Physical Sciences and Mathematics Commons^™

Generative Adversarial Game With Tailored Quantum Feature Maps For Enhanced Classification, Anais Sandra Nguemto Guiawa

Doctoral Dissertations

In the burgeoning field of quantum machine learning, the fusion of quantum computing and machine learning methodologies has sparked immense interest, particularly with the emergence of noisy intermediate-scale quantum (NISQ) devices. These devices hold the promise of achieving quantum advantage, but they grapple with limitations like constrained qubit counts, limited connectivity, operational noise, and a restricted set of operations. These challenges necessitate a strategic and deliberate approach to crafting effective quantum machine learning algorithms.

This dissertation revolves around an exploration of these challenges, presenting innovative strategies that tailor quantum algorithms and processes to seamlessly integrate with commercial quantum platforms. A …

Thermodynamic Laws Of Billiards-Like Microscopic Heat Conduction Models, Ling-Chen Bu

Doctoral Dissertations

In this thesis, we study the mathematical model of one-dimensional microscopic heat conduction of gas particles, applying both both analytical and numerical approaches. The macroscopic law of heat conduction is the renowned Fourier’s law J = −k∇T, where J is the local heat flux density, T(x, t) is the temperature gradient, and k is the thermal conductivity coefficient that characterizes the material’s ability to conduct heat. Though Fouriers’s law has been discovered since 1822, the thorough understanding of its microscopic mechanisms remains challenging [3] (2000). We assume that the microscopic model of heat conduction is a hard ball system. The …

Analysis Of Nonequilibrium Langevin Dynamics For Steady Homogeneous Flows, Abdel Kader A. Geraldo

Doctoral Dissertations

First, we propose using rotating periodic boundary conditions (PBCs) [13] to simulate nonequilibrium molecular dynamics (NEMD) in uniaxial or biaxial stretching flow. These specialized PBCs are required because the simulation box deforms with the flow. The method extends previous models with one or two lattice remappings and is simpler to implement than PBCs proposed by Dobson [10] and Hunt [24]. Then, using automorphism remapping PBC techniques such as Lees-Edwards for shear flow and Kraynik-Reinelt for planar elongational flow, we demonstrate expo-nential convergence to a steady-state limit cycle of incompressible two-dimensional
NELD. To demonstrate convergence [12], we use a technique similar …

Reducing Communication In The Solution Of Linear Systems, Neil S. Lindquist

Doctoral Dissertations

There is a growing performance gap between computation and communication on modern computers, making it crucial to develop algorithms with lower latency and bandwidth requirements. Because systems of linear equations are important for numerous scientific and engineering applications, I have studied several approaches for reducing communication in those problems. First, I developed optimizations to dense LU with partial pivoting, which downstream applications can adopt with little to no effort. Second, I consider two techniques to completely replace pivoting in dense LU, which can provide significantly higher speedups, albeit without the same numerical guarantees as partial pivoting. One technique uses randomized …

Space-Angle Discontinuous Galerkin Finite Element Method For Radiative Transfer Equation, Hang Wang

Doctoral Dissertations

Radiative transfer theory describes the interaction of radiation with scattering and absorbing media. It has applications in neutron transport, atmospheric physics, heat transfer, molecular imaging, and others. In steady state, the radiative transfer equation is an integro-differential equation of five independent variables, which are 3 dimensions in space and 2 dimensions in the angular direction. This high dimensionality and the presence of the integral term present serious challenges when solving the equation numerically. Over the past 50 years, several techniques for solving the radiative transfer equation (RTE) have been introduced. These include, but are certainly not limited to, Monte Carlo …

Data-Driven Computational Methods For Quasi-Stationary Distribution And Sensitivity Analysis, Yaping Yuan

Doctoral Dissertations

The goal of the dissertation is to develop the computational methods for quasi-stationary- distributions(QSDs) and the sensitivity analysis of a QSD against the modification of the boundary conditions and against the diffusion approximation.
Many models in various applications are described by Markov chains with absorbing states. For example, any models with mass-action kinetics, such as ecological models, epidemic models, and chemical reaction models, are subject to the population-level randomness called the demographic stochasticity, which may lead to extinction in finite time. There are also many dynamical systems that have interesting short term dynamics but trivial long term dynamics, such as …

