Browsing by Subject "Applied Mathematics"
Now showing items 1-6 of 6
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Asymptotic Analysis and Performance-based Design of Large Scale Service and Inventory Systems
(2010)Many types of services are provided using some equipment or machines, e.g. transportation systems using vehicles. Designs of these systems require capacity decisions, e.g., the number of vehicles. In my dissertation, I use ... -
Bayesian Model Uncertainty and Prior Choice with Applications to Genetic Association Studies
(2010)The Bayesian approach to model selection allows for uncertainty in both model specific parameters and in the models themselves. Much of the recent Bayesian model uncertainty literature has focused on defining these prior ... -
Estimating the Intrinsic Dimension of High-Dimensional Data Sets: A Multiscale, Geometric Approach
(2011)This work deals with the problem of estimating the intrinsic dimension of noisy, high-dimensional point clouds. A general class of sets which are locally well-approximated by <italic>k</italic> dimensional planes but which ... -
Maximum Norm Regularity of Implicit Difference Methods for Parabolic Equations
(2011)We prove maximum norm regularity properties of L-stable finite differencemethods for linear-second order parabolic equations with coefficientsindependent of time, valid for large time steps. These results are almostsharp; ... -
On Computing Smooth, Singular, and Nearly Singular Integrals on Implicitly Defined Surfaces
(2010)We present numerical methods for the approximation of smooth, singular, and nearly singular integrals on implicitly defined surfaces. We begin with a high-order quadrature formula for an integral over a compact smooth implicitly ... -
Stable Embedded Grid Techniques in Computational Mechanics
(2010)Engineering mechanics problems involving interfaces, whether physical or introduced by numerical methodologies, are commonplace. Just a few examples include fracture and fault mechanics, classical contact-impact, phase ...
