Computer Science Theses and Dissertationshttp://hdl.handle.net/1903/27562015-08-23T08:33:05Z2015-08-23T08:33:05ZHealth Care Management System for Diabetes Mellitus: A Model-based Systems Engineering FrameworkKatsipis, Iakovoshttp://hdl.handle.net/1903/168182015-07-18T02:32:03Z2015-01-01T00:00:00ZHealth Care Management System for Diabetes Mellitus: A Model-based Systems Engineering Framework
Katsipis, Iakovos
The present thesis develops a framework for Health Care Management Systems using modern Model-Based Systems Engineering methodologies and applies it to Diabetes Mellitus. The desired architecture of such systems is described. Tests and interventions, including Health Care IT, used for Diabetes 2 diagnosis and treatment, are described and modeled. A Controlled Markov Chain model for the progression of Diabetes Mellitus with three states, three diagnostic tests, ten interventions, three patient types, is developed. Evaluation metrics for healthcare quality and associated costs are developed. Using these metrics and disease models, two methods for tradeoff analysis between healthcare quality and costs are developed and analyzed. One is an exhaustive Monte Carlo simulation and the other utilizes multi-criteria optimization with full state information. The latter obtains similar results as the former at a fraction of the time. Practical examples illustrate the powerful capabilities of the framework. Future research directions and extensions are described.
2015-01-01T00:00:00ZComputational Framework for Parametric Modeling and Architecture-Energy Assessment of Building FloorplansTseng, Eddiehttp://hdl.handle.net/1903/168002015-07-18T02:31:34Z2015-01-01T00:00:00ZComputational Framework for Parametric Modeling and Architecture-Energy Assessment of Building Floorplans
Tseng, Eddie
Modern building systems can be exceedingly complex. In this research we develop a computational framework for the parametric modeling and architecture-energy assessment of building floorplans. Parametric representations of floorplans are formulated as multi-layer hierarchies, with adjacent layers coupled by dependency relationships. Software is developed for two approaches to floorplan specification: (1) scripting, and (2) interactive graphical techniques. Computational procedures are developed for assessment of building code regulations, electricity cost assessment, and simplified HVAC component selection and architecture-energy sensitivity analysis. A case study analysis of a two-apartment building system is presented.
2015-01-01T00:00:00ZMultiscale Analysis and Diffusion Semigroups with ApplicationsYacoubou Djima, Karamatou Adjokehttp://hdl.handle.net/1903/167082015-06-28T02:31:27Z2015-01-01T00:00:00ZMultiscale Analysis and Diffusion Semigroups with Applications
Yacoubou Djima, Karamatou Adjoke
Multiscale (or multiresolution) analysis is used to represent signals or functions at increasingly high resolution. In this thesis, we develop multiresolution representa- tions based on frames, which are overcomplete sets of vectors or functions that span an inner product space.
First, we explore composite frames, which generalize certain representations capable of capturing directionality in data. We show that we can obtain composite frames for L^2(R^n) given two main ingredients: 1) dilation operators based on matrices from admissible subgroups G_A and G, and 2) a generating function that is refinable with respect to G_A and G.
We also construct frame multiresolution analyses (MRA) for L^2-functions of spaces of homogeneous type. In this instance, dilations are represented by operators that come from the discretization of a compact symmetric diffusion semigroup. The eigenvectors shared by elements of the compact symmetric diffusion semigroup can be used to define an orthonormal MRA for L^2. We introduce several frame systems that yield an equivalent MRA, notably composite diffusion frames, which are built with the composition of two "similar" compact symmetric diffusion semigroups.
The last part of this thesis is an application of Laplacian Eigenmaps (LE) to a biomedical problem: Age-Related Macular Degeneration. LE, a tool in the family of diffusion methods, uses similarities at local scales to provide global analysis of data sets. We propose a novel approach with two steps. First, we apply LE to retinal images, provided by the National Institute of Health, for feature enhancement and dimensionality reduction. Then, using an original Vectorized Matched Filtering technique, we detect retinal anomalies in eigenimages produced by the LE algorithm.
2015-01-01T00:00:00ZStochastic Simulation: New Stochastic Approximation Methods and Sensitivity AnalysesChau, Mariehttp://hdl.handle.net/1903/167072015-06-28T02:31:18Z2015-01-01T00:00:00ZStochastic Simulation: New Stochastic Approximation Methods and Sensitivity Analyses
Chau, Marie
In this dissertation, we propose two new types of stochastic approximation (SA) methods and study the sensitivity of SA and of a stochastic gradient method to various input parameters. First, we summarize the most common stochastic gradient estimation techniques, both direct and indirect, as well as the two classical SA algorithms, Robbins-Monro (RM) and Kiefer-Wolfowitz (KW), followed by some well-known modifications to the step size, output, gradient, and projection operator.
Second, we introduce two new stochastic gradient methods in SA for univariate and multivariate stochastic optimization problems. Under a setting where both direct and indirect gradients are available, our new SA algorithms estimate the gradient using a hybrid estimator, which is a convex combination of a symmetric finite difference-type gradient estimate and an average of two associated direct gradient estimates. We derive variance minimizing weights that lead to desirable theoretical properties and prove convergence of the SA algorithms.
Next, we study the finite-time performance of the KW algorithm and its sensitivity to the step size parameter, along with two of its adaptive variants, namely Kesten's rule and scale-and-shifted KW (SSKW). We conduct a sensitivity analysis of KW and explore the tightness of an mean-squared error (MSE) bound for quadratic functions, a relevant issue for determining how long to run an SA algorithm. Then, we propose two new adaptive step size sequences inspired by both Kesten's rule and SSKW, which address some of their weaknesses. Instead of us- ing one step size sequence, our adaptive step size is based on two deterministic sequences, and the step size used in the current iteration depends on the perceived proximity of the current iterate to the optimum. In addition, we introduce a method to adaptively adjust the two deterministic sequences.
Lastly, we investigate the performance of a modified pathwise gradient estimation method that is applied to financial options with discontinuous payoffs, and in particular, used to estimate the Greeks, which measure the rate of change of (financial) derivative prices with respect to underlying market parameters and are central to financial risk management. The newly proposed kernel estimator relies on a smoothing bandwidth parameter. We explore the accuracy of the Greeks with varying bandwidths and investigate the sensitivity of a proposed iterative scheme that generates an estimate of the optimal bandwidth.
2015-01-01T00:00:00Z