Physical Sciences and Mathematics Commons^™

A Review Of Recent Gene Expression-Based And Dna Methylation-Based Mathematical Cell Type Deconvolution Methods, Chenxiao Tian

Arts & Sciences Electronic Theses and Dissertations

In recent years, many cell type deconvolution methods based on DNA methylation data and gene expression data have been developed. Both of these two methods have its special advantages and disadvantages, e.g., DNA methylation-based methods’ data source is usually more stable than gene expression and DNA methylation is easier to measure in FFPE tissues or formalin-fixed paraffin-embedded, while some gene-expression data like scRNA-seq data usually has high cost and complexity. On the other hand, gene expression-based deconvolution methods currently have many more available methods than DNA methylation-based deconvolution methods, which leads to DNA methylation-based methods in many cases can learn …

Non-Adjacent Anti Cyclobutane Pyrimidine Dimers As Intrinsic Probes Of Non-B Form Secondary Structures Of Dna, Natalia Eugenia Gutierrez Bayona

Arts & Sciences Electronic Theses and Dissertations

G-quadruplexes are four-stranded structures of DNA composed of G-quartets that have been proposed to play an extremely important role in replication, transcription, and translation. It has, however, been extremely difficult to unequivocally demonstrate that G-quadruplexes form in living cells due to the lack of probes that would allow for their unambiguous detection and location without disrupting the DNA or the cellular environment. To circumvent these problems, it was proposed that DNA itself could be used as an intrinsic photoprobe for certain classes of G-quadruplex structures and other non-B DNA conformations in vivo. Recently, we discovered that UVB irradiation of human …

Effects Of Functional Network Model Definition On Biomarker Outcome Prediction, Xinyang Feng

Arts & Sciences Electronic Theses and Dissertations

Machine learning (ML) models are widely used to investigate the human connectome and to predict and understand behavior, emotion, and cognition. Prior research has organized pediatric connectome data using adult functional network models. However, this assumes that adult functional network models are appropriate and useful for prediction developmental outcomes from pediatric connectome data. We hypothesize that the application of adult brain network models could result in poor model fit, limiting the generalizability of results. Here, we test whether prediction of biological age is improved by concordant brain network models matching underlying functional connectome data. To quantify the difference in age …

Dealing With Dimensionality: Problems And Techniques In High-Dimensional Statistics, Cezareo Rodriguez

Arts & Sciences Electronic Theses and Dissertations

In modern data analysis, problems involving high dimensional data with more variables than subjects is increasingly common. Two such cases are mediation analysis and distributed optimization. In Chapter 2 we start with an overview of high dimensional statistics and mediation analysis. In Chapter 3 we motivate and prove properties for a new marginal screening procedure for performing high dimensional mediation analysis. This screening procedure is shown via simulation to perform better than benchmark approaches and is applied to a DNA methylation study. In Chapter 4 we construct a cryptosystem that accurately performs distributed penalized quantile regression in the high-dimensional setting …

Kernel Estimation Of Spot Volatility And Its Application In Volatility Functional Estimation, Bei Wu

Arts & Sciences Electronic Theses and Dissertations

It\^o semimartingale models for the dynamics of asset returns have been widely studied in financial econometrics. A key component of the model, spot volatility, plays a crucial role in option pricing, portfolio management, and financial risk assessment. In this dissertation, we consider three problems related to the estimation of spot volatility using high-frequency asset returns. We first revisit the problem of estimating the spot volatility of an It\^o semimartingale using a kernel estimator. We prove a Central Limit Theorem with an optimal convergence rate for a general two-sided kernel under quite mild assumptions, which includes leverage effects and jumps of …

Local Spectroscopy Data Infrastructure: Solid State Nmr Crystallography With Experiment, First-Principal Analysis And Machine Learning, He Sun

Arts & Sciences Electronic Theses and Dissertations

Solid-state magnetic resonance (SSNMR) spectroscopy is a powerful tool for obtaining precise information about the local bonding and morphology of materials. The detailed local structure of crystalline materials cannot be easily solved by traditional experimental methods such as X-ray diffraction (XRD). SSNMR combined with first principal calculation methods such as density functional theory (DFT) can be of great use in this research area. The methodology that is called “NMR crystallography” today has been widely applied to the determination of a wide range of solid materials with an increasing amount of computationally simulated NMR spectra. The construction of a well-established computational …

Development Of Redox-Responsive Phenazine-Based Foldamers. Acylative Kinetic Resolution Of Hydroxamic Acids, Jingwei Yin

