allocation that outperforms overlying indices and market benchmarks by 5%-10% in annual gain with an increase of CAPM alpha over the standard momentum portfolio from -0.1 to 5.4. We expand on these strategies by showing applications generalized to comparable investing indicators including volatility.

No description available.

Thesis (MScEng)--Stellenbosch University, 2011. / ENGLISH ABSTRACT: This thesis addresses the complications that are encountered when characterising the performance of differential microwave LNAs. The predominant sources of noise in electronic circuits are introduced and equivalent two-port noise models for active devices are derived. Correlation between noise generators are defined by means of the noise correlation matrix and existing network theory is adapted to include noise analysis of twoport and multi-port networks. Mixed-mode scattering parameters are introduced in order to define the signal performance of differential and common-mode propagation in multi-port networks and, by applying the same theory, the mixed-mode correlation matrix for a three-port dLNA is derived. Furthermore, an expression is derived for de-embedding the differential noise figure of a three-port dLNA using two single ended measurements. Two dLNA designs, both incorporating wideband 180°-Hybrid ring couplers, are discussed and the differential signal and noise performance of the dLNAs are compared to that of their constituent single ended LNAs. / AFRIKAANSE OPSOMMING: Hierdie tesis behandel die komplikasies wat ontwerpers in die gesig staar tydens die karakterisering van mikrogolf differensiële laeruis versterkers. Die hoof ruisbronne in stroombane word bespreek en ekwivalente tweepoortnetwerkmodelle vir aktiewe toestelle word afgelei. Korrelasie tussen ruisbronne word gedefnieer deur middel van ruiskorrelasiematrikse en bestaande tweepoort- en multipoort-netwerkteorie word aangepas om ruismodelle in te sluit. Weens die feit dat differensiële- en gemene-wyse voortplanting van seine voorkom in multipoortnetwerke word gemengde-modus S-parameters behandel. Dieselfde teorie maak dit vervolgens moontlik om die gemengde-modus ruiskorrelasiematriks van ’n drie-poort differensiële laeruis versterker af te lei. Verder word daar ’n wyse voorgestel waarmee die differensiëleruissyfer van ’n drie-poort differensiële laeruis versterker vanuit twee enkel ruissyfermetings bereken kan word. Twee differensiële laeruis versterker ontwerpe, waarvan beide wyeband 180 -differensiaalkoppelaars implementeer, word bespreek en die differensiëlesein- asook die differensiëleruis-werking word vergelyk met die werking van die omsluite ongebalanseerde laeruis versterkers.

This thesis concerns the relations between correlation matrix, difference propagation matrix and other matrices used in the block cipher cryptanalysis. We show that some relations between these matrices can be seen just as a change of basis provided by the discrete Fourier transform. This can be used for an easier proof of a well-known theorem. We also study properties of difference propagation matrix, describe a class of vectorial Boolean functions which have the same difference propagation matrix and state a numerically justified hypothesis that this class contains all such functions.