Physical Sciences and Mathematics Commons^™

Learning Graphical Models Of Multivariate Functional Data With Applications To Neuroimaging, Jiajing Niu

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This dissertation investigates the functional graphical models that infer the functional connectivity based on neuroimaging data, which is noisy, high dimensional and has limited samples. The dissertation provides two recipes to infer the functional graphical model: 1) a fully Bayesian framework 2) an end-to-end deep model.

We first propose a fully Bayesian regularization scheme to estimate functional graphical models. We consider a direct Bayesian analog of the functional graphical lasso proposed by Qiao et al. (2019).. We then propose a regularization strategy via the graphical horseshoe. We compare both Bayesian approaches to the frequentist functional graphical lasso, and compare the …

Elucidation Of Active Site And Mechanism Of Metal Catalysts Supported In Nu-1000, Hafeera Shabbir

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Advances in extraction of shale oil and gas has increased the production of geographically stranded natural gas (primarily consisting of methane (C1) and ethane (C2)) that is burned on site. A potential utilization strategy for shale gas is to convert it into fuel range hydrocarbons by catalytic dehydrogenation followed by oligomerization by direct efficient catalysts. This work focuses on understanding metal cation catalysts supported on metal-organic framework (MOF) NU-1000 that will actively and selectively do this transformation under mild reaction conditions, while remaining stable to deactivation (via metal agglomeration or sintering). I built computational models validated by experimental methods to …

Computational And Experimental Investigations Of Alkali Cation Interactions At The Rutile – Water Interface, Isaac Johnston

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Overall, the objective of this dissertation was to investigate the degree of sorption for the alkali cations on rutile to ascertain the impact of different cation properties, such as ion size and charge density, on sorption mechanics as well as probe how the ion may alter the surface – aqueous interface. Initial molecular dynamic simulations and batch experiments showed minimal surface sorption for any alkali cation at relatively low concentrations while simultaneously suggesting the enthalpy of deprotonation shifts slightly in the presence of the alkali cations at different ionic strengths. The cations are likely causing small reorientations of the near-surface …

Improving Efficiency Of Rational Krylov Subspace Methods, Shengjie Xu

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This thesis studies two classes of numerical linear algebra problems, approximating the product of a function of a matrix with a vector, and solving the linear eigenvalue problem $Av=\lambda Bv$ for a small number of eigenvalues. These problems are solved by rational Krylov subspace methods (RKSM). We present several improvements in two directions: pole selection and applying inexact methods.

In Chapter 3, a flexible extended Krylov subspace method ($\mathcal{F}$-EKSM) is considered for numerical approximation of the action of a matrix function $f(A)$ to a vector $b$, where the function $f$ is of Markov type. $\mathcal{F}$-EKSM has the same framework as …

Uni-Prover: A Universal Automated Prover For Specificationally Rich Languages, Nicodemus Msafiri John Mbwambo

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Formal software verification systems must be designed to adapt to growth in the scope and complexity of software, driven by expanding capabilities of computer hardware and domain of potential usage. They must provide specification languages that are flexible and rich enough to allow software developers to write precise and comprehensible specifications for a full spectrum of object-based software components. Rich specification languages allow for arbitrary extensions to the library of mathematical theories, and critically, verification of programs with such specifications require a universal automated prover. Most existing verification systems either incorporate specification languages limited to first-order logic, which lacks the …

Developing And Facilitating Temporary Team Mental Models Through An Information-Sharing Recommender System, Geoffrey Musick

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It is well understood that teams are essential and common in many aspects of life, both work and leisure. Due to the importance of teams, much research attention has focused on how to improve team processes and outcomes. Of particular interest are the cognitive aspects of teamwork including team mental models (TMMs). Among many other benefits, TMMs involve team members forming a compatible understanding of the task and team in order to more efficiently make decisions. This understanding is sometimes classified using four TMM domains: equipment (e.g., operating procedures), task (e.g., strategies), team interactions (e.g., interdependencies) and teammates (e.g., tendencies). …

