Physical Sciences and Mathematics Commons^™

Matrix Factorizations With More Than Two Factors, Tim Tribone

Dissertations - ALL

Let $S$ be a regular local ring and $f$ a non-zero non-invertible element of $S$. In this thesis, we study the notion of a matrix factorization of $f$ with $d\ge 2$ factors, that is, we consider tuples of square matrices $(\phi_1,\phi_2,\dots,\phi_d)$, with entries in $S$, such that their product is $f$ times an identity matrix of the appropriate size. These objects have been studied thoroughly in the case $d=2$ and were originally introduced by Eisenbud in his study of free resolutions of modules over hypersurface rings. Many of the results given in this thesis are extensions of well-known results in …

Fairness In Social Networks, Zeinab Saghati Jalali

Dissertations - ALL

In professional and other social settings, networks play an important role in people's lives. The communication between individuals and their positions in the network, may have a large impact on many aspects of their lives.In this work, I evaluate fairness from different perspectives.First,tomeasurefairnessfromgroupperspective,Iproposethenovelinformation unfairness criterion, which measures whether information spreads fairly to different groups in a network. Using this criterion, I perform a case study and measure fairness in information flow in different computer science co-authorship networks with respect to gender. Then, I consider two applications and show how to increase fairness with respect to a fairness metric. The first …

Synthesis, Characterization And Cellular Uptake Of Magnesium Complexes Of Pyrones And Amino Acids, Derek Robert Case

Dissertations - ALL

This thesis focuses on the treatment of micronutrient deficiency, specifically hypomagnesemia, through the synthesis and solution- and solid-state characterization of "pharma grade", biorelevant magnesium complexes (nutraceuticals) utilizing short-chain peptides (di- and tri-), pyrones, and amino acids. There is further emphasis placed on determining the in vitro uptake of all produced complexes. This work aims to mitigate the shortcomings of current magnesium supplements and better illustrate an understanding of the factors impacting magnesium uptake. Specifically, 1) There is a paucity of information regarding the coordination of biorelevant ligands to magnesium, most of which was investigated between the 1950s and 1980s, and …

Applications Of Powerset Operators, Especially To Matroids, Nathan Uricchio

Dissertations - ALL

Let \(\mathcal{V}\) denote a vector space over an arbitrary field with an inner product. For any collection \(\mathcal{S}\) of vectors from \(\mathcal{V}\) the collection of all vectors orthogonal to each vector in \(\mathcal{S}\) is a subspace, denoted as \(\mathcal{S}^{\perp_v}\) and called the \textit{orthogonal complement} of \(\mathcal{S}\). One of the fundamental theorems of vector space theory states that, \((\mathcal{S}^{\perp_v})^{\perp_v}\) is the subspace \textit{spanned} by \(\mathcal{S}\). Thus the ``spanning'' operator on the subsets of a vector space is the square of the ``orthogonal complement'' operator.

In matroid theory, the orthogonal complement of a matroid \(M\) is also well-defined and similarly results in …

Detector Improvements And Optimization To Advance Gravitational-Wave Astronomy, Varun Srivastava

Dissertations - ALL

The thesis covers a range of topics relevant to the current and future gravitational-wave facilities. After the last science observing run, O3, that ended in March 2020, the aLIGO and VIRGO gravitational-wave detectors are undergoing upgrades to improve their sensitivity. My thesis focuses on the work done at the LIGO Hanford Observatory to facilitate these upgrade activities. I worked to develop two novel technologies with applications to gravitational-wave detectors. First, I developed a high-bandwidth, low-noise, flexure-based piezo-deformable mirror for active mode-matching. Mode-matching losses limit improvements from squeezing as they distort the ground state of the squeezed beam. For broadband sensitivity …

Subsurface Geophysical Investigations Of Oneida Lake Ny: Insights Into Ice Sheet Processes And Deglaciation At Termination I, Nicholas John Zaremba