Arts & Sciences Electronic Theses and Dissertations

Two different research directions have been presented in this thesis. The first project is about phenazine-based foldamers as molecular actuators. Researchers have been interested in the design and synthesis of foldamers and molecular actuators for years. We began our exploration by demonstrating that phenazine-1,6-dicarboxamides can function as redox-responsive molecular switches. We then designed and synthesized two generations of phenazine-based interleafed foldamers and studied their stability and redox behaviors under chemical and electrochemical conditions. In the second project, we have developed the first acylative kinetic resolution on hydroxamic acids. Although chiral hydroxamic acids have extensive applications, synthetic methods towards them are …

The Isotropic And Anisotropic Structure Of Antarctica From Seismic Inversion, Zhengyang Zhou

Arts & Sciences Electronic Theses and Dissertations

This dissertation utilizes multiple techniques of earthquake tomography to investigate the seismic structure of the crust and mantle beneath Antarctica. The isotropic structure of the Antarctic crust and upper mantle is now constrained by several seismic studies, but until now few studies have investigated the anisotropic structure. Therefore, in this study, I focus on the anisotropic structure, which is crucial information to understanding current or historic deformation and flow patterns, as well as the organic process of Antarctica. I use the data from the seismic stations deployed on the Antarctica continent during the past 20 years, as well as other …

Systems Level Analysis Of Organelle Biogenesis In Saccharomyces Cerevisiae, Kiandokht Panjtan Amiri

Arts & Sciences Electronic Theses and Dissertations

Eukaryotic cells contain hundreds of subcellular structures that serve different functions to maintain cellular homeostasis. A hallmark of Eukaryotic cells is its compartmentalization into membrane-bound organelles. One of the grand challenges in quantitative cell biology is understanding the precision with which cells assemble and maintain subcellular organelles. Despite identification of numerous molecular factors that regulate organelle sizes we lack insight into the quantitative principles underlying organelle size control. We examine organelle sizes from Saccharomyces cerevisiae and human iPS cells with mathematical theory to show that cells can robustly control average fluctuations in organelle size. By demonstrating that organelle sizes obey …

The Effect Of Ionization Density In Applications Of Radiation Detection, Dosimetry, And Therapy, Daniel Mulrow

Arts & Sciences Electronic Theses and Dissertations

This dissertation covers a wide range of topics but is linked by the common theme of radiation interacting with materials and studying the result of those interactions. The introduction describes the fundamentals of how radiation interacts with material and how we are able to detect that radiation and the application of how we use those interactions in radiation oncology. The thesis starts with a chapter detailing the temperature dependence of the photophysics in two organic scintillators. This chapter is the foundation for a future study that will look the degree to which these scintillators can distinguish between gammas and neutrons …

Toward Enhancing The Synthesis Of Renewable Polymers: Feedstock Conversions And Functionalizable Copolymers, Tedd Casey Wiessner

Arts & Sciences Electronic Theses and Dissertations

This thesis describes research under the rubric of the Center for Sustainable Polymers that is aimed at two separate goals. The goal of the first project (Chapters 1 and 2) was to develop a deeper mechanistic understanding of a method for the synthesis of linear α-olefins, while the second aimed at synthesizing statistical copolymers that incorporate olefin-containing monomers through ring-opening transesterification polymerization and showing that these copolymers could be functionalized. In Chapter 1, published methods for the conversion of fatty acids to linear α-olefins are reviewed to provide context for the mechanistic work we accomplished (Chapter 2). In Chapter 2 …

Contribution To Data Science: Time Series, Uncertainty Quantification And Applications, Dhrubajyoti Ghosh

Arts & Sciences Electronic Theses and Dissertations

Time series analysis is an essential tool in modern world statistical analysis, with a myriad of real data problems having temporal components that need to be studied to gain a better understanding of the temporal dependence structure in the data. For example, in the stock market, it is of significant importance to identify the ups and downs of the stock prices, for which time series analysis is crucial. Most of the existing literature on time series deals with linear time series, or with Gaussianity assumption. However, there are multiple instances where the time series shows nonlinear trends, or when the …

The Physics Of Associative Polymers And Applications To Biomolecular Condensates, Furqan Dar