On Variants Of Sliding And Frank-Wolfe Type Methods And Their Applications In Video Co-Localization, Seyed Hamid Nazari

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In this dissertation, our main focus is to design and analyze first-order methods for computing approximate solutions to convex, smooth optimization problems over certain feasible sets. Specifically, our goal in this dissertation is to explore some variants of sliding and Frank-Wolfe (FW) type algorithms, analyze their convergence complexity, and examine their performance in numerical experiments. We achieve three accomplishments in our research results throughout this dissertation. First, we incorporate a linesearch technique to a well-known projection-free sliding algorithm, namely the conditional gradient sliding (CGS) method. Our proposed algorithm, called the conditional gradient sliding with linesearch (CGSls), does not require the …

Statistical Methods For Modern Threats, Brandon Lumsden

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More than ever before, technology is evolving at a rapid pace across the broad spectrum of biological sciences. As data collection becomes more precise, efficient, and standardized, a demand for appropriate statistical modeling grows as well. Throughout this dissertation, we examine a variety of new age data arising from modern technology of the 21st century. We begin by employing a suite of existing statistical techniques to address research questions surrounding three medical conditions presenting in public health sciences. Here we describe the techniques used, including generalized linear models and longitudinal models, and we summarize the significant associations identified between research …

Lindley Processes With Correlated Changes, John Grant

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This dissertation studies a Lindley random walk model when the increment process driving the walk is strictly stationary. Lindley random walks govern customer waiting times in many queueing models and several natural and business processes, including snow depths, frozen soil depths, inventory quantities, etc. Probabilistic properties of a Lindley process with time-correlated stationary changes are explored. We provide a streamlined argument that the process admits a limiting stationary distribution when the mean of the incremental changes is negative and that the Lindley process is strictly stationary when starting from this stationary distribution. The Markov characteristics of the process are explored …

Ligand-Promoted Dissolution Of Uranyl Phosphate Across Scales, Brennan Ferguson

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The formation of uranyl phosphate precipitate is a remediation strategy because the low solubility of uranyl phosphate minerals, like chernikovite, limits the mobility of uranium in contaminated soils. However, organic ligands can complex with aqueous metal cations to form more soluble species. For example, citrate is a commonly occurring organic ligand produced by plants and microbes that increases the solubility of uranium and therefore the dissolution of uranyl phosphate minerals in the uranyl phosphate-citrate system. This effect is an important control on the mobility of uranium in organic-rich, and near-surface vegetated environments. Nevertheless, key aspects of the citrate-uranyl phosphate system …

Cohen-Macaulay Type Of Weighted Path Ideals, Shuai Wei

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In this dissertation we give a combinatorial characterization of all the weighted $r$-path suspensions for which the $f$-weighted $r$-path ideal is Cohen-Macaulay. In particular, it is shown that the $f$-weighted $r$-path ideal of a weighted $r$-path suspension is Cohen-Macaulay if and only if it is unmixed. Type is an important invariant of a Cohen-Macaulay homogeneous ideal in a polynomial ring $R$ with coefficients in a field. We compute the type of $R/I$ when $I$ is any Cohen-Macaulay $f$-weighted $r$-path ideal of any weighted $r$-path suspension, for some chosen function $f$. In particular, this computes the type for all weighted trees …

Green On The Map - The Influence Of Conservation Easements On The Naturalness Of Landscapes In The United States, Nakisha Fouch

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Large protected areas have long been the cornerstone of conservation biology, however, in an era branded by the human dominance of ecosystems, regional landscape structure and function are often a consequence of accumulated land-use decisions that may or may not include a nod to conservation planning. With underrepresentation of habitats in publicly protected areas, attention has focused on the function of alternative land conservation mechanisms. Private conservation easements (CEs) have proliferated in the United States, yet assessing landscape-level function is confounded by holder and donor intent, national and regional policy, regional landscape contexts, varying extents, resolution, and temporal scale. Over …

Geology-Based Shear-Wave Velocity Model Of Reference Site Conditions In South Carolina For Seismic Site Response Analysis, Camilius Amevorku

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Assessing earthquake hazard in the State of South Carolina is important because it is one of the most seismically active regions of the eastern United States and has experienced earthquakes of damaging levels in the historical past. Examples of these damaging seismic events are the 1886 Charleston earthquake (M 6.7 to 7.5) and the 1913 Union County earthquake (M 4.5 to 5.5).

