We consider the application of least-squares variational principles and the finite element method to the numerical solution of boundary value problems arising in the fields of solidand fluidmechanics.For manyof these problems least-squares principles offer many theoretical and computational advantages in the implementation of the corresponding finite element model that are not present in the traditional weak form Galerkin finite element model.Most notably, the use of least-squares principles leads to a variational unconstrained minimization problem where stability conditions such as inf-sup conditions (typically arising in mixed methods using weak form Galerkin finite element formulations) never arise. In addition, the least-squares based finite elementmodelalways yields a discrete system ofequations witha symmetric positive definite coeffcientmatrix.These attributes, amongst manyothers highlightedand detailed in this work, allow the developmentofrobust andeffcient finite elementmodels for problems of practical importance. The research documented herein encompasses least-squares based formulations for incompressible and compressible viscous fluid flow, the bending of thin and thick plates, and for the analysis of shear-deformable shell structures.

In this work are discussed a block parameter estimation method for linear periodically time varying system. The whole work consists of two parts: theoretical and practical. The theoretical part is based on model’s description, its creation and structure. There it is shown estimation Markova, or an estimation of the least squares generalized method and the description of the generalized model. The practical part is devoted to fulfilling experiments and their describing. The conclusion about estimation of block parameter method’s achievement was also made. The experiments have been fulfilled using Matlab program. In addition count correctly Matlab (matrica, period) have been used. The results of experiments are given in the tables and schedules.

A non-linear edge-preserving solution to the least-squares migration problem with sparseness & illumination constraints is proposed. The applied formalism explores Curvelets as basis functions. By virtue of their sparseness and locality, Curvelets not only reduce the dimensionality of the imaging problem but they also naturally lead to a dense preconditioning that almost diagonalizes the normal/Hessian operator. This almost diagonalization allows us to recast the imaging problem into a ’simple’ denoising problem. As such, we are in the position to use non-linear estimators based on thresholding. These estimators exploit the sparseness and locality of Curvelets and allow us to compute a first estimate for the reflectivity, which approximates the least-squares solution of the seismic inverse scattering problem. Given this estimate, we impose sparseness and additional amplitude corrections by solving a constrained optimization problem. This optimization problem is initialized and constrained by the thresholded image and is designed to remove remaining imaging artifacts and imperfections in the estimation and reconstruction.

Two complementary solution strategies to the least-squares migration problem with sparseness- & continuity constraints are proposed. The applied formalism explores the sparseness of curvelets on the reflectivity and their invariance under the demigration migration operator. Sparseness is enhanced by (approximately) minimizing a (weighted) l1-norm on the curvelet coefficients. Continuity along imaged reflectors is brought out by minimizing the anisotropic difussion or total variation norm which penalizes variations along and in between reflectors. A brief sketch of the theory is provided as well as a number of synthetic examples. Technical details on the implementation of the optimization strategies are deferred to an accompanying paper: implementation.

As wireless devices become more common, the ability to position a wireless device has become a topic of importance. Accurate positioning through technologies such as the Global Positioning System is possible for outdoor environments. Indoor environments pose a different challenge, and research continues to position users indoors. Due to the prevalence of wireless local area networks (WLANs) in many indoor spaces, it is prudent to determine their capabilities for the purposes of positioning. Signal strength and time based positioning systems have been studied for WLANs. Direction or angle of arrival (AOA) based positioning will be possible with multiple antenna arrays, such as those included with upcoming devices based on the IEEE 802.11n standard. The potential performance of such a system is evaluated. The positioning performance of such a system depends on the accuracy of the AOA estimation as well as the positioning algorithm. Two different maximum-likelihood (ML) derived algorithms are used to determine the AOA of the mobile user: a specialized simple ML algorithm, and the space- alternating generalized expectation-maximization (SAGE) channel parameter estimation algorithm. The algorithms are used to determine the error in estimating AOAs through the use of real wireless signals captured in an indoor office environment. The statistics of the AOA error are used in a positioning simulation to predict the positioning performance. A least squares (LS) technique as well as the popular extended Kalman filter (EKF) are used to combine the AOAs to determine position. The position simulation shows that AOA- based positioning using WLANs indoors has the potential to position a wireless user with an accuracy of about 2 m. This is comparable to other positioning systems previously developed for WLANs.

In this thesis, we consider the problem of constructing an additive risk model based on the right censored survival data to predict the survival times of the cancer patients, especially when the dimension of the covariates is much larger than the sample size. For microarray Gene Expression data, the number of gene expression levels is far greater than the number of samples. Such ¡°small n, large p¡± problems have attracted researchers to investigate the association between cancer patient survival times and gene expression profiles for recent few years. We apply Partial Least Squares to reduce the dimension of the covariates and get the corresponding latent variables (components), and these components are used as new regressors to fit the extensional additive risk model. Also we employ the time dependent AUC curve (area under the Receiver Operating Characteristic (ROC) curve) to assess how well the model predicts the survival time. Finally, this approach is illustrated by re-analysis of the well known AML data set and breast cancer data set. The results show that the model fits both of the data sets very well.

