Generating samples from generalized hyperbolic distributions and non-central chi-square distributions by inversion has become an important task for the simulation of recent models in finance in the framework of (quasi-) Monte Carlo. However, their distribution functions are quite expensive to evaluate and thus numerical methods like root finding algorithms are extremely slow. In this paper we demonstrate how our new method based on Newton interpolation and Gauss-Lobatto quadrature can be utilized for financial applications. Its fast marginal generation times make it competitive, even for situations where the parameters are not always constant. / Series: Research Report Series / Department of Statistics and Mathematics

We demonstrate that for the fast numerical inversion of the (generalized) inverse Gaussian distribution two algorithms based on polynomial interpolation are well-suited. Their precision is close to machine precision and they are much faster than the bisection method recently proposed by Y. Lai. / Series: Research Report Series / Department of Statistics and Mathematics

The theory and computation of line defects are discussed in the context of both solids and liquid crystals. This dissertation includes four parts. The Generalized Disclination theory is discussed and applied to numerous interfacial and bulk line defect problems. An augmented Oseen-Frank energy as well as a novel 2D-model is proposed and demonstrated for disclination dynamics in liquid crystal. A model based on kinematics and thermodynamics is devised to predict tactoid dynamics during the process of the isotropic-nematic phase transition in LCLC. In the first part of the thesis, the utility of the notion of generalized disclinations in materials science is discussed within the physical context of modeling interfacial and bulk line defects. The Burgers vector of a disclination dipole in linear elasticity is derived, clearly demonstrating the equivalence of its stress field to that of an edge dislocation. An explicit formula for the displacement jump of a single localized composite defect line in terms of given g.disclination and dislocation strengths is deduced based on the Weingarten theorem for g.disclination theory at finite deformation. The Burgers vector of a g.disclination dipole at finite deformation is also derived. In the second part, a numerical method is developed to solve for the stress and distortion fields of g.disclination systems. Problems of small and finite deformation theory are considered. The fields of various line defects and grain/phase boundary problems are approximated. It is demonstrated that while the far-field topological identity of a dislocation of appropriate strength and a disclinationdipole plus a slip dislocation comprising a disconnection are the same, the latter microstructure is energetically favorable. This underscores the complementary importance of all of topology, geometry, and energetics (plus kinetics) in understanding defect mechanics. It is established that finite element approximations of fields of interfacial and bulk line defects can be achieved in a systematic and routine manner, thus contributing to the study of intricate defect microstructures in the scientific understanding and predictive design of materials. In the third part, nonsingular disclination dynamics in a uniaxial nematic liquid crystal is modeled within a mathematical framework where the kinematics is a direct extension of the classical way of identifying these line defects with singularities of a unit vector field representing the nematic director. We devise a natural augmentation of the Oseen-Frank energy to account for physical situations where infinite director gradients have zero associated energy cost, as would be necessary for modeling half-integer strength disclinations within the framework of the director theory. A novel 2D-model of disclination dynamics in nematics is proposed, which is based on the extended Oseen-Frank energy and takes into account thermodynamics and the kinematics of conservation of defect topological charge. We validate this model through computations of disclination equilibria, annihilation, repulsion, and splitting. In the fourth part, the isotropic-nematic phase transition in chromonic liquid crystals is studied. We simulate such tactoid equilibria and dynamics with a model using degree of order, a variable length director as state descriptors, and an interfacial descriptor. We introduce an augmented Oseen-Frank energy, with non-convexity in both interfacial energy and the dependence of the energy on the degree of order. A strategy is devised based on continuum kinematics and thermodynamics. The model is used to predict tactoid dynamics during the process of phase transition. We reproduce observed behaviors in experiments and perform an experimentally testable parametric study of the effect of bulk elastic and tactoid interfacial energy constants on the interaction of interfacial and bulk fields in the tactoids.

A key challenge for manufacturing companies is to store parts in an efficient way atthe lowest cost possible. As the demand of differentiated products increases, togetherwith the fact that old products are not phased out at the same pace, the need of usingstorage space as dynamically as possible becomes vital.Scania’s engine assembly manufactures engines for various automotive vehicles andmarine & industry applications. The variation in engine range in Scania’s offeringleads to the need of holding a vast, and increasing, assortment of parts in the produc-tion. As a consequence, this puts more pressure on the logistics and furnishing withinthe engine assembly.This master thesis aims to facilitate the process of assigning parts’ storage locationsin the most profitable manner through an optimization model, the Location Model, inExcel VBA. Together with the model, suggestions of work methods are presented.By implementing the Location Model at Scania’s engine assembly, 4,98 % of all keptparts are recommended location changes, while resulting in cost savings, for the chosen30-day period. These location changes result in a cost saving of 6,73 % of the totallogistic costs for the same time period.

