<p>The main contributions in this thesis are advances in parametric programming. The thesis is divided into three parts; theoretical advances, application areas and constrained control allocation. The first part deals with continuity properties and the structure of solutions to convex parametric quadratic and linear programs. The second part focuses on applications of parametric quadratic and linear programming in control theory. The third part deals with constrained control allocation and how parametric programming can be used to obtain explicit solutions to this problem.</p>

Due to the increasing demand for high dimensional data analysis from various applications such as electrocardiogram signal analysis and gene expression analysis for cancer detection, dimensionality reduction becomes a viable process to extracts essential information from data such that the high-dimensional data can be represented in a more condensed form with much lower dimensionality to both improve classification accuracy and reduce computational complexity. Conventional dimensionality reduction methods can be categorized into stand-alone and hybrid approaches. The stand-alone method utilizes a single criterion from either supervised or unsupervised perspective. On the other hand, the hybrid method integrates both criteria. Compared with a variety of stand-alone dimensionality reduction methods, the hybrid approach is promising as it takes advantage of both the supervised criterion for better classification accuracy and the unsupervised criterion for better data representation, simultaneously. However, several issues always exist that challenge the efficiency of the hybrid approach, including (1) the difficulty in finding a subspace that seamlessly integrates both criteria in a single hybrid framework, (2) the robustness of the performance regarding noisy data, and (3) nonlinear data representation capability. This dissertation presents a new hybrid dimensionality reduction method to seek projection through optimization of both structural risk (supervised criterion) from Support Vector Machine (SVM) and data independence (unsupervised criterion) from Independent Component Analysis (ICA). The projection from SVM directly contributes to classification performance improvement in a supervised perspective whereas maximum independence among features by ICA construct projection indirectly achieving classification accuracy improvement due to better intrinsic data representation in an unsupervised perspective. For linear dimensionality reduction model, I introduce orthogonality to interrelate both projections from SVM and ICA while redundancy removal process eliminates a part of the projection vectors from SVM, leading to more effective dimensionality reduction. The orthogonality-based linear hybrid dimensionality reduction method is extended to uncorrelatedness-based algorithm with nonlinear data representation capability. In the proposed approach, SVM and ICA are integrated into a single framework by the uncorrelated subspace based on kernel implementation. Experimental results show that the proposed approaches give higher classification performance with better robustness in relatively lower dimensions than conventional methods for high-dimensional datasets.

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

A spectral element algorithm for solution of the incompressible Navier-Stokes and heat transfer equations is developed, with an emphasis on extending the classical conforming Galerkin formulations to nonconforming spectral elements. The new algorithm employs both the Constrained Approximation Method (CAM), and the Mortar Element Method (MEM) for p-and h-type nonconforming elements. Detailed descriptions, and formulation steps for both methods, as well as the performance comparisons between CAM and MEM, are presented. This study fills an important gap in the literature by providing a detailed explanation for treatment of p-and h-type nonconforming interfaces. A comparative eigenvalue spectrum analysis of diffusion and convection operators is provided for CAM and MEM. Effects of consistency errors due to the nonconforming formulations on the convergence of steady and time dependent problems are studied in detail. Incompressible flow solvers that can utilize these nonconforming formulations on both p- and h-type nonconforming grids are developed and validated. Engineering use of the developed solvers are demonstrated by detailed parametric analyses of oscillatory flow forced convection heat transfer in two-dimensional channels.

Time-optimal solutions provide us with the fastest means to regulate a system in presence of input constraints. This advantage of time-optimal control solutions is offset by the fact that their real-time implementation involves computationally intensive iterative techniques. Moreover, time-optimal controls depend on the initial state and have to be recalculated for even the slightest perturbation. Clearly time-optimal controls are not good candidates for online regulation. Consequently, the search for alternatives to time-optimal solutions is a very active area of research. The work described here is inspired by the simplicity of optimal-aim concept. The "optimal-aim strategies" provide online regulation in presence of bounded inputs with minimal computational effort. These are based purely on state-space geometry of the plant and are inherently adaptive in nature. Optimal-aim techniques involve aiming of trajectory derivative (or the state velocity vector) so as to approach the equilibrium state in the best possible manner. This thesis documents the efforts to develop an online regulation algorithm for systems with input constraints. Through a number of hypotheses focussed on trying to reproduce the exact time-optimal solution, the diffculty associated with this task is demonstrated. A modification of optimal-aim concept is employed to develop a novel regulation algorithm. In this algorithm, aim directions are chosen in a special manner to generate the time-optimal control approximately. The control scheme thus developed is shown to be globally stabilizing for systems having eigenvalues in the CLHP (closed left half-plane). It is expected that this method or its modifications can be extended to higher dimensional systems as a part of future research. An alternative control algorithm involving a simple state-space aiming concept is also developed and discussed.