Product management as an organizational system has a long history of practice, which predates most modern academic management research. Its activities span the external environment of the firm, while simultaneously spanning across internal functional specialties of the organization. Thus product management obtains, codifies, simplifies and stores external information making it available to a responsive organization, which uses it to establish competitive advantage and ultimately superior performance. Building on the resource based view of the firm and boundary theory, these spanning activities, which are heterogeneously dispersed across firms, are considered organizational capabilities. Drawing upon the extant product management literature, this research uses product management as a proxy for boundary spanning capabilities of the firm. These capabilities are then empirically measured against two well established firm capabilities; market orientation and firm-level innovativeness. This research addresses a gap in the literature by establishing product management as a set of firm-level capabilities, distinct from the well established constructs of market orientation and innovativeness. Results indicate that external product management capability, defined as channel bonding activities, fully mediates the market orientation – firm performance relationship, while firm level innovativeness continues to have a small mediating effect on performance. Internal product management capabilities, defined as market and technical integration are shown to negatively moderate the external product management capability - firm performance relationship. Theoretical implications include establishing a link between boundary theory and the resource based view of the firm. Practical implications include the strong relationship between external spanning capabilities and firm performance and the dampening effect of cross-functional integration on firm performance. This empirical link between product management boundary spanning practices and how firms ultimately perform could assist practitioners in allocating resources and managing the relationship between the marketing and technological factions of the organization. Most importantly this research establishes the hereto untested link between product management capability and firm performance.

The continuous growth in power system electric grid by adding new substations lead to construct many new transmission lines, transformers, control devices, and circuit breakers to connect the capacity (generators) to the demand (loads). These components will have a very heavy influence on the performance of the electric grid. The renewable technical solutions for these issues can be found by robust algorithms which can give us a full picture of the current state of the electrical network by monitoring the behavior of phase and voltage magnitude. In this thesis, the major idea is to implement several algorithms including weighted least square, extend kalman filter, and interior point method in three different electrical networks including IEEE 14, 30, and 118 to compare the performance of these algorithms which is represented by the behavior of phases and magnitude voltages as well as minimize the residual of the balance load flow real time measurements to distinguish which one is more robust. Also to have a particular understanding of the comparison between unconstraint and constraint algorithms.

An experiment was conducted to obtain a hepatic gene expression dataset from postpubertal dairy heifers that could be fit to a computational model capable of predicting future lactation performance values. The initial animal experiment was conducted to characterize the hepatic transcriptional response to 24-hour total feed withdrawal in one-hundred and two postpubertal Holstein dairy heifers using an 8329-gene oligonucleotide microarray in a randomized block design. Plasma concentration of non-esterified fatty acids was significantly higher, while levels of beta-hydroxybutyrate, triacylglycerol, and glucose were significantly lower with the 24-hour total feed withdrawal. In total, 505 differentially expressed genes were identified and microarray results were confirmed by real-time PCR. Upregulation of key gluconeogenic genes occurred despite diminished dietary substrate and lower hepatic glucose synthesis. Downregulation of ketogenic genes was contrary to the non-ruminant response to feed withdrawal, but was consistent with a lower ruminal supply of short-chain fatty acids as precursors. Following the microarray experiment, the first series of regression analyses was employed to identify relationships between gene expression signal and lactation performance measurements taken over the first lactation of 81 of the subjects from the original study. Regression models were evaluated using mean square prediction error (MSPE) and concordance correlation coefficient (CCC) analysis. The strongest validated stepwise regression models were constructed for milk protein percentage (r = 0.04) and lactation persistency (r = 0.09). To determine if another type of regression analysis would better predict lactation performance, partial least squares (PLS) regression analysis was then applied. Selection of gene expression data was based on an assessment of the linear dependence of all genes in normalized datasets for 81 subjects against 18 dairy herd index (DHI) variables using Pearson correlation analysis. Results were distributed into two lists based on correlation coefficient. Each gene expression dataset was used to construct PLS models for the purpose of predicting lactation performance. The strongest predictive models were generated for protein percentage (r = 0.46), 305-d milk yield (r = 0.44), and 305-d protein yield (r = 0.47). These results demonstrate the suitability of using hepatic gene expression in young animals to quantitatively predict future lactation performance. / Ontario Centre for Agricultural Genomics, NSERC Canada, and the Ontario Ministry of Agriculture, Food and Rural Affairs (OMAFRA)

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