Physical Sciences and Mathematics Commons^™

Emulating Condensed Matter Systems In Classical Wave Metamaterials, Matthew Weiner

Dissertations, Theses, and Capstone Projects

One of the best tools we have for the edification of physics is the analogy. When we take our classical set of states and dynamical variables in phase space and treat them as vectors and Hermitian operators respectively in Hilbert space through the canonical quantization, we lose out on a lot of the intuition developed with the previous classical physics. With classical physics, through our own experiences and understanding of how systems should behave, we create easy-to-understand analogies: we compare the Bohr model of the atom to the motion of the planets, we compare electrical circuits to the flow of …

Particle Dynamics In Anti-De Sitter Space By Eih Method, Jiusi Lei

Dissertations, Theses, and Capstone Projects

Following the work of Einstein, Infeld and Hoffmann, we show that particle dynamics in Anti-de Sitter spacetime can be built up by regarding singularities in spacetime manifold as the source of particles.

Since gauge fields play a foundational role in the action, the singularities are chosen to be point-like instantons. Their winding number, defined by an integration on the spheres surrounding those singularities, will turn out to be related to their masses. And their action, derived from the Chern-Simons forms, will be a co-adjoint orbit action, with group element g ∈ SO(4, 2) describing the collective coordinates of the particle. …

An Accurate Solution Of The Self-Similar Orbit-Averaged Fokker-Planck Equation For Core-Collapsing Isotropic Globular Clusters: Properties And Application, Yuta Ito

Dissertations, Theses, and Capstone Projects

Hundreds of dense star clusters exist in almost all galaxies. Each cluster is composed of approximately ten thousand through ten million stars. The stars orbit in the clusters due to the clusters' self-gravity. Standard stellar dynamics expects that the clusters behave like collisionless self-gravitating systems on short time scales (~ million years) and the stars travel in smooth continuous orbits. Such clusters temporally settle to dynamically stable states or quasi-stationary states (QSS). Two fundamental QSS models are the isothermal- and polytropic- spheres since they have similar structures to the actual core (central part) and halo (outskirt) of the clusters. The …

Tidal Wetland Inundation And Vegetation Phenology From Space: A Synthesis Of Approaches For Characterizing Ecological Status And Inundation Dynamics In Tidal Wetlands With Remote Sensing Observations, Brian T. Lamb

Dissertations, Theses, and Capstone Projects

This dissertation focuses on the monitoring and characterization of tidal marshes using remote sensing-based approaches. Chapter 1 introduces the topics of wetland ecology and remote sensing. Chapters 2-4 are the main research chapters of the dissertation covering the topics of tidal marsh mapping, tidal marsh vegetation characterization, and assessment of tidal marsh inundation patterns. Chapter 5 summarizes the preceding chapters and highlights future research directions.

The primary research objective of Chapter 2 is the mapping and study of tidal marshes of the Chesapeake and Delaware Bays. This chapter also features a thematic focus on the evaluation of various forms of …

Machine Learning Applications For Drug Repurposing, Hansaim Lim

Dissertations, Theses, and Capstone Projects

The cost of bringing a drug to market is astounding and the failure rate is intimidating. Drug discovery has been of limited success under the conventional reductionist model of one-drug-one-gene-one-disease paradigm, where a single disease-associated gene is identified and a molecular binder to the specific target is subsequently designed. Under the simplistic paradigm of drug discovery, a drug molecule is assumed to interact only with the intended on-target. However, small molecular drugs often interact with multiple targets, and those off-target interactions are not considered under the conventional paradigm. As a result, drug-induced side effects and adverse reactions are often neglected …

Wave Propagation In Random And Topological Media, Yuhao Kang

Dissertations, Theses, and Capstone Projects

This thesis discusses wave propagation in two kinds of systems, random media and topological insulators. In a disordered system, the wave is randomized by multiple scattering. The scattering matrix and associated delay times are powerful tools with which to describe wave transport. We discuss the relation among the Wigner time, the transmission time, and energy density in a lossless or lossy system. We propose the zeros of the transmission matrix and show how to manipulate the zero-transmission mode in a nonunitary system. In a photonic topological insulator, we realize an edge mode and discuss its robustness in the face of …