Fourth Order Dispersion In Nonlinear Media, Georgios Tsolias

Doctoral Dissertations

In recent years, there has been an explosion of interest in media bearing quartic
dispersion. After the experimental realization of so-called pure-quartic solitons, a
significant number of studies followed both for bright and for dark solitonic struc-
tures exploring the properties of not only quartic, but also setic, octic, decic etc.
dispersion, but also examining the competition between, e.g., quadratic and quartic
dispersion among others.
In the first chapter of this Thesis, we consider the interaction of solitary waves in
a model involving the well-known φ⁴ Klein-Gordon theory, bearing both Laplacian and biharmonic terms with different prefactors. As a …

Towards Reduced-Order Model Accelerated Optimization For Aerodynamic Design, Andrew L. Kaminsky

Doctoral Dissertations

The adoption of mathematically formal simulation-based optimization approaches within aerodynamic design depends upon a delicate balance of affordability and accessibility. Techniques are needed to accelerate the simulation-based optimization process, but they must remain approachable enough for the implementation time to not eliminate the cost savings or act as a barrier to adoption.

This dissertation introduces a reduced-order model technique for accelerating fixed-point iterative solvers (e.g. such as those employed to solve primal equations, sensitivity equations, design equations, and their combination). The reduced-order model-based acceleration technique collects snapshots of early iteration (pre-convergent) solutions and residuals and then uses them to project …

Hyperspectral Unmixing: A Theoretical Aspect And Applications To Crism Data Processing, Yuki Itoh

Doctoral Dissertations

Hyperspectral imaging has been deployed in earth and planetary remote sensing, and has contributed the development of new methods for monitoring the earth environment and new discoveries in planetary science. It has given scientists and engineers a new way to observe the surface of earth and planetary bodies by measuring the spectroscopic spectrum at a pixel scale. Hyperspectal images require complex processing before practical use. One of the important goals of hyperspectral imaging is to obtain the images of reflectance spectrum. A raw image obtained by hyperspectral remote sensing usually undergoes conversion to a physical quantity representing the intensity of …

Model Based Force Estimation And Stiffness Control For Continuum Robots, Vincent A. Aloi

Doctoral Dissertations

Continuum Robots are bio-inspired structures that mimic the motion of snakes, elephant trunks, octopus tentacles, etc. With good design, these robots can be naturally compliant and miniaturizable, which makes Continuum Robots ideal for traversing narrow complex environments. Their flexible design, however, prevents us from using traditional methods for controlling and estimating loading on rigid link robots.

In the first thrust of this research, we provided a novel stiffness control law that alters the behavior of an end effector during contact. This controller is applicable to any continuum robot where a method for sensing or estimating tip forces and pose exists. …

Numerical Methods For Stochastic Stokes And Navier-Stokes Equations, Liet Vo

Doctoral Dissertations

This dissertation consists of three main parts with each part focusing on numerical approximations of the stochastic Stokes and Navier-Stokes equations.

Part One concerns the mixed finite element methods and Chorin projection methods for solving the stochastic Stokes equations with general multiplicative noise. We propose a modified mixed finite element method for solving the Stokes equations and show that the numerical solutions converge optimally to the PDE solutions. The convergence is under energy norms (strong convergence) for the velocity and in a time-averaged norm (weak convergence) for the pressure. In addition, after establishing the error estimates in second moment, high …

A Weak Fractional Calculus Theory And Numerical Methods For Fractional Differential Equations, Mitchell D. Sutton

Doctoral Dissertations

This dissertation is comprised of four integral parts. The first part comprises a self-contained new theory of weak fractional differential calculus in one-dimension. The crux of this new theory is the introduction of a weak fractional derivative notion which is a natural generalization of integer order weak derivatives; it also helps to unify multiple existing fractional derivative definitions.

