Physical Sciences and Mathematics Commons^™

Large Deviation Theory In Stochastic Processes: Applications To Biological Modeling, Moshe C. Silverstein

Dissertations

This dissertation delves into developing and applying stochastic models to analyze complex biological systems. It leverages Large Deviation Theory (LDT) to gain insights into these systems, focusing on two key examples: neural networks and calcium signaling dynamics. Traditional deterministic methods frequently fail to capture biological processes' randomness and inherent variability. Meanwhile, many stochastic approaches struggle to be mathematically tractable or provide accessible insights. The approach introduced in this study provides rigorous mathematical frameworks to enhance understanding of these stochastic behaviors while remaining tractable and insightful.

A stochastic model for a random biological neural network is constructed that addresses the dependencies …

Efficient Numerical Methods For Monge-Ampere Type Equations, Jake S. Brusca

Dissertations

Current numerical methods for Monge-Ampere-type equations and Optimal Transport problems face challenges when handling higher dimensions and large-scale data. This dissertation aims to develop and analyze efficient, highly parallelizable numerical algorithms for solving the Monge-Ampere equation to address these issues. Two approaches are employed:

(1) The discretization method is enhanced by introducing an integral repre-sentation of the Monge-Ampere operator. This integral can be discretized using higher-order quadrature, yielding a more efficient, higher-order monotone scheme that allows for narrower stencils. An additional advantage of this discretization is its natural extension to arbitrary dimensions.

(2) The nonlinear solvers for this scheme are …

Localized Hermite Method Of Approximate Particular Solutions, Kwesi Acheampong

Dissertations

A localized Hermite method of approximate particular solutions (LHMAPS) is presented in this dissertation. This method is designed to improve the accuracy of the localized method of approximate particular solutions (LMAPS) for solving partial differential equations. LMAPS is a strong-form method that defines local radial basis function approximations to the solution values at a group of collocation points before applying the differential operator to this approximation function. Based on the LMAPS's local scheme, LHMAPS seeks Hermite-type local approximations based on both function values and derivatives. Numerical experiments validate the superior accuracy of the proposed method to the LMAPS by solving …

Elevating Commodity Polymers To Advanced Applications In Polymer Photonics And Polymer-Derived Porous Materials, Mark Robertson

Dissertations

Since the inception of synthetic polymers, polymer-derived materials have permeated into essentially all aspects of our daily lives. The most commonly thought of examples of polymer materials involve single-use, disposable products to increase shelf lives of perishable items, act as personal protective equipment, or provide some degree of convenience for the consumer. However, as we have furthered our understanding of polymer chemistry and polymer physics to develop increasingly sophisticated polymer systems, polymer materials have been employed in incredibly advanced applications. These include solid electrolytes for energy storage, matrices for aerospace grade carbon fiber-reinforced composites, membranes for liquid and gas separations, …

Scalable Solution Of Time-Dependent Pdes Through Component-Wise Exponential Integrator, Chelsea Drum

Dissertations

Exponential integrators, such as exponential Runge-Kutta or Rosenbrock methods, are designed specifically for the time integration of stiff systems of ordinary differential equations (ODEs) and allow the use of larger time steps than other general-purpose ODE solvers. However, these methods rely on computing matrix function-vector products that are traditionally computed using a Krylov projection, such as Lanczos or Arnoldi iteration, that involves substantial computational expense at high spatial resolution. Krylov Subspace Spectral (KSS) methods' frequency-dependent approach, designed to circumvent stiffness in linear problems, computes these products with greater scalability. We propose the combination of such KSS methods with exponential integrators …

Delta-Shaped Approximation Based Homotopy Analysis Method For Nonlinear Poisson-Type Partial Differential Equations, Cyril Ocloo

Dissertations

This research aims to solve nonlinear Poisson-type partial differential equations (PDEs) by the approach of the homotopy analysis method (HAM) incorporated with approximate particular solutions (APS) using Delta-shaped basis (DSB) approximations.

With the inclusion of the h auxiliary parameters, we tackle nonlinear problems by studying the mathematical characteristics of the h curve. This is to ensure the numerical convergence of the HAM.

