The use of a stochastic model to predict the likelihood of future outcomes forms an integral part of decision optimization under uncertainty. In classical stochastic modeling uncertain parameters are often assumed to be driven by a particular form of probability distribution. In practice however, the distributional form is often difficult to infer from the observed data, and the incorrect choice of distribution can lead to significant quality deterioration of resultant decisions and unexpected losses. In this thesis, we present new approaches for evaluating expected future performance that do not rely on an exact distributional specification and can be robust against the errors related to committing to a particular specification. The notion of comprehensive robustness is promoted, where various degrees of model misspecification are studied. This includes fundamental one such as unknown distributional form and more involved ones such as stochastic moments and moment outliers. The approaches are developed based on the techniques of moment-based optimization, where bounds on the expected performance are sought based solely on partial moment information. They can be integrated into decision optimization and generate decisions that are robust against model misspecification in a comprehensive manner. In the first part of the thesis, we extend the applicability of moment-based optimization to incorporate new objective functions such as convex risk measures and richer moment information such as higher-order multivariate moments. In the second part, new tractable optimization frameworks are developed that account for various forms of moment uncertainty in the context of decision analysis and optimization. Financial applications such as portfolio selection and option pricing are studied.

This study investigates the use of the divergence speed as an additional constraint to a multi-disciplinary optimization (MDO) problem. The goal of the project is to expand the MDO toolbox by adding an aeroelastic module used where the aeroelastic characteristics present a possible safety hazard. This paper examines aeroelastic theory and MDO disciplines. The divergence constraint function is developed on a BAH wing. The optimization problem is executed on the HANSA HFB 320 transport jet using the FEAP structural solver and a Vortex Lattice Method as the aerodynamic solver. The study shows that divergence speed can function as a safety constraint but the stress constraints determine the optimum design. Furthermore, obtaining a true divergence constraint will require a finer mesh, a more efficient aerodynamic solver and non-finite difference approach to gradient determination. Thus, the addition of the divergence constraint does not yet directly benefit this MDO framework.

The use of a stochastic model to predict the likelihood of future outcomes forms an integral part of decision optimization under uncertainty. In classical stochastic modeling uncertain parameters are often assumed to be driven by a particular form of probability distribution. In practice however, the distributional form is often difficult to infer from the observed data, and the incorrect choice of distribution can lead to significant quality deterioration of resultant decisions and unexpected losses. In this thesis, we present new approaches for evaluating expected future performance that do not rely on an exact distributional specification and can be robust against the errors related to committing to a particular specification. The notion of comprehensive robustness is promoted, where various degrees of model misspecification are studied. This includes fundamental one such as unknown distributional form and more involved ones such as stochastic moments and moment outliers. The approaches are developed based on the techniques of moment-based optimization, where bounds on the expected performance are sought based solely on partial moment information. They can be integrated into decision optimization and generate decisions that are robust against model misspecification in a comprehensive manner. In the first part of the thesis, we extend the applicability of moment-based optimization to incorporate new objective functions such as convex risk measures and richer moment information such as higher-order multivariate moments. In the second part, new tractable optimization frameworks are developed that account for various forms of moment uncertainty in the context of decision analysis and optimization. Financial applications such as portfolio selection and option pricing are studied.

This study investigates the use of the divergence speed as an additional constraint to a multi-disciplinary optimization (MDO) problem. The goal of the project is to expand the MDO toolbox by adding an aeroelastic module used where the aeroelastic characteristics present a possible safety hazard. This paper examines aeroelastic theory and MDO disciplines. The divergence constraint function is developed on a BAH wing. The optimization problem is executed on the HANSA HFB 320 transport jet using the FEAP structural solver and a Vortex Lattice Method as the aerodynamic solver. The study shows that divergence speed can function as a safety constraint but the stress constraints determine the optimum design. Furthermore, obtaining a true divergence constraint will require a finer mesh, a more efficient aerodynamic solver and non-finite difference approach to gradient determination. Thus, the addition of the divergence constraint does not yet directly benefit this MDO framework.

