Yes

When applying optimization techniques to complex physical systems, using very large numerical models for the solution of a system of parameter dependent partial differential equations (PDEs) is usually intractable. Surrogate models are used to provide an approximation to the high fidelity models while being computationally cheaper to evaluate. Typically, for time dependent nonlinear problems a reduced order model is built using a basis obtained through proper orthogonal decomposition (POD) and Galerkin projection of the system dynamics. In this thesis we present theoretical and numerical results for parameter dependent model reduction techniques. The methods are motivated by the need for surrogate models specifically designed for nonlinear parameter dependent systems. We focus on methods in which the projection basis also depends on the parameter through extrapolation and interpolation. Numerical examples involving 1D Burgers' equation, 2D Navier-Stokes equations and 2D Boussinesq equations are presented. For each model problem comparison to traditional POD reduced order models will also be presented. / Ph. D.

Investigated in this study was whether a university education course that covers the topics of diversity and cultural responsiveness would change teacher candidates\' existing prejudicial attitudes.  The major variables reported in this study were exposure to diversity coursework which served as the independent variable and teacher candidates\' prejudicial attitudes, which served as the dependent variable. Using the Yoder-Hartman Survey of Beliefs Scale, three research questions were addressed: (a) Are there differences in prejudice level between preservice teachers who have taken a diversity course and those who have not taken a diversity course? (b) Are there differences in prejudice level in preservice teachers before and after taking a diversity course? and (c) Do preservice teachers who have taken a diversity course and those who have not taken a diversity course display different pre/post levels of assessed prejudice? No differences were found between students who had taken a diversity course and those who had not. The current study suggests that one diversity course is not sufficient to have a significant effect on prejudice reduction among preservice teachers. Analyses of the current study results suggest that the coursework designed to reduce prejudicial attitudes was ineffective. Continued investigation will be required to: (1) refine and develop a program that will reduce prejudicial attitudes among teacher candidates and (2) refine and develop measures of prejudice reduction. / Ph. D.

The dissolved oxygen content of market milk fluctuates enough to cause a variation in the test. / Master of Science

In the past, water treatment plants have stopped the application of pre-filter oxidants to create a bioactive filtration process to remove soluble Mn. After the cessation of pre-filter oxidants, a Mn desorption phenomenon was seen where effluent Mn exceeds influent Mn concentrations. The reason for the sudden increase in effluent Mn was not known, but it was hypothesized that Mn-reducing bacteria on the filter media play a substantial role in this phenomenon. The primary goal of this research was to assess the role of Mn-reducing microorganisms in the desorption of MnOx(s) from coated filters once pre-filtration chlorine ceased. A secondary objective included the development of a molecular detection method for Mn-reducing microorganisms in laboratory and environmental samples. Bench-scale filter column studies were completed to investigate the impacts of Mn-reducing microbial populations on desorption of Mn from MnOx(s) coatings. Secondarily, the effects of influent carbon loading and MnOx(s) age on Mn desorption were investigated. In situ vial assays were created to gain insight into the impacts of MnOx(s) age on Mn reducing microorganism bioavailability. Lastly, a qPCR detection method was developed that targeted the mtrB gene. Results determined that microbially mediated Mn desorption was possible when sufficient numbers of Mn-reducing microorganisms were present on the MnOx(s) surface and that those organisms contributed to the Mn desorption phenomenon. qPCR detection methods were able to show a greater number of Mn-reducing microorganisms in studies where Mn desorption was observed. Lastly, MnOx(s) age was shown to play an important, but unexplained, role in bioavailability. / Master of Science

Presented in this paper are experiments to test the hypothesis that drag reduction is possible over hydrophobic surfaces in the Wenzel state during laminar and turbulent flows. Quantification of surface drag reduction in rectangular channel flow over walls with specific hydrophobic or hydrophilic properties was obtained with pressure drop measurements along the channel for a range of Reynolds numbers between 350 and 5900. Several commercially available materials and coatings were chosen in order to span a range of contact angles between 30° and 135°. The results are within the bounds of the theoretical values calculated with the Colebrook equation, and do not show any reduction in wall shear stress as a function of material properties or surface chemistry. The differences between this experiment and others measuring pressure drop over hydrophobic surfaces is the macro-scale conditions and the hydrophobic surfaces being fully wetted. These experiments are further proof of the importance of a liquid-vapor interface for increasing the shear free area to produce drag reduction. / Master of Science