In the solution process, we use the homotopy analysis method to convert a nonlinear PDE into linear inhomogeneous PDEs, which are solved using the method of approximate particular solutions with DSB.

A proper value of the h is …

Poly(Thioether) Thermosets With Gated Photodegradation, Surabhi Jha

Dissertations

Photodegradable polymer networks are attractive due to the precise spatiotemporal control and large-area applicability of light. Chemical linkages that enable these polymer networks to be photo-responsive, also hinder their applicability in ambient light. Photostable and photodegradable networks have recently been reported to overcome this challenge by combining other stimuli with light for degradation. We report the design of a network that responds to a simultaneous, dual stimulus for photodegradation. We design poly(thioether acetal) networks with benzylidene acetal moieties that are known to undergo β-scission in the presence of free thiols. By blocking these free thiols with a thermally labile protecting …

Synthetic Assembly Of Antibacterial Agents And Metal Chelating Ligands, Zachary Joseph Liveris

Dissertations

The exploitation of chemical synthesis exemplifies the notion of bridging both innovation and curiosity for the strategic assembly of sophisticated molecular infrastructures. By exerting this continuously evolving and versatile tool, synthesis has been applied in the development and influence of a myriad of ligands, biological probes, and persists to direct pharmaceutical innovation and modern medicine alike. Since pathogenic multidrug-resistant (MDR) microbial strains remain to be a persistent threat to both clinical healthcare and society, the need to develop selective and efficacious antibacterial agents that can impede microbe pathogenicity and regulate cellular mortality is paramount. In contrast to pharmaceutical development, organic …

Quasi-Monte Carlo Estimation For Functional Generalized Linear Mixed Models., Ruvini Kumari Jayamaha Hitihamilage

Dissertations

Functional Data Analysis (FDA) is a topic of growing interest in the statistics community and is applied in a wide range of fields such as Anthropology, Epidemiology, Meteorology, Neurology and Engineering. The data in FDA are smooth curves or surfaces in time or space which can be conceptualized as functions. Because of the smooth nature of the data and the measurements are highly correlated, making the classical methods such as univariate or multivariate analysis are infeasible for such data. Functional data Analysis (FDA) deals with these kinds of more detailed, complex, and structured data.

In this dissertation, we propose a …

On Near-Linear Cellular Automata Over Near Spaces, Abdul-Rahman M. Nasser

Dissertations

Cellular Automata can be considered as examples of massively parallel machines. They are computational mathematical objects consisting of a grid of cells, each of which can exist in a finite number of states. These cells evolve over discrete time steps according to a set of predefined rules based on the states of neighboring cells. The notion of cellular automata was first introduced by Ulam and von Neumann and then popularized by John H. Conway in the 1970s with one of the most famous examples being The Game of Life.

This research builds on and generalizes the work of Tullio Ceccherini-Silberstein …

Estimating And Applying Parameters Necessary To Plan Cluster Randomized Trials (Crts) And Multisite Cluster Randomized Trials (Mscrts), Dea Mulolli

Dissertations

Cluster randomized trials (CRTs) are commonly used to study the effectiveness of educational interventions. During the design phase of a study, it is critical for researchers to ensure their studies are adequately powered to detect meaningful treatment effects, including both main and moderator effects. Designing CRTs with adequate power to detect main and moderator effects requires accurate estimates of design parameters. This research aims to advance the literature on design parameters for power analyses, specifically focusing on empirical estimates of intraclass correlations (ICCs). The work consists of three research papers that examine the role of including the teacher level in …

A Contingency Table Alternative To Poisson Regression In Comparing The Frequency Distributions Of Two Populations, Sandra Tay

Dissertations

When testing the conditional independence between a binary outcome and a binary treatment indicator, conditioned on a categorical variable with k levels, typically represented by a K × 2 frequency table, researchers often turn to Poisson regression and the Cochran-Mantel-Haenszel (CMH) test. However, a common challenge encountered in these analyses is the presence of treatment effect heterogeneity. Introducing an interaction term between treatment indicators and effect modifiers in log-linear regression offers potential solutions, yet the equidispersion assumption of Poisson regression remains problematic. On the other hand, the CMH test assumes similar treatment effects across all strata, disregarding potential variations among …