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Due to the increasing competition from developing countries, companies are struggling to reduce their manufacturing costs. In the field of tool manufacturing, manufacturers are under pressure to produce new products as quickly as possible at minimum cost with high accuracy. Laminated tooling, where parts are manufactured layer by layer, is a promising technology to reduce production costs. Laminated tooling is based on taking sheets of metal and stacking them to produce the final product after cutting each layer profile using laser cutting or other techniques. It is also a powerful tool to make complex tools with conformal cooling channels. In conventional injection moulds and casting dies the cooling channels are drilled in straight paths whereas the cavity has a complex profile. In these cases the cooling system may not be sufficiently effective resulting in a longer cooling time and loss of productivity. Furthermore, conventional cooling channels are limited to circular cross sections, while conformal cooling channels could follow any curved path with variable and non circular cross sections. One of the issues in laminated tooling is the surface jaggedness. The surface jaggedness depends on the layers' thicknesses and surface geometry. If the sheets are thin, the surface quality is improved, but the cost of layer profile cutting is increased. On the other hand, increasing the layers' thicknesses reduces the lamination process cost, but it increases the post processing cost. One solution is having variable thicknesses for the layers and optimally finding the set of layer thicknesses to achieve the minimum surface jaggedness and the number of layers at the same time. In practice, the choice of layers thicknesses depends on the availability of commercial sheet metals. One solution to reduce the number of layers without compromising the surface jaggedness is to use a non-uniform lamination technique in which the layers' thicknesses are changed according to the surface geometry. Another factor in the final surface quality is the lamination direction which can be used to reduce the number of laminations. Optimization by considering lamination direction can be done assuming one or multiple directions. In this thesis, an optimization method to minimize the surface jaggedness and the number of layers in laminated tooling is presented. In this optimization, the layers' thicknesses are selected from a set of available sheet metals. Also, the lamination direction as one of the optimization parameters is studied. A modified version of genetic algorithm is created for the optimization purpose in this research. The proposed method is presented as an optimization package which is applicable to any injection mould, hydroforming or sheet metal forming tool to create an optimized laminated prototype based on the actual model.

This thesis deals with questions relating to the maximum density of rank-n matroids in a minor-closed class. Consider a minor-closed class M of matroids that does not contain a given rank-2 uniform matroid. The growth rate function is defined by h_M(n) = max(|N| : N ∈ M simple, r(N) ≤ n). The Growth Rate Theorem, due to Geelen, Kabell, Kung, and Whittle, shows that the growth rate function is either linear, quadratic, or exponential in n. In the case of exponentially dense classes, we conjecture that, for sufficiently large n, h_M(n) = (q^(n+k) − 1)/(q-1) − c, where q is a prime power, and k and c are non-negative integers depending only on M. We show that this holds for several interesting classes, including the class of all matroids with no U_{2,t}-minor. We also consider more general minor-closed classes that exclude an arbitrary uniform matroid. Here the growth rate, as defined above, can be infinite. We define a more suitable notion of density, and prove a growth rate theorem for this more general notion, dividing minor-closed classes into those that are at most polynomially dense, and those that are exponentially dense.

Side channel attacks, where an attacker learns some physical information about the state of a device, are one of the ways in which cryptographic schemes are broken in practice. "Provably secure" schemes are subject to these attacks since the traditional models of security do not account for them. The theoretical community has recently proposed leakage resilient cryptography in an effort to account for side channel attacks in the security model. This thesis provides an in-depth look into what security guarantees public key leakage resilient schemes provide in practice.

Immanants are a generalization of the well-studied determinant and permanent. Although the combinatorial interpretations for the determinant and permanent have been studied in excess, there remain few combinatorial interpretations for the immanant. The main objective of this thesis is to consider the immanant, and its possible combinatorial interpretations, in terms of recursive structures on the character. This thesis presents a comprehensive view of previous interpretations of immanants. Furthermore, it discusses algebraic techniques that may be used to investigate further into the combinatorial aspects of the immanant. We consider the Temperley-Lieb algebra and the class of immanants over the elements of this algebra. Combinatorial tools including the Temperley-Lieb algebra and Kauffman diagrams will be used in a number of interpretations. In particular, we extend some results for the permanent and determinant based on the $R$-weighted planar network construction, where $R$ is a convenient ring, by Clearman, Shelton, and Skandera. This thesis also presents some cases in which this construction cannot be extended. Finally, we present some extensions to combinatorial interpretations on certain classes of tableaux, as well as certain classes of matrices.

Spectral moment interpolation find application in a wide array of use cases: robust control, system identification, model reduction to name the most notable ones. This thesis aims to expand the theory of such methods in three different directions. The first main contribution concerns the practical applicability. From this point of view various solving algorithm and their properties are considered. This study lead to identify a globally convergent method with excellent numerical properties. The second main contribution is the introduction of an extended interpolation problem that allows to model ARMA spectra without any explicit information of zero’s positions. To this end it was necessary for practical reasons to consider an approximated interpolation insted. Finally, the third main contribution is the application to some problems such as graphical model identification and ARMA spectral approximation. / QC 20110906