Alternative Cichoń Diagrams And Forcing Axioms Compatible With Ch, Corey B. Switzer

Dissertations, Theses, and Capstone Projects

This dissertation surveys several topics in the general areas of iterated forcing, infinite combinatorics and set theory of the reals. There are two parts. In the first half I consider alternative versions of the Cichoń diagram. First I show that for a wide variety of reduction concepts there is a Cichoń diagram for effective cardinal characteristics relativized to that reduction. As an application I investigate in detail the Cichoń diagram for degrees of constructibility relative to a fixed inner model of ZFC. Then I study generalizations of cardinal characteristics to the space of functions from Baire space to Baire space. …

Pointing The Zinc Finger On Protein Folding: Energetic Investigation Into The Role Of The Metal-Ion In The Metal-Induced Protein Folding Of Zinc Finger Motifs, Inna Bakman-Sanchez

Dissertations, Theses, and Capstone Projects

Interactions between inorganic metal-ion cofactors and organic protein scaffolds are important for the proper structure and function of metalloproteins. Zinc finger proteins (ZFPs) are an example of proteins with such crucial metal-protein interactions. Incorporation of the Zn(II)-ion into ZFPs allows for their correct folding into structures that can carry out vital biological functions which include gene expression and tumor suppression. In addition, engineered ZFPs have shown to be promising genetic therapeutics in the clinic. And yet, there is still a gap in a quantitative understanding of the energetic contribution of the metal-protein interactions towards the structure and function of these …

Spectral Sequences For Almost Complex Manifolds, Qian Chen

Dissertations, Theses, and Capstone Projects

In recent work, two new cohomologies were introduced for almost complex manifolds: the so-called J-cohomology and N-cohomology [CKT17]. For the case of integrable (complex) structures, the former cohomology was already considered in [DGMS75], and the latter agrees with de Rham cohomology. In this dissertation, using ideas from [CW18], we introduce spectral sequences for these two cohomologies, showing the two cohomologies have natural bigradings. We show the spectral sequence for the J-cohomology converges at the second page whenever the almost complex structure is integrable, and explain how both fit in a natural diagram involving Bott-Chern cohomology and the Frolicher spectral sequence. …

I. Selective Chlorination And Fluorination Of Quinols Ii. Synthetic Study Of Strongylophorine-26, Sihan Li

Dissertations, Theses, and Capstone Projects

Organic compounds containing halogen are an important and useful class of intermediates that can be converted to other functionalities. This thesis describes our strategy in selective chlorination and fluorination of quinols to offer the corresponding aromatic structures. Quinols, or cyclohexadienones, as oxidized derivatives of phenols, have their remarkable chemical reactivities, including additions to enone, enolate alkylations, aldol reactions, cycloadditions, and rearrangements. Dienone-phenol rearrangement provides the asymmetric route since the stereocenters located in the six-membered ring of various cyclohexadienone were widely using in building larger chiral arrays for many total syntheses

Chapter one of this thesis discusses our new selective nucleophilic …

Small Molecule Synthetic Carbohydrate Receptors, Marcelo F. Bravo Carranco

Dissertations, Theses, and Capstone Projects

Carbohydrate – receptor interactions are often involved in the attachment of viruses to host cells, and this docking is a necessary step in the virus life cycle that precedes infection and, ultimately, replication. Despite the conserved structures of the glycans involved in docking, they are still considered “undruggable”, meaning these glycans are beyond the scope of conventional pharmacological strategies. Recent advances in the development of synthetic carbohydrate receptors (SCRs) – small molecules that bind carbohydrates – could bring carbohydrate-receptor interactions within the purview of druggable targets. Here we discuss the role of carbohydrate-receptor interactions in viral infection, the evolution of …

A Semi-Automated Approach To Medical Image Segmentation Using Conditional Random Field Inference, Yu-Chi Hu

Dissertations, Theses, and Capstone Projects

Medical image segmentation plays a crucial role in delivering effective patient care in various diagnostic and treatment modalities. Manual delineation of target volumes and all critical structures is a very tedious and highly time-consuming process and introduce uncertainties of treatment outcomes of patients. Fully automatic methods holds great promise for reducing cost and time, while at the same time improving accuracy and eliminating expert variability, yet there are still great challenges. Legally and ethically, human oversight must be integrated with ”smart tools” favoring a semi-automatic technique which can leverage the best aspects of both human and computer.