Arts & Sciences Electronic Theses and Dissertations

Biomolecular condensates represent a new and ubiquitous class of membraneless organelles (MLOs) that are essential for healthy cellular functioning. The constituent molecules of such condensates span a vast bio-macromolecular gamut from intrinsically disordered regions and proteins (IDPs/IDRs), to RNA and RNA-binding proteins (RNPs), to polymerases and DNA etc. Apart from being part of the regular healthy cell cycle, these condensates are also implicated in many diseases, most notably progressive neurodegenerative diseases like Amyotropic Lateral Sclerosis (ALS) and Huntingtin's Disease (HD). Since the constituent molecules of these condensates span a broad range of length scales and modes of interaction, uncovering a …

Quasiparticle And Excitonic Effects In Two-Dimensional Van Der Waals Materials, Linghan Zhu

Arts & Sciences Electronic Theses and Dissertations

Since their discovery, low dimensional van der Waals materials have attracted increasing research interests. They serve as ideal platforms to study novel physics in reduced-dimensional systems, and are critical in nowadays’ nanotechnology applications. Due to the reduced dielectric screening in low dimensions, strong excited state properties dictate their electronic, transport and optical properties, the study of which calls for a description of the many-particle interactions beyond the traditional density functional theory. This is where the many-body perturbation theory comes into play. In this thesis, I will present a comprehensive study of the quasiparticle and excitonic properties of a variety of …

A Synthesis-Based Approach To The Study Of Fe(Ii) Oxidation In Smectites, Robert Joe Kupper Ii

Arts & Sciences Electronic Theses and Dissertations

Smectite clay minerals are present in diverse environments on Earth as a major product of silicate weathering. Although smectites are compositionally varied, they almost always incorporate iron. Iron-bearing smectites are an important component of the biogeochemical iron cycle, serving as a major iron fraction in many soils and altered rocks as well as participating in redox reactions within the surrounding environment. Iron incorporates into smectites in the ferric [Fe(III)] form at the modern, oxygenated surface of Earth but clays forming in anoxic settings instead incorporate ferrous iron [Fe(II)]. Owing to their ubiquity at the surface of the modern Earth, the …

Geometry And Dynamics Of Rolling Systems, Bowei Zhao

Arts & Sciences Electronic Theses and Dissertations

Billiard systems, broadly speaking, may be regarded as models of mechanical systems in which rigid parts interact through elastic impulsive collision forces. When it is desired or necessary to account for linear/angular momentum exchange in collisions involving a spherical body, a type of billiard system often referred to as no-slip has been used. Previous work indicated that no-slip billiards resemble non-holonomic systems, specifically, systems consisting of a ball rolling on surface. In prior research, such connections were only observed numerically and were restricted to very special surfaces. In this thesis, it is shown that no-slip billiard and rolling systems are …

Effects Of Surface Ligation On Charge Extraction From Wurtzite Cadmium Selenide Quantum Platelets And Quantum Belts, Hailey Meyer

Arts & Sciences Electronic Theses and Dissertations

This dissertation presents the synthesis of flat, colloidal wurtzite CdSe quantum platelets and quantum belts for ligand exchange to novel and existing organic and inorganic L-, X-, and Z- type ligands. Use of these ligands in conjunction with the semiconductor nanocrystals allows for examination of their ligand exchange abilities, photoluminescence quenching efficiencies, and charge transfer properties.

First, zinc and cadmium dithiocarbamate compounds [M(S2CNR1R2)2] are used as ligands on wurtzite CdSe quantum belts. Complete ligand exchange is achieved when the belts are initially ligated with Cd(oleate)2, a Z-type ligand, prior to the exchange, as opposed to n-octylamine or ammonia, which are …

Functionalized Plasmonic Nanostructures For Ultrasensitive Single Cell Analysis, Priya Rathi

Arts & Sciences Electronic Theses and Dissertations

Ultrasensitive detection and quantification of soluble, secreted and cell surface-bound proteins is critical for advancing our understanding of cellular systems, enabling effective drug development, novel therapies, and bio-diagnostics. However, exiting technologies are largely limited by their sensitivity, making the detection and quantification of low-abundant proteins extremely challenging. This forms a major barrier in various fields of biology and biomedical sciences. In this work, we introduce novel cellular analysis methodologies based on plasmon-enhanced fluorescence for analyzing cell structure and probing surface and secreted proteins from cells. In the first part, we introduce plasmon-enhanced expansion microscopy and demonstrate the effectiveness of employing …

Contribution To Data Science: Time Series, Uncertainty Quantification And Applications, Dhrubajyoti Ghosh