The second part of this work presents three new families of fractional Sobolev spaces and their accompanying theory in one-dimension. The new construction and theory are based on a newly developed notion of weak fractional derivatives, which are natural generalizations of the …

Decision-Analytic Models Using Reinforcement Learning To Inform Dynamic Sequential Decisions In Public Policy, Seyedeh Nazanin Khatami

Doctoral Dissertations

We developed decision-analytic models specifically suited for long-term sequential decision-making in the context of large-scale dynamic stochastic systems, focusing on public policy investment decisions. We found that while machine learning and artificial intelligence algorithms provide the most suitable frameworks for such analyses, multiple challenges arise in its successful adaptation. We address three specific challenges in two public sectors, public health and climate policy, through the following three essays. In Essay I, we developed a reinforcement learning (RL) model to identify optimal sequence of testing and retention-in-care interventions to inform the national strategic plan “Ending the HIV Epidemic in the US”. …

Data-Driven Modeling And Simulations Of Seismic Waves, Yixuan Wu

Doctoral Dissertations

"In recent decades, nonlocal models have been proved to be very effective in the study of complex processes and multiscale phenomena arising in many fields, such as quantum mechanics, geophysics, and cardiac electrophysiology. The fractional Laplacian(−Δ)^𝛼/2 can be reviewed as nonlocal generalization of the classical Laplacian which has been widely used for the description of memory and hereditary properties of various material and process. However, the nonlocality property of fractional Laplacian introduces challenges in mathematical analysis and computation. Compared to the classical Laplacian, existing numerical methods for the fractional Laplacian still remain limited. The objectives of this research are …

Variational Data Assimilation For Two Interface Problems, Xuejian Li

Doctoral Dissertations

“Variational data assimilation (VDA) is a process that uses optimization techniques to determine an initial condition of a dynamical system such that its evolution best fits the observed data. In this dissertation, we develop and analyze the variational data assimilation method with finite element discretization for two interface problems, including the Parabolic Interface equation and the Stokes-Darcy equation with the Beavers-Joseph interface condition. By using Tikhonov regularization and formulating the VDA into an optimization problem, we establish the existence, uniqueness and stability of the optimal solution for each concerned case. Based on weak formulations of the Parabolic Interface equation and …

Mathematical Model For Osteosarcoma Progression And Treatments, Trang M. Le

Doctoral Dissertations

Cancer is a complex disease where every tumor has its own characteristics, and thus different tumors may respond differently to the same treatments. Osteosarcoma, which is a rare type of cancer with poor prognosis, is especially characterized by its high heteogeneity. Therefore, it is important to study the progression of osteosarcoma tumors in different groups of patients with distinct characteristics. The immune system has been reported to play an important role in the development of various cancers with some immune cells having anti-tumor effects and others having pro-tumor effects. With recent advances in digital cytometry methods, which are techniques to …

Monitoring Mammals At Multiple Scales: Case Studies From Carnivore Communities, Kadambari Devarajan

Doctoral Dissertations

Carnivores are distributed widely and threatened by habitat loss, poaching, climate change, and disease. They are considered integral to ecosystem function through their direct and indirect interactions with species at different trophic levels. Given the importance of carnivores, it is of high conservation priority to understand the processes driving carnivore assemblages in different systems. It is thus essential to determine the abiotic and biotic drivers of carnivore community composition at different spatial scales and address the following questions: (i) What factors influence carnivore community composition and diversity? (ii) How do the factors influencing carnivore communities vary across spatial and temporal …

Birds And Bioenergy: A Modeling Framework For Managed Landscapes At Multiple Spatial Scales, Jasmine Asha Kreig

Doctoral Dissertations

This dissertation examines the design and management of bioenergy landscapes at multiple spatial scales given numerous objectives. Objectives include biodiversity outcomes, biomass feedstock yields, and economic value.