This note proposes the continuous treatment approach as a valuable alternative to propensity score matching for evaluating economic effects of merger and acquisitions (M&As). This framework allows considering the variation in treatment intensities explicitly, and it does not call for an arbitrary definition of cutoff values in traded ownership shares to construct a binary treatment indicator. We demonstrate the usefulness of this approach using data from European M&As and by relying on the example of post-M&A employment effects. The empirical exercise reveals some heterogeneities over the whole distribution of acquired ownership shares and across different types of M&As and country groups.

Class of 2013 Abstract / Specific Aims: To assess the association between marginal tax rates (MTR) and innovative output of biotechnology firms. The MTR plays an important role in firms’ financing choices. Assessment of a firm’s tax status may reveal how firms decide on investment policies that affect R&D. Methods: A retrospective database analysis was used. Subjects included were firms within the biotechnology sector with the Standard Industrial Classification code of 2836 from 1980 - 2011. MTR Data was obtained from the S&P Compustat database, and Patent data was obtained from the U.S. Patent and Trademark Office. Changes in MTR’s on outcomes of patents were analyzed by performing an inferential analysis. Generalized estimating equations (GEE) were used, specifically utilizing a GEE regression with a negative binomial distributional family with log link, independent correlation structure and robust standard error variance calculation. Patents were regressed by the lagged change in MTR, after interest deductions. Main Results: The lag years 2 and 5 of the MTR change were statistically significant, (p = 0.031) and (p = 0.026) for each model respectively. Every one unit increase in the change of the MTRs was associated with large and significant drops in patents 78.8% (IRR = 0.212), 90.7% (IRR = 0.093), 92.7% (IRR = 0.073) at year 2 lag and 84.8% (IRR = 0.152), 92.6% (IRR = 0.074) at year 5 lag. Conclusion: An increase in the change of the MTR results in significant drops in patenting activity.

La prise en compte des incertitudes en mécanique des structures constitue un challenge et mène à une importante activité de recherche. L’objectif est d’accroître la capacité prédictive des modèles numériques en couplant le calcul éléments finis et les incertitudes. Dans cette thèse, les incertitudes de type aléatoire sont considérées et les entrées incertaines sont définies par des lois statistiques. En sortie, les résultats sont des quantités statistiques : moyenne, écart-type et densité de probabilité des réponses de la structure. L’objectif de cette recherche est de développer une méthodologie basée sur la méthode des efforts généralisés certains (CGSM) pour l’analyse statique par éléments finis des plaques et coques avec variabilité. L’hypothèse de base est que les efforts généralisés ne dépendent pas des perturbations des paramètres d’entrée. La méthode CGSM est non intrusive et ne nécessite qu’une seule analyse par éléments finis avec un certain nombre de cas de charge pour calculer la variabilité des quantités d’intérêt. Les résultats statistiques sont obtenus par simulations de Monte Carlo, en utilisant une formule semi-analytique. Les paramètres d’entrée incertains sont les modules d’élasticité, les coefficients de Poisson et les épaisseurs. Des variables aléatoires uniformes ainsi que des champs aléatoires sont considérés. Les résultats observés sont les déplacements et les déformations. Plusieurs exemples de plaques en membrane, de plaques en flexion, de coques homogènes ou multicouches, ont été traités. Les résultats sont comparés avec des simulations de Monte Carlo directes. Des résultats très satisfaisants sont obtenus pour la moyenne, l’écart-type et la densité de probabilité des déplacements et des déformations. Les limitations de la méthodologie développée sont aussi mises en évidence, en particulier des écarts ont été observés lorsque des champs aléatoires avec de très petites longueurs de corrélation sont considérés. En résumé, la méthode CGSM présente plusieurs avantages. Elle permet un interfaçage facile avec un logiciel éléments finis standard, une diminution très importante des temps de calcul élevés qui caractérisent la plupart des approches existantes et elle fournit des résultats précis. Par conséquent, l’application de la méthode CGSM à des exemples industriels constitue une perspective prometteuse. / Taking into account uncertainties in structural mechanics is a real challenge and leads to intensive research activities. The aim is to increase the predictive capability of numerical models coupling computational mechanics and uncertainties. In this thesis, aleatory uncertainties are considered and uncertain inputs are defined by probabilistic laws. The outputs are statistical quantities: mean value, standard deviation and probability density functions of the structural responses. The objective of this research is to develop a methodology based on the Certain Generalized Stresses Method (CGSM), for the static finite element analysis of plates and shells with variability. The basic assumption is that the generalized stresses do not depend on input parameters perturbations. The CGSM is a non-intrusive method that requires only one finite element analysis with some load cases to calculate the variability of mechanical quantities of interest. The statistical results are obtained by Monte Carlo simulations, using a semi-analytical formula. The uncertain input parameters are elasticity moduli, Poisson’s ratios and thicknesses. Uniform random parameters as well as random fields have been considered. The output parameters retained for the study are displacements and strains. Several examples of membrane plates, bending plates, and homogeneous as well as multilayered shells, are treated. The results are compared with the direct Monte Carlo Simulation considered as a reference. Very satisfactory results are obtained for the mean value, standard deviation and probability densities of displacements and strains. The limitations of the methodology developed are also highlighted, in particular some discrepancies have been observed when random fields and very small correlation lengths are considered. In summary the CGSM has several advantages. It allows an easy interfacing with standard finite element software, a large reduction of the high computational costs that characterize most of the existing approaches, and leads to accurate results. Consequently, application of the CGSM to real industrial examples is a promising perspective.