For parameter inversion problems governed by systems of partial differential equations, such as those arising in Diffuse Optical Tomography (DOT), even the cost of repeated objective function evaluation can be overwhelming. Despite the linear (in the state variable) nature of the DOT problem, the nonlinear parameter inversion process is dominated by the computational burden of solving a large linear system for each source and frequency. To compute the Jacobian for use in Newton-type methods, an adjoint solve is required for each detector and frequency. When a three-dimensional tomography problem may have nearly 1,000 sources and detectors, the computational cost of an optimization routine is a large burden. While techniques from model order reduction can partially alleviate the computational cost, obtaining error bounds in parameter space is typically not feasible. In this work, we examine two different remedies based on stochastic estimates of the objective function. In the first manuscript, we focus on maximizing the efficiency of using stochastic estimates by replacing our objective function with a surrogate objective function computed from a reduced order model (ROM). We use as few as a single sample to detect a misfit between the full-order and surrogate objective functions. Once a sufficiently large difference is detected, it is necessary to update the ROM to reduce the error. We propose a new technique for improving the ROM with very few large linear solutions. Using this techniques, we observe a reduction of up to 98% in the number of large linear solutions for a three-dimensional tomography problem. In the second manuscript, we focus on establishing a robust algorithm. We propose a new trust region framework that replaces the objective function evaluations with stochastic estimates of the improvement factor and the misfit between the model and objective function gradients. If these estimates satisfy a fixed multiplicative error bound with a high, but fixed, probability, we show that this framework converges almost surely to a stationary point of the objective function. We derive suitable bounds for the DOT problem and present results illustrating the robust nature of these estimates with only 10 samples per iteration. / Doctor of Philosophy / For problems such as medical imaging, the process of reconstructing the state of a system from measurement data can be very expensive to compute. The ever increasing need for high accuracy requires very large models to be used. Reducing the computational burden by replacing the model with a specially constructed smaller model is an established and effective technique. However, it can be difficult to determine how well the smaller model matches the original model. In this thesis, we examine two techniques for estimating the quality of a smaller model based on randomized combinations of sources and detectors. The first technique focuses on reducing the computational cost as much as possible. With the equivalent of a single randomized source, we show that this estimate is an effective measure of the model quality. Coupled with a new technique for improving the smaller model, we demonstrate a highly efficient and robust method. The second technique prioritizes robustness in its algorithm. The algorithm uses these randomized combinations to estimate how the observations change for different system states. If these estimates are accurate with a high probability, we show that this leads to a method that always finds a minimum misfit between predicted values and the observed data.

When exploring large, high-dimensional datasets, analysts often utilize two techniques for reducing the data to make exploration more tractable. The first technique, dimension reduction, reduces the high-dimensional dataset into a low-dimensional space while preserving high-dimensional structures. The second, clustering, groups similar observations while simultaneously separating dissimilar observations. Existing work presents a number of systems and approaches that utilize these techniques; however, these techniques can cooperate or conflict in unexpected ways. The core contribution of this work is the systematic examination of the design space at the intersection of dimension reduction and clustering when building intelligent, interactive tools in visual analytics. I survey existing techniques for dimension reduction and clustering algorithms in visual analytics tools, and I explore the design space for creating projections and interactions that include dimension reduction and clustering algorithms in the same visual interface. Further, I implement and evaluate three prototype tools that implement specific points within this design space. Finally, I run a cognitive study to understand how analysts perform dimension reduction (spatialization) and clustering (grouping) operations. Contributions of this work include surveys of existing techniques, three interactive tools and usage cases demonstrating their utility, design decisions for implementing future tools, and a presentation of complex human organizational behaviors. / Doctor of Philosophy / When an analyst is exploring a dataset, they seek to gain insight from the data. With data sets growing larger, analysts require techniques to help them reduce the size of the data while still maintaining its meaning. Two commonly-utilized techniques are dimension reduction and clustering. Dimension reduction seeks to eliminate unnecessary features from the data, reducing the number of columns to a smaller number. Clustering seeks to group similar objects together, reducing the number of rows to a smaller number. The contribution of this work is to explore how dimension reduction and clustering are currently being used in interactive visual analytics systems, as well as to explore how they could be used to address challenges faced by analysts in the future. To do so, I survey existing techniques and explore the design space for creating visualizations that incorporate both types of computations. I look at methods by which an analyst could interact with those projections in other to communicate their interests to the system, thereby producing visualizations that better match the needs of the analyst. I develop and evaluate three tools that incorporate both dimension reduction and clustering in separate computational pipelines. Finally, I conduct a cognitive study to better understand how users think about these operations, in order to create guidelines for better systems in the future.