Dissertations - ALL

Reconstructing the retreat of the Laurentide Ice Sheet (LIS) provides insight into understanding end-Pleistocene climate, a critical set of boundary conditions prior to the onset of Holocene climates that were optimal for human dispersal and societal growth. Constraining ice sheet dynamics, glacier retreat rates, and the timing of still-stands and readvances requires identifying glacial landforms such as moraines, drumlins, and mega-scale glacial lineations (MSGLs). Drumlins and MSGLs indicate ice sheet flow directions and provide the location of paleo-ice streams, which were accelerated and localized pathways for ice discharge. Ice streams control ice sheet mass balance; therefore, identifying the location of …

Monitoring Bacteria Cultures Using Near Infrared (Nir) Binary Spectronephelometry (Bsn), Raman Spectra And Principal Component Analysis (Pca), Steven Ortiz

Dissertations - ALL

Current noninvasive methods cannot continuously and simultaneously monitor the concentrations of cells and media components that define the state of native bacterial cultures, because of changing turbidity. A new technique, binary spectronephelometry (BSN) has the same or better sensitivity and precision for population monitoring as optical density at 600nm (OD600), while simultaneously measuring metabolic processes. The BSN algorithm uses laser induced emission to probe mildly turbid media i.e., propagation of light occurs in the single scattering regime. A BSN "training set" associates a grid of elastic emission measurements, comprising Rayleigh and Mie scattering, and inelastic emission measurements, comprising fluorescence and …

Trichloroacetimidates As Outstanding Electrophiles For The Carbon-Nitrogen, Carbon-Oxygen And Carbon-Carbon Bonds Formation And Synthetic Studies Of Protein Phosphatase-5 (Pp5) Small Molecule Inhibitors, Nilamber Mate

Dissertations - ALL

Trichloroacetimidates have been previously used for glycosidic bond formation in carbohydrate chemistry and in Friedel-Craft reactions. Traditionally, trichloroacetimidates had be synthesized using an alcohol and strongly basic conditions, but in recent years milder preparation methods have been reported. Given the ease of preparation of these versatile reagents, their chemistry has been explored intensely in recent years. While few reported methods suggest they can react under promoter free conditions, activation by Lewis or Brønsted acid leads to a formation of a carbocation from benzylic trichloroacetimidates. Work described herein makes use of these convenient carbocation precursors for new reactions.Isatin is an ambidentate …

Stable Carbon And Nitrogen Isotopes Of Shell Bound Organic Matter, Implications For Modern And Ancient Food Web Dynamics, Shibajyoti Das

Dissertations - ALL

Stable isotopes are an important tool for solving biogeochemical problems and have been increasingly applied in ecosystem studies because of their utility as source-to-sink tracers and for ecological information. Elements like C and N have more than one stable isotope, and their isotopic compositions (δ15N and δ13C) vary in a foreseeable way and are specifically useful in studying global elemental cycles and energy flow through ecosystems. δ15N and δ13C of organic matter (OM) are diagnostic of an organism's diet and have been used as a proxy for trophic level reconstructions. However, because of several analytical constraints, the use of stable …

Probing Lepton Flavour Universality With $\Bz \To \Kstarz \Taup \Taum$, Aravindhan Venkateswaran

Dissertations - ALL

Neutral current $\bquark \to \squark ll$ processes have long been known to be precise probes of physics beyond the Standard Model. A pattern of anomalies seen in $\bquark \to \squark \mup \mun$ and in $\bquark \to \cquark \tau \nu$ data has hinted at the violation of lepton flavour universality. Effective field theories which attempt to find an explanation for these anomalies predict sizeable enhancements to the rate of $\bquark \to \squark \taup \taum$ currents. We use $pp$ collision data collected by the LHCb detector to estimate a sensitivity of $\BF(\Bz \to \Kstarz \taup \taum) < 1.5 \times 10^{-3}$ at 95\% C.L.