Our study examined biodiversity metrics for 25 avian species in Iowa, including subsets of these species related to ecosystem services. We used our species distribution model (SDM) framework to determine the importance of predictors related to switchgrass production on species richness. We found that distance to water, mean diurnal temperature range, and herbicide application rate were the three most important predictors of biodiversity overall. We found that 76% of species responded positively to …

Preconditioned Nesterov’S Accelerated Gradient Descent Method And Its Applications To Nonlinear Pde, Jea Hyun Park

Doctoral Dissertations

We develop a theoretical foundation for the application of Nesterov’s accelerated gradient descent method (AGD) to the approximation of solutions of a wide class of partial differential equations (PDEs). This is achieved by proving the existence of an invariant set and exponential convergence rates when its preconditioned version (PAGD) is applied to minimize locally Lipschitz smooth, strongly convex objective functionals. We introduce a second-order ordinary differential equation (ODE) with a preconditioner built-in and show that PAGD is an explicit time-discretization of this ODE, which requires a natural time step restriction for energy stability. At the continuous time level, we show …

Machine Learning With Topological Data Analysis, Ephraim Robert Love

Doctoral Dissertations

Topological Data Analysis (TDA) is a relatively new focus in the fields of statistics and machine learning. Methods of exploiting the geometry of data, such as clustering, have proven theoretically and empirically invaluable. TDA provides a general framework within which to study topological invariants (shapes) of data, which are more robust to noise and can recover information on higher dimensional features than immediately apparent in the data. A common tool for conducting TDA is persistence homology, which measures the significance of these invariants. Persistence homology has prominent realizations in methods of data visualization, statistics and machine learning. Extending ML with …

Proper Orthogonal Decomposition: New Approximation Theory And A New Computational Approach, Sarah Katherine Locke

Doctoral Dissertations

“Proper orthogonal decomposition (POD) projection errors and error bounds for POD reduced order models of partial differential equations have been studied by many. In this research we obtain new results regarding POD data approximation theory and present a new difference quotient (DQ) approach for computing the POD modes of the data.

First, we improve on earlier results concerning POD projection errors by extending to a more general framework that allows for non-orthogonal POD projections and seminorms. We obtain new exact error formulas and convergence results for POD data approximation errors, and also prove new pointwise convergence results and error bounds …

Nonparametric Bayesian Deep Learning For Scientific Data Analysis, Devanshu Agrawal

Doctoral Dissertations

Deep learning (DL) has emerged as the leading paradigm for predictive modeling in a variety of domains, especially those involving large volumes of high-dimensional spatio-temporal data such as images and text. With the rise of big data in scientific and engineering problems, there is now considerable interest in the research and development of DL for scientific applications. The scientific domain, however, poses unique challenges for DL, including special emphasis on interpretability and robustness. In particular, a priority of the Department of Energy (DOE) is the research and development of probabilistic ML methods that are robust to overfitting and offer reliable …

Root Stage Distributions And Their Importance In Plant-Soil Feedback Models, Tyler Poppenwimer

Doctoral Dissertations

Roots are fundamental to PSFs, being a key mediator of these feedbacks by interacting with and affecting the soil environment and soil microbial communities. However, most PSF models aggregate roots into a homogeneous component or only implicitly simulate roots via functions. Roots are not homogeneous and root traits (nutrient and water uptake, turnover rate, respiration rate, mycorrhizal colonization, etc.) vary with age, branch order, and diameter. Trait differences among a plant’s roots lead to variation in root function and roots can be disaggregated according to their function. The impact on plant growth and resource cycling of changes in the distribution …

Applications With Discrete And Continuous Models: Harvesting And Contact Tracing, Danielle L. Burton

Doctoral Dissertations

Harvest plays an important role in management decisions, from fisheries to pest control. Discrete models enable us to explore the importance of timing of management decisions including the order of events of particular actions. We derive novel mechanistic models featuring explicit within season harvest timing and level. Our models feature explicit discrete density independent birth pulses, continuous density dependent mortality, and density independent harvest level at a within season harvest time. We explore optimization of within-season harvest level and timing through optimal control of these population models. With a fixed harvest level, harvest timing is taken as the control. Then …