A Microgenetic Learning Analysis Of Contextuality In Reasoning About Exponential Modeling, Elahe Allahyari

Dissertations

This work explores the complex cognitive processes students engage in when addressing contextual tasks requiring linear and exponential models. Grounded within Piagetian constructivism and the Knowledge in Pieces (KiP) epistemological perspective (diSessa, 1993, 2018), this empirical study in a clinical setting develops a Microgenetic Learning Analysis (MLA) of the reasoning of 14 students from an Algebra II course. It reveals the critical role of cognitive disequilibrium as an essential cognitive state for conceptual development and the process of reorganizing knowledge systems. The study uncovers the fluctuations in students’ reasoning patterns and the significant impact on students’ reasoning patterns of task-specific …

An Experimental Study Of Supervised Machine Learning Techniques For Minor Class Prediction Utilizing Kernel Density Estimation: Factors Impacting Model Performance, Abdullah Mana Alfarwan

Dissertations

This dissertation examined classification outcome differences among four popular individual supervised machine learning (ISML) models (logistic regression, decision tree, support vector machine, and multilayer perceptron) when predicting minor class membership within imbalanced datasets. The study context and the theoretical population sampled focus on one aspect of the larger problem of student retention and dropout prediction in higher education (HE): identification.

This study differs from current literature by implementing an experimental design approach with simulated student data that closely mirrors HE situational and student data. Specifically, this study tested the predictive ability of the four ISML classification models (CLS) under experimentally …

Alternative Adjacency Matrices And Spatial Analysis, Jaeseong Hwang

Dissertations

Spatial analysis is essential for comprehending the spatial distribution of diseases and various phenomena across geographic regions. This study investigates the utilization of alternative adjacency matrices in spatial analysis, with a specific focus on implementing Poisson regression models. This study intricately explores the methodology behind constructing alternative weight matrices, specifying weight matrices, and comparing the performance of Poisson models using five different weight matrices.

The popular Poisson model model is described, and five different definitions of weight matrices are defined, which are the following: binary weight matrix, inverse distance weight matrix using Euclidean distance, Graph distance matrix, Path matrix, and …

Design, Synthesis And Characterization Of Zinc And Gold-Based Metal Organic Frameworks And Complexes For The Detection And Treatment Of Cancer, May Reda Mohamed

Dissertations

The early detection of cancer plays a pivotal role in improving patient outcomes, emphasizing the urgent need for highly sensitive and selective biosensing platforms. Metal-Organic Frameworks (MOFs) have emerged as promising candidates in this domain due to their tunable properties, large surface area, and high porosity. Herein, the utilization of zinc-based MOF as a sophisticated biosensing platform tailored for the precise detection of the HER2 cancer biomarker is presented. HER2, a critical protein marker in breast cancer diagnostics and treatment, demands highly selective and accurate detection methods for effective patient management. Simple hydrothermal synthesis methodology has been adopted to synthetize …

Development Of Highly Efficient Hybridfunctionalized Membranes For Sustainable Water Harvesting, Ahmed Z. Abuibaid

Dissertations

Water scarcity has emerged as a critical global challenge. This problem catches the world's interest through events such as the severe drought in Europe during the summer of 2022. While desalination plants offer a solution, their high energy consumption necessitates the exploration of alternative, sustainable water resources. Addressing the urgent need for alternative water resources in the face of increasing water scarcity. A viable option was presented by fog harvesting, which is a method to collect water from atmospheric fog. This method was initially developed to meet the demands of a variety of sectors such as agricultural purposes, and household …

Empirical Exploration Of Software Testing, Samia Alblwi

Dissertations

Despite several advances in software engineering research and development, the quality of software products remains a considerable challenge. For all its theoretical limitations, software testing remains the main method used in practice to control, enhance, and certify software quality. This doctoral work comprises several empirical studies aimed at analyzing and assessing common software testing approaches, methods, and assumptions. In particular, the concept of mutant subsumption is generalized by taking into account the possibility for a base program and its mutants to diverge for some inputs, demonstrating the impact of this generalization on how subsumption is defined. The problem of mutant …