Small-strain shear-wave velocity (V_S) is an important parameter in performing site response analysis. The deep nature of the top of reference firm rock (i.e., V_S ≥ 760 m/s or B-C boundary) due to …

Advanced High Dimensional Regression Techniques, Yuan Yang

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This dissertation focuses on developing high dimensional regression techniques to analyze large scale data using both Bayesian and frequentist approaches, motivated by data sets from various disciplines, such as public health and genetics. More specifically, Chapters 2 and Chapter 4 take a Bayesian approach to achieve modeling and parameter estimation simultaneously while Chapter 3 takes a frequentist approach. The main aspects of these techniques are that they perform variable selection and parameter estimation simultaneously, while also being easily adaptable to large-scale data. In particular, by embedding a logistic model into traditional spike and slab framework and selecting of proper prior …

Competition Between Halogen And Chalcogen Bonding And Their Role In Probing Organic Transformations, Andrew Peloquin

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Halogen bonding, the attractive interaction of an electrophilic region on a halogen atom with a nucleophilic region on another atom or molecule, provides a highly directional tool in forming solid-state motifs. This interaction, along with the related chalcogen bonding interactions, forms powerful synthons, which, when combined with other typical intermolecular attractions such as hydrogen bonding, allow for the design of supramolecular structures and inputs to crystal engineering. This dissertation research serves two primary purposes: (1) to catalog halogen and chalcogen bonding interactions with various donor molecules and (2) to utilize these interactions to probe interesting organic transformations.

In order to …

Evaluating Privacy Adaptation Presentation Methods To Support Social Media Users In Their Privacy-Related Decision-Making Process, Moses Namara

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Several privacy scholars have advocated for user-tailored privacy (UTP). A privacy-enhancing adaptive privacy approach to help reconcile users' lack of awareness, privacy management skills and motivation to use available platform privacy features with their need for personalized privacy support in alignment with their privacy preferences. The idea behind UTP is to measure users' privacy characteristics and behaviors, use these measurements to create a personalized model of the user's privacy preferences, and then provide adaptive support to the user in navigating and engaging with the available privacy settings---or even implement certain settings automatically on the user's behalf. To this end, most …

Development Of A Reverse Engineered, Parameterized, And Structurally Validated Computational Model To Identify Design Parameters That Influence American Football Faceguard Performance, William Ferriell

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Traumatic brain injury (TBI) continues to have the greatest incidence among athletes participating in American football. The headgear design research community has focused on developing accurate computational and experimental analysis techniques to better assess the ability of headgear technology to attenuate impacts and protect athletes from TBI. Despite efforts to innovate the headgear system, minimal progress has been made to innovate the faceguard. Although the faceguard is not the primary component of the headgear system that contributes to impact attenuation, faceguard performance metrics, such as weight, structural stiffness, and visual field occlusions, have been linked to athlete safety. To improve …

Radioluminescence Based Biochemical Sensing And Imaging Strategies To Measure Local Drug Release And Ph, Gretchen B. Schober

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In this dissertation we describe methods for measuring infection relevant biochemical analytes using radioluminescent and ultrasound luminescent materials. Films and nanoparticles fabricated with europium doped gadolinium oxysulfide (Gd₂O₂S:Eu³⁺) are used to quantitatively measure radiolabeled pharmaceutical concentration, specifically tritium labeled vancomycin (³H-vancomycin). Europium and dysprosium doped strontium aluminate is used to fabricate an ultrasound modulated, pH sensing film. These methods are indicated for theranostic evaluation of implant associated infection. Bacterial biofilms are inherently resistant to traditional antibiotic treatment and can coat biomedical implants. These biofilm related infections are difficult or impossible to eradicate …

Revealing The Role Of Electrostatics In Molecular Recognition, Ion Binding And Ph-Dependent Phenomena, Mihiri Hewa Bosthanthirige

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In this dissertation, we study the role of electrostatics in molecular recognition, ion binding and pH-dependent phenomena. In this work that includes three different research projects, the Poisson-Boltzmann (PB) model is used to describe the biological system and Delphi (which is a popular tool for solving the PB equation (PBE)) to study the electrostatics of biomolecular systems.