In this work …

Growth Of Conjugacy Classes Of Reciprocal Words In Triangle Groups, Blanca T. Marmolejo

Dissertations, Theses, and Capstone Projects

In this thesis we obtain the growth rates for conjugacy classes of reciprocal words for triangle groups of the form G = Z2 ∗ H where H is finitely generated and does not contain an order 2 element. We explore cases where H is infinite cyclic and finite cyclic. The quotient O = H/G is an orbifold and contains a cone point of order 2, due to the first factor Z2 in the free product G. The reciprocal words in G correspond to geodesics on O which pass through the order 2 cone point on O. We use methods from …

Asymmetric Alpha-Stannylation Of Heterocycles And Their Subsequent Use In Cross-Coupling Reactions, Haoran Zhao

Dissertations, Theses, and Capstone Projects

α-Substituted oxygen-containing heterocycles are commonly present in biologically active molecules. Statistics shows that at least one α-substituted ether moiety appears in over 20% of the top 200 small-molecule pharmaceuticals. This project illustrates a reliable regioselective method to introduce simple cyclic ethers towards the diversification of small molecules. Aryl halides bearing various functional groups were well tolerated independent of their electronic properties. It was found that cyclohexyl spectator ligands on tin selectively slows transmetallation of undesired units, circumventing the competitive transfer of n-butyl group from ⁿBu₃SnR reagents. Compared to the normally used ⁿBu₃SnR reagents, Cy …

Applying A Systems Approach To The Legacy Of Lead In Soil, Sara Perl Egendorf

Dissertations, Theses, and Capstone Projects

Lead (Pb) in soil is a global environmental issue. The particularly high lead concentrations found in surface soils have been emplaced by humans and bring with them life-altering and life-shortening effects for our species and countless others. While much of the general population is unaware of lead lurking in our soils, scientists from a range of backgrounds have generated a body of research documenting this ubiquitous phenomenon, arising from sources such as lead in gasoline, paint, industry, and incineration. Scientists have also explored ways to remediate soil and continue calling for efforts to limit toxicant exposure. Why, then, does this …

Excitons In Self-Assembled Hybrid Systems Of Molecular Aggregate Light-Harvesting Nanotubes: Charge-Transfer Substrates And Solution-Stabilized Nanocomposites, Kara Ng

Dissertations, Theses, and Capstone Projects

Delocalized Frenkel excitons-coherently-shared excitations among chromophores-are responsible for the remarkable effciency of supramolecular light-harvesting aggregates within photosynthetic organisms. Despite tremendous progress towards a deeper understanding of these photosynthetic complexes, as well as progress in the development of organic solar cells, the possibility of using bio-inspired molecular nanostructures for large-scale solar energy conversion has not been realized yet. The persistent limitations in translating natures design principles for applications in optoelectronic devices have been the supramolecular structures fragility, and the Frenkel excitons delicate nature. The structural instability, both dis-assembly and spontaneous re-assembly of aggregates. Analysis of the absorption spectrum of a model …

Matrix Low Rank Approximation At Sublinear Cost, Qi Luan

Dissertations, Theses, and Capstone Projects

A matrix algorithm runs at sublinear cost if the number of arithmetic operations involved is far fewer than the number of entries of the input matrix. Such algorithms are especially crucial for applications in the field of Big Data, where input matrices are so immense that one can only store a fraction of the entire matrix in memory of modern machines. Typically, such matrices admit Low Rank Approximation (LRA) that can be stored and processed at sublinear cost. Can we compute LRA at sublinear cost? Our counter example presented in Appendix C shows that no sublinear cost algorithm can compute …