The Relationship Between Urban Heat Islands And Redline Districts, Emily Cornwell

Undergraduate Theses and Capstone Projects

As climate change worsens and the world attempts to find solutions to global changes, it is important to identify how climate change will affect individual communities. Climate resilience tactics aim to protect vulnerable populations against environmental harms, such as excess heat. Historically, communities of color face forms of environmental racism. One example of structural racism includes the loans given out by the Home Owners Loan Corporation during the 1940s which “redlined” certain communities of color by refusing to give these neighborhoods loans and rated these areas undesirable for loaners. Urban heat islands occur in residential, densely populated areas with lots …

Effects Of Precipitation On Groundwater Level In An Urban Watershed, Andrew Golladay

Undergraduate Theses and Capstone Projects

Groundwater is an important aspect of a watershed, as it is a reservoir for the storage of water. It both releases water to the surface in dry periods and absorbs excess water in wet periods. Precipitation provides surface water that is then absorbed to replenish groundwater. The specific purpose of this research was to determine the recharge rate of the water table after a rainfall event, with a goal to also develop a framework or long-term monitoring of the water table along an urban stream in Lynchburg, Virginia, and to establish baseline groundwater data before a dam is removed from …

Dementia Classification Through Textual Analysis With Machine Learning Algorithms, Joseph Hurowitz

Undergraduate Theses and Capstone Projects

The goal of this work is to build a classifier that can identify whether a patient is suffering from Alzheimer’s Disease of the Dementia Type (AD). A corpus of 2751 texts was used from the DementiaBank database, where each conversation is transcribed and marked using the CHAT format. Each text was analyzed by frequency of disfluencies, use of aphasic language, and lexical features. All parsed data was used to train a Random Forest, Naïve Bayes, and Support Vector Machine algorithm. These classification algorithms will be tested on the combination of all features, as well as each set of features individually.

The Behaviors Of Bert Attention Heads In Stereotype Detection, Joseph H. Hajjar

Dartmouth College Master’s Theses

We are living in the age of information, where it has become increasingly easy to share ideas, news, and content which are seen by an increasingly large number of people. This increasing scope of the increasing amount of data that is being shared lends itself to the question: how can we determine whether what we are reading promotes a stereotype? Previous work has applied transformer based models in this domain yielding impressive performance, but few studies exist interpreting the nature of attention heads in this task. Our work explores the feature encoding and extraction behaviors of attention heads in transformer …

An Observational Retrospective Study Of Adverse Events And Behavioral Outcomes During Pediatric Dental Sedation, Muhammad F Walji

Faculty, Staff and Student Publications

Purpose: The purpose of this study was to examine a university-based dental electronic health records (EHR) database to identify sedation-related adverse events (AEs) and assess patients' behavioral outcomes during routine pediatric dental sedations (PDSs) in a dental school clinic.

Methods: A database was screened for patients younger than 18 years old who had received dental sedation in 2019. The qualifying EHRs were then accessed and sedations were reviewed for AEs, which were categorized using a 12-point classification system and the Tracking and Reporting Outcomes of Procedural Sedation Tool. Patient behaviors were assessed using provider progress notes and categorized as presence/ …

Correlation Functions Of The Anharmonic Oscillator: Numerical Verification Of Two-Loop Corrections To The Large-Order Behavior, Ludovico T. Giorgini, Ulrich D. Jentschura, Enrico M. Malatesta, Giorgio Parisi, Tommaso Rizzo, Jean Zinn-Justin

Physics Faculty Research & Creative Works

Recently, the large-order behavior of correlation functions of the O(N)-anharmonic oscillator has been analyzed by us [L. T. Giorgini et al., Phys. Rev. D 101, 125001 (2020)PRVDAQ2470-001010.1103/PhysRevD.101.125001]. Two-loop corrections about the instanton configurations were obtained for the partition function, the two-point and four-point functions, and the derivative of the two-point function at zero momentum transfer. Here, we attempt to verify the obtained analytic results against numerical calculations of higher-order coefficients for the O(1), O(2), and O(3) oscillators, and we demonstrate the drastic improvement of the agreement of the large-order asymptotic estimates and perturbation theory upon the inclusion of the two-loop …