Chapter two aims to investigate the role of electrostatic forces in molecular recognition. We calculated electrostatic forces between binding partners separated at various distances. To accomplish this goal, we developed a method to find an appropriate direction to move one chain of protein …

The Pursuit For Gamma-Ray Emitting Pulsar Wind Nebulae With The Fermi-Large Area Telescope, Jordan Eagle

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Pulsar wind nebulae are highly magnetized particle winds, descending from core collapse supernovae (CC SNe), and each powered by an energetic, rapidly rotating neutron star. There are at least 125 Galactic pulsar wind nebulae (PWNe) that have been discovered from radio wavelengths to TeV gamma-rays, the majority of which were first identified in radio or X-ray surveys. An increasing number of PWNe are being identified in the TeV band by ground-based air Cherenkov Telescopes such as HESS, MAGIC, and VERITAS such that they constitute the dominant source class of Galactic TeV emitters. High-energy sources like PWNe may be responsible for …

Controlled Manipulation Of Droplets On Fibers: Fundamentals And Printing Applications, Yueming Sun

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In this dissertation, the drop interactions with a single fiber is discussed under an application angle for the development on new Drop-on-Demand (DOD) printhead using a fiber-in-a-tube platform[1] to print highly viscous materials[2]. To control the drop formation and manipulation on fiber, one needs to know how the fiber wetting properties and the fiber diameter influence drop formation. And then, one needs to know the effects of fiber movement in the device on drop formation. These two questions constitute the main theme of this dissertation.

Before this study, it was accepted that the liquids could not form axisymmetric droplets if …

Minimal Differential Graded Algebra Resolutions Related To Certain Stanley-Reisner Rings, Todd Anthony Morra

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We investigate algebra structures on resolutions of a special class of Cohen-Macaulay simplicial complexes. Given a simplicial complex, we define a pure simplicial complex called the purification. These complexes arise as a generalization of certain independence complexes and the resultant Stanley-Reisner rings have numerous desirable properties, e.g., they are Cohen-Macaulay. By realizing the purification in the context of work of D'alì, et al., we obtain a multi-graded, minimal free resolution of the Alexander dual ideal of the Stanley-Reisner ideal. We augment this in a standard way to obtain a resolution of the quotient ring, which is likewise minimal and multi-graded. …

Tempering The Adversary: An Exploration Into The Applications Of Game Theoretic Feature Selection And Regression, Stephen Mcgee

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Most modern machine learning algorithms tend to focus on an "average-case" approach, where every data point contributes the same amount of influence towards calculating the fit of a model. This "per-data point" error (or loss) is averaged together into an overall loss and typically minimized with an objective function. However, this can be insensitive to valuable outliers. Inspired by game theory, the goal of this work is to explore the utility of incorporating an optimally-playing adversary into feature selection and regression frameworks. The adversary assigns weights to the data elements so as to degrade the modeler's performance in an optimal …

Quantum-Mechanical Evaluation Of Defects In Uranium-Bearing Materials, Megan Hoover

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Quantum-mechanical calculations using density functional theory with the generalized gradient approximation were employed to investigate the effects dopants have on the uranium dioxide (UO₂) structure. Uraninite is a common U⁴⁺ mineral in the Earth's crust and an important material used to produce energy and medical isotopes. Though the incorporation mechanism remains unclear, divalent cations are known to incorporate into the uranium dioxide system. Three charge-balancing mechanisms were evaluated to achieve a net neutral system, including the substitution of (1) a divalent cation for a tetravalent uranium atom and oxygen atom; (2) two divalent cations for a tetravalent …