Network Slicing And Noma Enabled Mobile Edge Computing For Next-Generation Networks, Mohammad Arif Hossain

Dissertations

The advent of next-generation wireless networks ushers in a new era of potential, harnessing cutting-edge technologies like mobile edge computing (MEC), non-orthogonal multiple access (NOMA), and network slicing as pivotal drivers of transformation. Within this landscape, an innovative approach is proposed by introducing a NOMA-enabled network slicing technique within MEC networks. This approach aims to achieve multiple objectives: meeting stringent quality of service requirements, minimizing service latency, and enhancing spectral efficiency. By seamlessly integrating NOMA with network slicing in edge computing environments, significant reductions in overall latency are achieved, alongside ensuring optimal resource allocation for NOMA users. To address these …

On The Ubiquity, Properties And Evolution Of Small-Scale Magnetic Flux Ropes In The Heliosphere, Hameedullah Farooki

Dissertations

The solar wind is a plasma constantly blowing out from the Sun with a large-scale magnetic field having significant local complexity at small scales. Small-scale magnetic flux ropes (SMFRs), plasma structures with twisted field lines, are an important element of this complexity. This dissertation contributes several studies that further our understanding of SMFRs. The first study applies machine learning to measurements from Wind labeled by the presence of SMFRs and magnetic clouds (MCs). MCs were distinguished from non-MFRs with an AUC of 94% and SMFRs with an AUC of 89% and had distinctive plasma properties, whereas SMFRs appeared to be …

Computational Microscopy For Biomedical Imaging With Deep Learning Assisted Image Analysis, Yuwei Liu

Dissertations

Microscopy plays a crucial role across various scientific fields by enabling structural and functional imaging with microscopic resolution. In biomedicine, microscopy contributes to basic research and clinical diagnosis. Conventionally, optical microscopy derives its contrast from the amplitude of the optical wave and provides visualization of the physical structure of the sample qualitatively. To understand the function at the cellular or tissue level, there is a need to characterize the sample quantitatively and explore contrast mechanisms other than light intensity. Image enhancement or reconstruction from microscopic imaging systems is known as computational microscopy, and it involves the application of computational techniques …

Machine Learning-Based Design Of Doppler Tolerant Radar, Kyle Peter Wensell

Dissertations

In this work, machine learning theory is applied to the design of a radar detector in order to train a machine learning-based detector that is robust against Doppler shifts. The radar system is designed to work with data that would be otherwise intractable to conventional optimal detector design, such as transmitted noise waveforms and the effects of one-bit quantization at the receiver. The detection performance of the one-bit receiver is shown to match the performance of the derived square-law sign correlator detector. The resulting learning-based detector also introduces Doppler tolerance to the system, which allows for the successful detection of …

Information Theoretic Bounds For Capacity And Bayesian Risk, Ian Zieder

Dissertations

In this dissertation, the problem of finding lower error bounds on the minimum mean-squared error (MMSE) and the maximum capacity achieving distribution for a specific channel is addressed. Presented are two parts, a new lower bound on the MMSE and upper and lower bounds on the capacity achieving distribution for a Binomial noise channel. The new lower bound on the MMSE is achieved via use of the Poincare inequality. It is compared to the performance of the well known Ziv-Zakai error bound. The second part considers a binomial noise channel and is concerned with the properties of the capacity-achieving distribution. …

Financial Time Series Fusion, Completion, And Prediction With Deep Neural Networks, Dan Zhou

Dissertations

Time-series analysis is essential for a wide range of financial applications, including but not limited to bond valuation, firm earnings forecasts, firm fundamentals predictions, and firm characteristics imputations. Given its considerable value, the financial community has shown a strong interest in refining and advancing time-series analysis techniques. The study in this dissertation contributes to this field by employing advanced machine learning approaches, specifically graph neural networks, deep neural networks, and matrix/tensor methods. The primary objectives are twofold: first, to reveal complex correlations within financial time series to improve prediction accuracy, and second, to enhance the process of integrating and imputing …

Sensing With Integrity: Responsible Sensor Systems In An Era Of Ai, David Eisenberg