Hodge Theoretic Compactification Of Period Maps, Haohua Deng

Arts & Sciences Graduate Student 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 …

Some Problems In Reproducing Kernel Spaces, Christopher Felder

Arts & Sciences Graduate Student 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 …

The Evaluation Of Radiometal Labeled Biomolecules For Imaging And Therapeutic Applications, Truc Huynh

Arts & Sciences Graduate Student Theses and Dissertations

Radiometals play a crucial role in nuclear medicine for the diagnosis and therapy of various diseases including cancer and neurological disorders. In fact, there is a broad range of radiometals that are currently in use for imaging and therapy such as 99mTc, 89Zr, 68Ga, 177Lu, and 64/67Cu. Radiometal use in nuclear medicine has been stimulated by advances in radionuclide production that allow for fast, reliable, and cost-efficient production and an extensive understanding of molecular targets and tumor biomarkers. In recent years, there has been a growing interest in theranostics - the combination of imaging and therapy related to the same …

Properties Of Cyclic Functions, Jeet Sampat

Arts & Sciences Graduate Student 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.

Quantum Curves And Asymptotic Hodge Theory, Soumya Sinha Babu

Arts & Sciences Graduate Student 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 …

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

Arts & Sciences Graduate Student 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 …

Information Provenance For Mobile Health Data, Taylor A. Hardin

Dartmouth College Ph.D Dissertations

Mobile health (mHealth) apps and devices are increasingly popular for health research, clinical treatment and personal wellness, as they offer the ability to continuously monitor aspects of individuals' health as they go about their everyday activities. Many believe that combining the data produced by these mHealth apps and devices may give healthcare-related service providers and researchers a more holistic view of an individual's health, increase the quality of service, and reduce operating costs. For such mHealth data to be considered useful though, data consumers need to be assured that the authenticity and the integrity of the data has remained intact---especially …

Distributed X-Ray Sources For X-Ray Imaging And Small Animal Flash Irradiator, Yuewen Tan

Arts & Sciences Graduate Student Theses and Dissertations

Emerging distributed x-ray source technology enables new designs for x-ray imaging systems. The multi-pixel thermionic emission X-ray (MPTEX) source, a distributed x-ray source developed in our lab, was assembled and tested. With a multi-row CdTe photon-counting detector, forty-eight x-ray fan beams of MPTEX source were able to cover a 25-cm cross-sectional and 8-cm axial field of view. Tetrahedron-beam x-ray imaging techniques using MPTEX source were demonstrated.Ultra-high dose rate radiotherapy or FLASH radiotherapy (RT) potentially can reduce normal tissue toxicity in radiation treatments. A compact irradiator that can deliver FLASH-RT treatments similar to conventional RT treatments is needed for preclinical studies. …

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

Arts & Sciences Graduate Student 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 …

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

Arts & Sciences Graduate Student 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 …

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

Arts & Sciences Graduate Student 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 …

Signaling Studies Of Protein-Peptide Binding On Microelectrode Arrays, Kendra White

Arts & Sciences Graduate Student Theses and Dissertations

Electrochemical methods provide unique opportunities for non-traditional synthesis and analytical studies. Using electrochemistry, we are able to synthesize individually addressable molecular surfaces on microelectrode arrays and then utilize the surface to probe interactions between receptors and their biological targets. To date, cyclic voltammetry signals can be used to detect biological interactions between proteins and small molecules on the surface of an array, however those signals are often amplified by the presence of a large number of small molecules by any given electrode. This amplification makes it difficult to obtain binding data using the arrays that can be compared with existing …

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

Arts & Sciences Graduate Student 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 …

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

Arts & Sciences Graduate Student 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 …