Arts & Sciences Electronic Theses and Dissertations

Time series analysis is an essential tool in modern world statistical analysis, with a myriad of real data problems having temporal components that need to be studied to gain a better understanding of the temporal dependence structure in the data. For example, in the stock market, it is of significant importance to identify the ups and downs of the stock prices, for which time series analysis is crucial. Most of the existing literature on time series deals with linear time series, or with Gaussianity assumption. However, there are multiple instances where the time series shows nonlinear trends, or when the …

Quantum Curves And Asymptotic Hodge Theory, Soumya Sinha Babu

Arts & Sciences Electronic Theses and Dissertations

This dissertation explores a 2015 conjecture of Codesido-Grassi-Marino in topologicalstring theory that relates the enumerative invariants of toric CY 3-folds to the spectra of operators attached to their mirror curves. In the maximally supersymmetric case, our first theorem relates zeroes of the higher normal function associated to an integral K2-class on the mirror curve to the spectra of the operators for curves of genus one, and suggests a new link between analysis and arithmetic geometry. On the other hand in the ’t Hooft limit, [KM, MZ] deduced from the [CGM] conjecture that the limiting values of the local mirror map …

Exploring The Solar System Through Space And Time Via Laboratory Investigations Of Extraterrestrial Material, Kainen Lee Utt

Arts & Sciences Electronic Theses and Dissertations

This dissertation reports the results of laboratory studies of lunar soil samples, gas-to-solid filamentary enstatite grains from a likely-cometary interplanetary dust particle (IDP), and exogenous clasts in the CH3 chondrite Acfer 182 that likely originated from a differentiated basaltic planetesimal. These studies were performed using multi-instrument analyses involving high-resolution scanning and transmission electron microscopy (SEM/TEM) techniques, nanoscale secondary ion mass spectrometry (NanoSIMS), synchrotron infrared nanospectroscopy (SINS), electron probe microanalysis (EPMA), and Raman spectroscopy. The results of these analyses are used to examine space weathering phenomena, energetic processing and radial transport in the protoplanetary disk, and the origins of igneous inclusions …

A Nonconforming Finite Element Method For The 2d Vector Laplacian, Mary Barker

Arts & Sciences Electronic Theses and Dissertations

The vector Laplacian presents difficulties in finite element ap- proximation. It is well known that for nonconvex domains, H1- conforming approximation spaces form a closed subspace of the solution space H(div; Ω) ∩ H(curl; Ω). Hence H1-conforming approximations will fail to converge. This is problematic as it is highly difficult to construct more general finite dimensional ap- proximation spaces for this space. We will present an extension of a nonconforming method introduced by Brenner et al. The method was originally given for P1-nonconforming spaces in two dimensions. Our extension is given for degree r polynomials, but which agrees with the …

Hodge Theoretic Compactification Of Period Maps, Haohua Deng

Arts & Sciences Electronic Theses and Dissertations

In this article, we review some aspects regarding Hodge-theoretic completion and boundarybehavior of period maps. First, we recall some classical results on compactification of classical period domains e.g. Baily-Borel, Ash-Mumford-Rapoport-Thai. The works produced by Kato-Usui aims at generalizing Mumford’s toroidal compactification to nonclassical period domain, which depends on construction of a strongly compatible fan. We prove such a fan can not exists universally, but for a single geometric variation of Hodge structure. We proceed such a construction on a 2-parameter geometric variation coming from Hosono-Takagi’s family of Calabi-Yau threefolds of type (1, 2, 2, 1). Moreover, we briefly review the …

Properties Of Cyclic Functions, Jeet Sampat

Arts & Sciences Electronic Theses and Dissertations

For $1 \leq p < \infty$, consider the Hardy space $H^p(\mathbb{D}^n)$ on the unit polydisk. Beurling's theorem characterizes all shift cyclic functions in the Hardy spaces when $n = 1$. Such a theorem is not known to exist in most other analytic function spaces, even in the one variable case. Therefore, it becomes natural to ask what properties these functions satisfy in order to understand them better. The goal of this thesis is to showcase some important properties of cyclic functions in two different settings.

1. Fix $1 \leq p,q < \infty$ and $m, n \in \mathbb{N}$. Let $T : H^p(\mathbb{D}^n) \xrightarrow{} H^q(\mathbb{D}^m)$ be a bounded linear operator. Then $T$ preserves cyclic functions, i.e. $Tf$ is cyclic whenever $f$ is, if and only if $T$ is a weighted composition operator. 2. Let $\mathcal{H}$ be a normalized complete Nevanlinna-Pick space, and let $f, g \in \mathcal{H}$ be such that $fg \in \mathcal{H}$. Then $f$ and $g$ are multiplier cyclic if and only if their product $fg$ is.

