Physical Sciences and Mathematics Commons^™

Mathematical Analysis Of Feedback Targets Of Bmp Signaling In Drosophila Embryonic Development, Yan Luo

Open Access Theses

Bone morphogenetic proteins (BMPs) drive a range of cellular processes especially in the early stages of embryonic development. This family of proteins acts as one of the most important extracellular signals in development pattern formation across the animal kingdom. Cells in embryos differentiate into different cell types in response to the concentration level of BMP. This complex process is regulated by multiple regulators that serve to tune the signal response.

Extensive experimental and computational research has been performed to analyze BMP regulation in Drosophila, a widely studied model organism, and has advanced our understanding of animal development. Because of …

Generalized Partial Directed Coherence And Centrality Measures In Brain Networks For Epileptogenic Focus Localization, Joshua Aaron Adkinson

Doctoral Dissertations

Accurate epileptogenic focus localization is required prior to surgical resection of brain tissue for treatment of patients with intractable temporal lobe epilepsy, a clinical need that is partially fulfilled to date through a subjective, and at times inconclusive, evaluation of the recorded electroencephalogram (EEG). Using brain connectivity analysis, patterns of causal interactions between brain regions were derived from multichannel EEG of 127 seizures in nine patients with focal, temporal lobe epilepsy (TLE). The statistically significant directed interactions in the reconstructed brain networks were estimated from three second intracranial multi-electrode EEG segments using the Generalized Partial Directed Coherence (GPDC) and validated …

Parametric Approaches To Fractional Programs: Analytical And Empirical Study, Chong Hyun Park

Open Access Dissertations

Fractional programming is used to model problems where the objective function is a ratio of functions. A parametric modeling approach provides effective technique for obtaining optimal solutions of these fractional programming problems. Although many heuristic algorithms have been proposed and assessed relative to each other, there are limited theoretical studies on the number of steps to obtain the solution. In this dissertation, I focus on the linear fractional combinatorial optimization problem, a special case of fractional programming where all functions in the objective function and constraints are linear and all variables are binary that model certain combinatorial structures. Two parametric …

Implementing And Testing A Panel-Based Method For Modeling Acoustic Scattering From Cfd Input, S. Hales Swift

Open Access Dissertations

Exposure of sailors to high levels of noise in the aircraft carrier deck environment is a problem that has serious human and economic consequences. A variety of approaches to quieting exhausting jets from high-performance aircraft are undergoing development. However, testing of noise abatement solutions at full-scale may be prohibitively costly when many possible nozzle treatments are under consideration. A relatively efficient and accurate means of predicting the noise levels resulting from engine-quieting technologies at personnel locations is needed. This is complicated by the need to model both the direct and the scattered sound field in order to determine the resultant …

Local Polynomial Chaos Expansion Method For High Dimensional Stochastic Differential Equations, Yi Chen

Open Access Dissertations

Polynomial chaos expansion is a widely adopted method to determine evolution of uncertainty in dynamical system with probabilistic uncertainties in parameters. In particular, we focus on linear stochastic problems with high dimensional random inputs. Most of the existing methods enjoyed the efficiency brought by PC expansion compared to sampling-based Monte Carlo experiments, but still suffered from relatively high simulation cost when facing high dimensional random inputs. We propose a localized polynomial chaos expansion method that employs a domain decomposition technique to approximate the stochastic solution locally. In a relatively lower dimensional random space, we are able to solve subdomain problems …

Thermal Analysis In A Triple-Layered Skin Structure With Embedded Vasculature, Tumor, And Gold Nanoshells, Casey O. Orndorff

Doctoral Dissertations

In hyperthermia skin cancer treatment, the objective is to control laser heating of the tumor (target temperatures of 42-46 °C) so that the temperatures of the normal tissue surrounding the tumor remains low enough not to damage the normal tissue. However, obtaining accurate temperature distributions in living tissue related to hyperthermia skin cancer treatment without using an intruding sensor is a challenge. The objective of this dissertation research is to develop a mathematical model that can accurately predict the temperature distribution in the tumor region and surrounding normal tissue induced by laser irradiation. The model is based on a modified …

Computational Micro-Flow With Spectral Element Method And High Reynolds Number Flow With Discontinuous Galerkin Finite Element Method, Haibo Zhang

Doctoral Dissertations

In this dissertation, two numerical methods with high order accuracy, Spectral Element Method (SEM) and Discontinuous Galerkin Finite Element Method (DG-FEM), are chosen to solve problems in Computational Fluid Dynamics (CFD). The merits of these two methods will be discussed and utilized in different kinds of CFD problems. The simulations of the micro-flow systems with complex geometries and physical applications will be presented by SEM. Moreover, the numerical solutions for the Hyperbolic Flow will be obtained by DG-FEM. By solving problems with these two methods, the differences between them will be discussed as well.

Compressible Navier-Stokes equations with Electro-osmosis body …

Regularity Of Solutions And The Free Boundary For A Class Of Bernoulli-Type Parabolic Free Boundary Problems With Variable Coefficients, Thomas H. Backing

Open Access Dissertations

In this work the regularity of solutions and of the free boundary for a type of parabolic free boundary problem with variable coefficients is proved. After introducing the problem and its history in the introduction, we proceed in Chapter 2 to prove the optimal Lipschitz regularity of viscosity solutions under the main assumption that the free boundary is Lipschitz. In Chapter 3, we prove that Lipschitz free boundaries possess a classical normal in both space and time at each point and that this normal varies with a Hölder modulus of continuity. As a consequence, the viscosity solution is in fact …

Supervised Learning-Based Explicit Nonlinear Model Predictive Control And Unknown Input Estimation In Biomedical Systems, Ankush Chakrabarty

Open Access Dissertations

Application of nonlinear control theory to biomedical systems involves tackling some unique and challenging problems. The mathematical models that describe biomedical systems are typically large and nonlinear. In addition, biological systems exhibit dynamics which are not reflected in the model (so-called 'un-modeled dynamics') and hard constraints on the states and control actions, which exacerbate the difficulties in designing model-based controllers or observers.

This thesis investigates the design of scalable fast explicit nonlinear model predictive controllers (ENMPCs). The design involves (i) the estimation of a feasible region using Lyapunov stability methods and support vector machines; and (ii) within the estimated feasible …