Holistic Performance Analysis And Optimization Of Unified Virtual Memory, Tyler Allen

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The programming difficulty of creating GPU-accelerated high performance computing (HPC) codes has been greatly reduced by the advent of Unified Memory technologies that abstract the management of physical memory away from the developer. However, these systems incur substantial overhead that paradoxically grows for codes where these technologies are most useful. While these technologies are increasingly adopted for use in modern HPC frameworks and applications, the performance cost reduces the efficiency of these systems and turns away some developers from adoption entirely. These systems are naturally difficult to optimize due to the large number of interconnected hardware and software components that …

Development Of Plasmonic And X-Ray Luminescence Nanoparticles For Bioimaging And Sensing Applications, Meenakshi Ranasinghe

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This dissertation discusses the development of plasmonic and X-ray luminescence nanoparticles (~100 nm) to use in bioimaging and sensing applications. The nanoparticles have interesting optical properties compared to their atomic levels and bulk materials. The optical properties of nanomaterials can be controlled by changing size, shape, crystal structure, etc. Also, they have a large surface area that can be functionalized with biomolecules. Therefore, the optical properties and biofunctionalized nanomaterials are useful in biomedical applications such as targeted drug delivery, bioimaging, and sensing. The overall theme is to use nanoparticles with interesting optical properties compared to their atomic levels and bulk …

Electrical And Optical Characterization Of Two-Dimensional Semiconductors Using Ultrafast Spectroscopy, Pan Adhikari

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The emergence of two-dimensional (2D) layered materials provides unprecedented opportunities for studying excitonic physics due to the strong Coulomb interaction between the electron-hole pair. Because of the reduced dimensionality and weak dielectric screening, the exciton is stable at room temperature, unlike bulk semiconductors. The evolution from low to high carrier density for optical gain in 2D semiconductors involves insulating exciton gas, exciton condensation, co-existence of various excitonic complexes, electron-hole plasmas (EHPs), or electron-hole liquids (EHLs), leading to the Mott transition. Strong interaction among the excitons, such as exciton-exciton annihilation (EEA), serves as a hot-carrier generation. A bound exciton dissociates into …

Unsupervised Contrastive Representation Learning For Knowledge Distillation And Clustering, Fei Ding

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Unsupervised contrastive learning has emerged as an important training strategy to learn representation by pulling positive samples closer and pushing negative samples apart in low-dimensional latent space. Usually, positive samples are the augmented versions of the same input and negative samples are from different inputs. Once the low-dimensional representations are learned, further analysis, such as clustering, and classification can be performed using the representations. Currently, there are two challenges in this framework. First, the empirical studies reveal that even though contrastive learning methods show great progress in representation learning on large model training, they do not work well for small …

Subwavelength Engineering Of Silicon Photonic Waveguides, Farhan Bin Tarik

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The dissertation demonstrates subwavelength engineering of silicon photonic waveguides in the form of two different structures or avenues: (i) a novel ultra-low mode area v-groove waveguide to enhance light-matter interaction; and (ii) a nanoscale sidewall crystalline grating performed as physical unclonable function to achieve hardware and information security. With the advancement of modern technology and modern supply chain throughout the globe, silicon photonics is set to lead the global semiconductor foundries, thanks to its abundance in nature and a mature and well-established industry. Since, the silicon waveguide is the heart of silicon photonics, it can be considered as the core …

On Complete Integral Closure Of Integral Domains, Todd Fenstermacher

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Given an integral domain D with quotient field K, an element x in K is called integral over D if x is a root of a monic polynomial with coefficients in D. The notion of integrality has roots in Dedekind's work with algebraic integers, and was later developed more rigorously by Emmy Noether. Different variations or generalizations of integrality have since been studied, including almost integrality and pseudo-integrality. In this work we give a brief history of integrality and almost integrality before developing the basic theory of these two notions. We will continue the theory of almost integrality further by …