Arsenic sorbs strongly to the surfaces of Fe(III) (hydr)oxides. Under aerobic conditions, oxygen acts as the terminal electron acceptor in microbial respiration and Fe(III) (hydr)oxides are highly insoluble, thus arsenic remains associated with Fe(III) (hydr)oxide phases. However, under anaerobic conditions Fe(III)-reducing microorganisms can couple the reduction of solid phase Fe(III) (hydr)oxides with the oxidation of organic carbon. When ferric iron is reduced to ferrous iron, arsenic is mobilized into groundwater. Although this process has been documented in a variety of pristine and contaminated environments, minimal information exists on the mechanisms causing this arsenic mobilization. Arsenic mobilization was studied by conducting controlled microcosm experiments containing an arsenic-bearing ferrihydrite and an Fe(III)-reducing microorganism, Geobacter metallireducens. Results show that arsenic mobility is strongly controlled by microbially-mediated disaggregation of arsenic-bearing iron nanoparticles. The most likely controlling mechanism of this disaggregation of iron oxide nanoparticles is a change in mineral phase from ferrihydrite to magnetite, a mixed Fe(III) and Fe(II) mineral, due to the microbially-mediated reduction of Fe(III). Although arsenic remained associated with the iron oxide nanoparticles and was not released as a hydrated oxyanion, the arsenic-bearing nanoparticles could be readily mobilized in aquifers. These results have significant implications for understanding arsenic behavior in aquifers with Fe(III) reducing conditions, and may aid in improving remediation of arsenic-contaminated waters. / Master of Science

Making sense of large collections of images is difficult. Dimension reductions (DR) assist by organizing images in a 2D space based on similarities, but provide little support for explaining why images were placed together or apart in the 2D space. Additionally, they do not provide support for modifying and updating the 2D space to explore new relationships and organizations of images. To address these problems, we present an interactive DR method for images that uses visual features extracted by a deep neural network to project the images into 2D space and provides visual explanations of image features that contributed to the 2D location. In addition, it allows people to directly manipulate the 2D projection space to define alternative relationships and explore subsequent projections of the images. With an iterative cycle of semantic interaction and explainable-AI feedback, people can explore complex visual relationships in image data. Our approach to human-AI interaction integrates visual knowledge from both human mental models and pre-trained deep neural models to explore image data. Two usage scenarios are provided to demonstrate that our method is able to capture human feedback and incorporate it into the model. Our visual explanations help bridge the gap between the feature space and the original images to illustrate the knowledge learned by the model, creating a synergy between human and machine that facilitates a more complete analysis experience. / Master of Science / High-dimensional data is everywhere. A spreadsheet with many columns, text documents, images, ... ,etc. Exploring and visualizing high-dimensional data can be challenging. Dimension reduction (DR) techniques can help. High dimensional data can be projected into 3d or 2d space and visualized as a scatter plot.Additionally, DR tool can be interactive to help users better explore data and understand underlying algorithms. Designing such interactive DR tool is challenging for images. To address this problem, this thesis presents a tool that can visualize images to a 2D plot, data points that are considered similar are projected close to each other and vice versa. Users can manipulate images directly on this scatterplot-like visualization based on own knowledge to update the display, saliency maps are provided to reflect model's re-projection reasoning.