Dissertations

Deep and machine learning now offer immense benefits for consumer choice, decision-making, medicine, mental health and education, smart cities, and intelligent transportation and driver safety. However, as communication and Internet technology further advances, these benefits have the potential to be outweighed by compromises to privacy, personal freedom, consumer trust, and discrimination. While ethical consequences for personal freedom and equity rise from these technological advances, the issue may not be the technology itself but a lack of regulation and policy that allow abuses to occur. A first study examines how emerging sensor-based technologies, limited to only accelerometer and gyroscope data from …

A Molecular Dynamics Study On The Destruction Mechanism Of Per And Polyfluoroalkyl Substances Due To Ultrasound Technology, Bruno Bezerra De Souza

Dissertations

Per- and polyfluoroalkyl substances (PFAS) are a group of stable synthetic chemicals that are highly persistent and harmful pollutants to the environment and human health. PFAS have caused a strong public and regulatory response due to their ubiquitous presence in the environment and toxicity to humans. The application of ultrasound is one of the most effective treatment technologies for the mineralization of PFAS in contaminated water. However, this technology is treated as a black box causing the inability to be optimized. Therefore, there is a pressing need to investigate the intricate dynamics of PFAS degradation under ultrasound to unlock its …

Molecular-To-Continuum Scale Modeling Of Aerosols: Atmospheric Application And Beyond, Ella Ivanova

Dissertations

Aerosol modeling is critical for various applications, such as climate forecasting, air quality, and human health impact assessment. During their lifetime, aerosols undergo a complex evolution, usually divided into several stages — formation, processing, transport, and removal — that occur on different scales. Thus, the choice of modeling methods depends on the stage considered. For example, certain stages of particle formation may require nano-scale modeling while aerosol-cloud interactions span from microscale to mesoscale. This study examines the modeling of aerosol behavior over a wide range of scales, from nano to microscale, with implications to mesoscale.

This dissertation focuses on two …

A Machine Learning-Assisted Steering And Scheduling Framework For Big-Data Scientific Workflows On Heterogeneous Computing Platforms, Yijie Zhang

Dissertations

In next-generation scientific applications, the exponential growth of big data necessitates advanced techniques for efficient data storage, processing, and analysis. This has led to the construction of intricate computing workflows, managed and orchestrated by powerful engines in big data systems as exemplified by Hadoop. As scientific applications increasingly shift towards simulation-centric approaches, traditional methodologies face new challenges in accommodating the complexity of extreme-scale numerical modeling with numerous tunable parameters. To address these challenges, this dissertation propose to develop a machine learning-assisted framework that enables autonomous computational steering of scientific simulations and optimized execution of big-data workflows on heterogeneous platforms. This …

Development Of Super Hydrophobic Membranes And Their Applications, Sumona Paul

Dissertations

Effective liquid phase separation is vital across industries, especially in aviation, chemicals, fuels, and textiles. Membrane technology offers advantages over traditional methods like distillation, with low energy consumption and protection for heat-sensitive molecules. Membrane performance is assessed based on factors such as materials, surface modification, and interactions. This research targets superhydrophobic membranes for liquid-liquid filtration and antiwetting omniphobic membranes for membrane distillation, focusing on properties like contact angle and thermal resistance.

This study presents a highly hydrophobic membrane achieved by immobilizing carbon nanotubes (CNTs) onto a PTFE microfiltration membrane. It's designed for dewatering organic-water mixtures with trace water content via …

The Effects Of Free Volume And Processing On The Development Of Gas Separation Membranes, Jacob Schekman

Dissertations

Structure, thermal, mechanical, gas transport, and free volume properties of thiol-ene based systems are investigated and discussed. In the pursuit of generating low energy-cost polymer membranes for gas separation, it became apparent that UV-curing of thiol-ene materials presented several routes toward achieving this goal. Network structure plays a vital role in determining the gas transport properties of membrane materials. UV photopolymerization techniques provide a means to rapidly vitrify network morphologies which can be tuned depending on choice of monomer. Thiol-ene monomers offer a broad range of precursor materials from which to choose for the design of functional membrane materials.

Chapter …