The cytoskeleton is a diverse, multi-protein framework that plays a fundamental role in many cellular activities including mitosis, cell division, intracellular transport, cell motility, muscle contraction, and the regulation of cell polarity and organization. Furthermore, cytoskeletal filaments have been implicated in the pathogenesis of a wide variety of diseases including cancer, blood disease, cardiovascular disease, inflammatory disease, neurodegenerative disease, and problems with skin, nail, cornea, hair, liver and colon. Increasing evidence suggests that the distribution and organization of the cytoskeleton in living cells are affected by mechanical stresses and the cytoskeleton determines cell stiffness. We developed a fully nonlinear, constrained mixture model for adherent cells that allows one to account separately for the contributions of the primary structural constituents of the cytoskeleton and extended a prior solution from the finite elasticity literature for use in a sub-class of atomic force microscopy (AFM) studies of cell mechanics. The model showed that the degree of substrate stretch and the geometry of the AFM tip dramatically affect the measured cell stiffness. Consistent with previous studies, the model showed that disruption of the actin filaments can reduce the stiffness substantially, whereas there can be little contribution to the overall cell stiffness by the microtubules or intermediate filaments. To investigate the effect of mechanical stretching on cytoskeletal remodeling and cell stiffness, we developed a simple cell-stretching device that can be combined with an AFM and confocal microscopy. Results demonstrate that cyclic stretching significantly and rapidly alters both cell stiffness and focal adhesion associated vinculin and paxillin, suggesting that focal adhesion remodeling plays a critical role in cell stiffness by recruiting and anchoring F-actin. Finally, we estimated cytoskeletal remodeling by synthesizing data on stretch-induced dynamic changes in cell stiffness and focal adhesion area using constrained mixture approach. Results suggest that the acute increase in stiffness in response to an increased cyclic stretch was probably due to an increased stretch of the original filaments whereas the subsequent decrease back towards normalcy was consistent with a replacement of the highly stretched original filaments with less stretched new filaments.

A Hamiltonian system in potential form (formula in the original abstract) subject to smooth constraints on q can be viewed as a Hamiltonian system on a manifold, but numerical computations must be performed in Rn. In this paper methods which reduce "Hamiltonian differential algebraic equations" to ODEs in Euclidean space are examined. The authors study the construction of canonical parameterizations or local charts as well as methods based on the construction of ODE systems in the space in which the constraint manifold is embedded which preserve the constraint manifold as an invariant manifold. In each case, a Hamiltonian system of ordinary differential equations is produced. The stability of the constraint invariants and the behavior of the original Hamiltonian along solutions are investigated both numerically and analytically.

The main contributions in this thesis are advances in parametric programming. The thesis is divided into three parts; theoretical advances, application areas and constrained control allocation. The first part deals with continuity properties and the structure of solutions to convex parametric quadratic and linear programs. The second part focuses on applications of parametric quadratic and linear programming in control theory. The third part deals with constrained control allocation and how parametric programming can be used to obtain explicit solutions to this problem.

One of the most important challenges in dynamic magnetic resonance imaging (MRI) is to achieve high spatial and temporal resolution when it is limited by system performance. It is desirable to acquire data fast enough to capture the dynamics in the image time series without losing high spatial resolution and signal to noise ratio. Many techniques have been introduced in the recent decades to achieve this goal. Newly developed algorithms like Highly Constrained Backprojection (HYPR) and Compressed Sensing (CS) reconstruct images from highly undersampled data using constraints. Using these algorithms, it is possible to achieve high temporal resolution in the dynamic image time series with high spatial resolution and signal to noise ratio (SNR). In this thesis we have analyzed the performance of HYPR to CS algorithm. In assessing the reconstructed image quality, we considered computation time, spatial resolution, noise amplification factors, and artifact power (AP) using the same number of views in both algorithms, and that number is below the Nyquist requirement. In the simulations performed, CS always provides higher spatial resolution than HYPR, but it is limited by computation time in image reconstruction and SNR when compared to HYPR. HYPR performs better than CS in terms of SNR and computation time when the images are sparse enough. However, HYPR suffers from streaking artifacts when it comes to less sparse image data.

The knowledge regarding certain issues in polymer crystallization e.g. the possible existence of short–lived mesophases remains inconclusive due to experimental limitations. Polymers undergo chain folding upon crystallization, which introduces some complications that are not found in crystallization of low molar mass materials. Chain–folded crystals are far from their equilibrium shape and they rearrange rapidly at the crystallization temperature. This, together with the slow experimental techniques traditionally used, impedes the observation of the originally formed structures. To approach this problem, molecularly constrained polymer structures (in which the crystallizing chains are fixed at one end whereas the other end is free to move) have been studied by X–ray diffraction, differential scanning calorimetry, polarized optical microscopy, transmission electron microscopy and atomic force microscopy. The crystallization studies performed in star–branched polyesters showed that the dendritic cores have a pronounced effect on the crystallization of the linear poly(ε–caprolactone) (PCL) arms attached to them. The star–branched polymers showed slower crystal rearrangement, higher equilibrium melting point, higher fold surface free energy, moderately lower crystallinity, and a greater tendency to form spherulites in comparison with linear PCL. The crystal unit cell was the same in both linear and star–branched PCL. Single crystals of the star–branched polymers were more irregular and showed smoother fold surfaces than linear PCL crystals. No sectorial preference was observed in the crystals of the star–branched polymers upon melting while the single crystals of linear PCL showed earlier melting in the {100} sectors than in the {110} sectors. Some of the differences observed can be attributed to the dendritic cores, which must be placed in the vicinity of the fold surface and thus influence the fold surface structure, the possibility of major crystal rearrangement and the presence of a significant cilia phase during crystal growth causing diverging crystal lamellae and consequent spherulite formation. The attachment of the many crystallizable chains to a single core reduces the melt entropy, which explains the higher equilibrium melting point of star–branched PCL. The crystallization behavior of a series of poly(ethylene oxybenzoate)s was also studied. The polymers showed a profound tendency for crystal rearrangement during melting even at high heating rates. The Hoffman–Weeks extrapolation method was found to be unsuitable to calculate the equilibrium melting point of the samples studied because the melting point vs. crystallization temperature data were sensitive to the variations in crystallisation time, which led to significant variations in the equilibrium melting points obtained. / QC 20100914