One of the major tasks in electronic circuit design is the ability to predict the performance of general circuits in the presence of uncertainty in key design parameters. In the mathematical literature, such a task is referred to as uncertainty quantification. Uncertainty about the key design parameters arises mainly from the difficulty of controlling the physical or geometrical features of the underlying design, especially at the nanometer level. With the constant trend to scale down the process feature size, uncertainty quantification becomes crucial in shortening the design time. To achieve the uncertainty quantification, this thesis presents a new approach based on the concept of generalized Polynomial Chaos (gPC) to perform variability analysis of general nonlinear circuits. The proposed approach is built upon a decoupling formulation of the Galerkin projection (GP) technique, where the large matrix is transformed into a block-diagonal whose diagonal blocks can be factorized independently. The proposed methodology provides a general framework for decoupling the GP formulation based on a general system of orthogonal polynomials. Moreover, it provides a new insight into the error level that is caused by the decoupling procedure, enabling an assessment of the performance of a wide variety of orthogonal polynomials. For example, it is shown that, for the same order, the Chebyshev polynomials outperforms other commonly used gPC polynomials.

Limited research has been performed in Ontario to ascertain risk factors for West Nile Virus (WNV) and to develop a unified risk prediction strategy. The aim of the current body of work was to use spatio-temporal modelling in conjunction with surveillance and environmental data to determine which pre-WNV season factors could forecast a high risk season and to explore how well mosquito surveillance data could predict human cases in space and time during the WNV season. Generalized linear mixed modelling found that mean minimum monthly temperature variables and annual WNV-positive mosquito pools were most significantly predictive of number of human WNV cases (p<0.001). Spatio-temporal cluster analysis found that positive mosquito pool clusters could predict human case clusters up to one month in advance. These results demonstrate the usefulness of mosquito surveillance data as well as publicly available climate data for assessing risk and informing public health practice.

A software program was written that implements a finite element analysis (FEA) solution as the basis of an optimization function used for guiding the inverse design problem of aligning fibres, minimizing displacements in a fibre-reinforced polymer composite part in response to a given loading condition, for various part geometries. The FEA solution makes use of the superlinear RGNTet4 element, which includes 3 displacement and 3 rotational degrees of freedom at 4 nodes. Convergence testing verified the accuracy of the solver versus symbolic results for simple cases. Multivariate optimization over fibre orientations and volume fractions was carried out for a simple test case using the NLOpt nonlinear optimization library. Both derivative-free and gradient-based algorithms were tested. Low-Storage Broyden-Fletcher-Goldfarb-Shannon was the most effective algorithm. Four more complex cases were examined, and by varying fibre orientations, reductions of 48%, 66%, 58% and 32% were achieved in displacements at the loaded nodes.