We also extend $(1)$ to a large class of analytic function spaces that includes the Dirichlet space, and the Drury-Arveson space on the unit ball $\mathbb{B}_n$ among others. Both of these properties generalize all previously known results of this type.

Weighted Estimates For The Bergman And Szegö Projections, Nathan Andrew Wagner

Arts & Sciences Electronic Theses and Dissertations

This thesis is a study of various weighted estimates for the Bergman and Szegö projections on domains in several complex variables. The starting point of our analysis is a bounded, pseudoconvex domain D ⊂ Cn. The Bergman and Szegö projections are both orthogonal projections onto spaces of holomorphic functions associated with D. While it is immediate that both of these operators are bounded on L2, it has been a topic of substantial interest to determine their mapping properties on Lp, where the boundary geometry of D plays amajor role. Given a linear operator T acting on measurable functions that is …

Electronic, Optical, And Thermal Probes Of The Layered Mott Insulator Α-Rucl3 In The Atomically Thin Limit, Jesse Balgley

Arts & Sciences Electronic Theses and Dissertations

Alpha-ruthenium(III) chloride (α-RuCl3) is a layered Mott insulator and van der Waals material that can be cleaved down to a single atomic layer. This material is a promising candidate to realize the Kitaev quantum spin liquid, a strongly correlated phase of matter expected to host fractionalized quasiparticles and a potential platform for topological quantum computation. When α-RuCl3 is placed in direct contact with the layered semimetal graphene we observe a strong charge transfer between the two materials despite the electrically insulating nature of α-RuCl3, which absorbs ≈ 4 × 10^13 electrons/cm^2 from the graphene. Remarkably, this charge transfer persists and …

Some Problems In Reproducing Kernel Spaces, Christopher Felder

Arts & Sciences Electronic Theses and Dissertations

The two chapters of this thesis are comprised of work in the setting of reproducing kernel (Hilbert) spaces. These are Banach (or Hilbert) spaces of functions defined on some set, with the special property that point evaluation, on the underlying set, is bounded.

The first chapter deals with the study of inner functions. These functions have a rich history in function and operator theory in the Hardy spaces of the unit disk. The first section of this chapter studies the relationship between generalized inner functions and optimal polynomial approximants. The second section, which is joint work with Trieu Le, deals …

Trace Metal Speciation And Impacts On Iron Oxide Transformations And Biogeochemical Cycling, Jinshu Yan

Arts & Sciences Electronic Theses and Dissertations

Trace metals in anoxic aquatic systems are of great importance for iron oxide transformations and biogeochemical cycling. The presence of trace metal can alter iron oxide transformations under anoxic conditions. Trace metals are also essential for microbially-mediated biogeochemical processes occurring in anoxic wetland soils and stream bed sediments, but low availability of these elements may inhibit anaerobic element cycling and transformations. Trace metal speciation is also vital for understanding the environmental control on nutrients and contaminants. Three projects were conducted to explore trace metal speciation and its associated effect on iron oxide transformations and biogeochemical cycling. First, the Fe(II)-promoted conversion …

Low-Temperature Plasticity Of Rock-Forming Minerals, Michael Keith Sly

Arts & Sciences Electronic Theses and Dissertations

The rheology of the Earth’s crust and mantle is in part governed by the physical and mechanical properties of feldspar, quartz, calcite, and olivine. Over the past several decades a significant number of experimental studies have been performed on these minerals. Conventional experiments are generally performed at elevated temperatures because much of the viscoplastic deformation of these minerals is accommodated by high-temperature mechanisms. There is, however, evidence of viscoplastic deformation at lower temperatures (T ≤ 0.3Tm) in the uppermost mantle and throughout the crust. Micromechanical experimental techniques, including nanoindentation and micropillar deformation, can be used to achieve plastic deformation at …

Classical And Quantum Markov Chains Derived From Billiard-Like Systems, Joshua Covey

Arts & Sciences Electronic Theses and Dissertations

Random billiards are a class of random dynamical systems related to dynamical billiards. We extend the study of random billiards and their associated Markov chains in two new directions. First, we introduce a new class of billiard-like systems called lensed billiards, which introduce a step potential to the usual billiard set-up, and conduct an exploratory study of random lensed billiards where we are mainly interested in how the newly-introduced potential parameter relates to the spectral gap and set of moments of the Markov operator associated to the random lensed system.

Second, we recast the mathematical set-up of random billiards to …