No / This paper presents a methodology for efficient shape parametrisation for automatic design optimisation using a partial differential equation (PDE) formulation. It is shown how the choice of an elliptic PDE enables one to define and parametrise geometries corresponding to complex shapes. By using the PDE formulation it is shown how the shape definition and parametrisation can be based on a boundary value approach by which complex shapes can be created and parametrised based on the shape information at the boundaries or the character lines defining the shape. Furthermore, this approach to shape definition allows complex shapes to be parametrised intuitively using a very small set of design parameters.

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One of two project reports: The other part is designated as Part A / <p> A fundamental and important part of nuclear reactor development and analysis today is the study of neutronics following a breach in the primary heat transport circuit. In the past, much of this analysis has concentrated on the calculation of the thermalhydraulic changes which occur following a loss of coolant accident and the effects these subsequently have on neutron kinetics. The purpose of this present study is to examine the influence of neutronic parameters on the size and shape of power pulses which result from loss of coolant accidents. The parameters studied are shutdown system delay times, shutoff rod drop curves, and fuel burnup distribution. </p> / Thesis / Master of Engineering (MEngr)

<p> In this thesis parametric analysis for conic quadratic optimization problems is studied. In parametric analysis, which is often referred to as parametric optimization or parametric programming, a perturbation parameter is introduced into the optimization problem, which means that the coefficients in the objective function of the problem and in the right-hand-side of the constraints are perturbed. First, we describe linear, convex quadratic and second order cone optimization problems and their parametric versions. Second, the theory for finding solutions of the parametric problems is developed. We also present algorithms for solving such problems. Third, we demonstrate how to use parametric optimization techniques to solve multiobjective optimization problems and compute Pareto efficient surfaces. </p> <p> We implement our novel algorithm for hi-parametric quadratic optimization. It utilizes existing solvers to solve auxiliary problems. We present numerical results produced by our parametric optimization package on a number of practical financial and non-financial computational problems. In the latter we consider problems of drug design and beam intensity optimization for radiation therapy. </p> <p> In the financial applications part, two risk management optimization models are developed or extended. These two models are a portfolio replication framework and a credit risk optimization framework. We describe applications of multiobjective optimization to existing financial models and novel models that we have developed. We solve a number of examples of financial multiobjective optimization problems using our parametric optimization algorithms. </p> / Thesis / Doctor of Philosophy (PhD)

<p> This project is a contribution towards the development of one component of an analytical audit flowcharting system using computer graphics. The component to be developed will be concerned with producing graphical displays on an intelligent graphics terminal; the configuration of these displays is determined by parametric data supplied through the terminal keyboard. The software is designed in such a way that input options may be exercised to experiment with the shape and size of the component parts of the flowchart.</p> / Thesis / Master of Science (MSc)

This thesis pertains to the uses of functional data analysis and nonlinear mixed-effects model with applications to PET data. In the first part of this dissertation, we consider a permutation-based inference for function-on-scalar regression. While PET imaging data analysis is most commonly performed on data that are aggregated into several discrete a priori regions of interest, our primary interest is on measures of 5-HTT binding potential that are made at many locations along a continuous anatomically defined tract, one that was chosen to follow serotonergic axons. Our goal is to characterize the binding patterns along this tract, determine how such patterns differ between diagnostic groups, and also to investigate the question of homogeneity. We utilize function-on-scalar regression modeling to make optimal use of our data and inference is made using permutation testing strategies that do not require distributional assumptions. Simulations are conducted to examine the validity of our methods and compare the performance of competing methods. We illustrate this approach by applying it to PET data. In the second part of this dissertation, we introduce shape-based distance metrics for comparison of IRFs. The common practice involves summarizing the estimated IRF using a single scalar measure, such as VT, and comparing it across subjects/groups using standard univariate analyses. However, this approach neglects the nature and structure of the IRFs and overlooks their shapes. We propose a k-nearest-neighbor ensemble approach that optimally combines distance metrics based on principles of functional data analysis and shape data analysis. Simulations are conducted to compare the predictive performance of our approach to the traditional approach of using VT. We illustrate this approach by applying it to PET data. In the third part of this dissertation, we discuss the a nonlinear mixed-effects modeling approach for PET data analysis under the assumption of a simplified reference tissue model. The conventional two-stage approach uses NLS estimates of the population parameters, although statistically valid, it is possible to allow for more complex models that consider all subjects simultaneously. We propose a nonlinear mixed-effects (NLME) model that can estimate not only the individual-level parameters, but also the effects of covariates on the parameters. In this way, estimation of kinetic parameters and statistical inference can be performed simultaneously. Simulations are conducted to compare the power for detection of group differences and population- and individual-level parameter estimation for both NLS and NLME models. We apply our NLME approach to PET data to illustrate the modeling procedure.

This thesis focuses on the development, parameterization and optimization of a novel meso-scale pattern used to induce auxetic behavior, i.e., negative Poisson's ratio, at the bulk scale. Currently, the majority of auxetic structures are too porous to be utilized in conventional load-bearing applications. For others, manufacturing methods have yet to realize the meso-scale pattern. Consequently, new auxetic structures must be developed in order to confer superior thermo-mechanical responses to structures at high temperature. Additionally, patterns that take into account manufacturing limitations, while maintaining the properties characteristically attached to negative Poisson's Ratio materials, are ideal in order to utilize the potential of auxetic structures. A novel auxetic pattern is developed, numerically analyzed, and optimized via design of experiments. The parameters of the meso-structure are varied, and the bulk response is studied using finite element analysis (FEA). Various attributes of the elasto-plastic responses of the bulk structure are used as objectives to guide the optimization process

This thesis work presents a non-parametric learning method, the Extended Nearest Neighbor (ENN) algorithm, as a tool for data disaggregation in smart grids. The ENN algorithm makes the prediction according to the maximum gain of intra-class coherence. This algorithm not only considers the K nearest neighbors of the test sample but also considers whether these K data points consider the test sample as their nearest neighbor or not. So far, ENN has shown noticeable improvement in the classification accuracy for various real-life applications. To further enhance its prediction capability, in this thesis we propose to incorporate a metric learning algorithm, namely the Large Margin Nearest Neighbor (LMNN) algorithm, as a training stage in ENN. Our experiments on real-life energy data sets have shown significant performance improvement compared to several other traditional classification algorithms, including the classic KNN method and Support Vector Machines.

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