Examining The Accumulation Statistics Of Index1 Saddle Points On The Potential Energy Surface And Imposing Early Termination On A Rejection Scheme For Off Lattice Kinetic Monte Carlo, Jonathan W. Hicks

Doctoral Dissertations

In the calculation of time evolution of an atomic system where a chemical reaction and/or diffusion occurs, off-lattice kinetic Monte Carlo methods can be used to overcome timescale and lattice based limitations from other methods such as Molecular Dynamics and kinetic Monte Carlo procedures. Off-lattice kinetic Monte Carlo methods rely on a harmonic approximation to Transition State Theory, in which the rate of the rare transitions from one energy minimum to a neighboring minimum require surmounting a minimum energy barrier on the Potential Energy Surface, which is found at an index-1 saddle point commonly referred to as a transition state. …

Metabolic Modeling Of Multispecies Microbial Biofilms, Poonam Phalak

Doctoral Dissertations

Biofilms are ubiquitous in medical, environmental, and engineered microbial systems. The majority of naturally occurring microbes grow as mixed species biofilms. These complicated biofilm consortia are comprised of many cell phenotypes with complex interactions and self-organized into three-dimensional structures. Approximately 2% of the US population suffers from non-healing chronic wounds infected by a combination of commensal and pathogenic bacteria whereas about 500,000 cases of Clostridium difficile infections (CDI) are reported annually. These polymicrobial infections are often resilient to antibiotic treatment due to the nutrient-rich environments and species interactions that promote community stability and robustness. This thesis focusses on developing metabolic …

A Framework Of Multi-Dimensional And Multi-Scale Modeling With Applications, Zilong Li

Doctoral Dissertations

In this dissertation, a framework for multi-dimensional and multi-scale modeling is proposed. The essential idea is based on oriented space curves, which can be represented as a 3D slender object or 1D step parameters. SMILES and Masks provide functionalities that extend slender objects into branched and other objects. We treat the conversion between 1D, 2D, 3D, and 4D representations as data unification. A mathematical analysis of different methods applied to helices (a special type of space curves) is also provided. Computational implementation utilizes Model-ViewController design principles to integrate data unification with graphical visualizations to create a dashboard. Applications of multi-dimensional …

Novel Approaches For Constructing Persistent Delaunay Triangulations By Applying Different Equations And Different Methods, Esraa Habeeb Khaleel Al-Juhaishi

Doctoral Dissertations

“Delaunay triangulation and data structures are an essential field of study and research in computer science, for this reason, the correct choices, and an adequate design are essential for the development of algorithms for the efficient storage and/or retrieval of information. However, most structures are usually ephemeral, which means keeping all versions, in different copies, of the same data structure is expensive. The problem arises of developing data structures that are capable of maintaining different versions of themselves, minimizing the cost of memory, and keeping the performance of operations as close as possible to the original structure. Therefore, this research …

Pattern Selection Models: From Normal To Anomalous Diffusion, Hatim K. Khudhair

Doctoral Dissertations

“Pattern formation and selection is an important topic in many physical, chemical, and biological fields. In 1952, Alan Turing showed that a system of chemical substances could produce spatially stable patterns by the interplay of diffusion and reactions. Since then, pattern formations have been widely studied via the reaction-diffusion models. So far, patterns in the single-component system with normal diffusion have been well understood. Motivated by the experimental observations, more recent attention has been focused on the reaction-diffusion systems with anomalous diffusion as well as coupled multi-component systems. The objectives of this dissertation are to study the effects of superdiffusion …

Fuzzy Logistic Regression For Detecting Differential Dna Methylation Regions, Tarek M. Bubaker Bennaser

Doctoral Dissertations

“Epigenetics is the study of changes in gene activity or function that are not related to a change in the DNA sequence. DNA methylation is one of the main types of epigenetic modifications, that occur when a methyl chemical group attaches to a cytosine on the DNA sequence. Although the sequence does not change, the addition of a methyl group can change the way genes are expressed and produce different phenotypes. DNA methylation is involved in many biological processes and has important implications in the fields of biomedicine and agriculture.

Statistical methods have been developed to compare DNA methylation at …