Valid Time Rdf, Hsien-Tseng Wang

Dissertations, Theses, and Capstone Projects

The Semantic Web aims at building a foundation of semantic-based data models and languages for not only manipulating data and knowledge, but also supporting decision making by machines. Naturally, time-varying data and knowledge are required in Semantic Web applications to incorporate time and further reason about it. However, the original specifications of Resource Description Framework (RDF) and Web Ontology Language (OWL) do not include constructs for handling time-varying data and knowledge. For simplicity, RDF model is confined to binary predicates, hence some form of reification is needed to represent higher-arity predicates. To this date, there are many proposals extending RDF …

Control Of Molecular Energetics And Transport Via Strong Light-Matter Interaction, Rong Wu

Dissertations, Theses, and Capstone Projects

Strong light-matter coupling in excitonic systems results in the formation of half-light half-matter quasiparticles called exciton polaritons. These hybrid quasiparticles take on the best of both systems, namely, the long-range propagation and coherence arising from the photonic component and the nonlinear interaction from the excitonic component. We develop methods for making high quality factor cavities and investigate the potential applications of these strongly coupled states arising specifically in organic molecular systems.

In the first project we investigate the potential of organic dye molecules to undergo condensation in an optical cavity at room temperature. The second study involves the use of …

Unclonable Secret Keys, Marios Georgiou

Dissertations, Theses, and Capstone Projects

We propose a novel concept of securing cryptographic keys which we call “Unclonable Secret Keys,” where any cryptographic object is modified so that its secret key is an unclonable quantum bit-string whereas all other parameters such as messages, public keys, ciphertexts, signatures, etc., remain classical. We study this model in the authentication and encryption setting giving a plethora of definitions and positive results as well as several applications that are impossible in a purely classical setting.

In the authentication setting, we define the notion of one-shot signatures, a fundamental element in building unclonable keys, where the signing key not only …

A Data Exploration Of Jeopardy! From 1984 To The Present, Brian S. Hamilton

Dissertations, Theses, and Capstone Projects

The gameshow Jeopardy! has been around in its current iteration—hosted by Alex Trebek—since 1984. During this time, it has accumulated data on clues, contestants, and possible strategies on how to win. Using a crowd-sourced archive called J! Archive, this project seeks to find trends in the topics that the game covers and take a deeper look into the performance of its contestants. It employs topic modeling, a text-analysis method, to organize the hundreds of thousands of archived clues and statistical analysis to rate the performance of contestants by gender. Using web-based visualization tools, the data is shown in an …

Set Operators, Xiaojin Ye

Dissertations, Theses, and Capstone Projects

My research is centered on set operators. These are universally applicable regardless of the internal structure (numeric or non-numeric) of each individual observed datum. In our research, we have developed the theory of set operators to fill holes and gaps in observed data and eliminate paper shred garbage, thereby changing the observed symbolic data set into one whose pattern is closer to the pattern in the underlying population from which the observed data set was sampled with perturbations.

We describe different set operators including increasing operators, decreasing operators, ex- pansive operators, contractive operators, union preserving operators, intersection preserving op- erators, …

Role Of Influence In Complex Networks, Nur Dean

Dissertations, Theses, and Capstone Projects

Game theory is a wide ranging research area; that has attracted researchers from various fields. Scientists have been using game theory to understand the evolution of cooperation in complex networks. However, there is limited research that considers the structure and connectivity patterns in networks, which create heterogeneity among nodes. For example, due to the complex ways most networks are formed, it is common to have some highly “social” nodes, while others are highly isolated. This heterogeneity is measured through metrics referred to as “centrality” of nodes. Thus, the more “social” nodes tend to also have higher centrality.

In this thesis, …

Linear And Non-Linear Elastic Constants Of Crystalline Materials From First-Principles Calculations, David Cuffari

Dissertations, Theses, and Capstone Projects

Novel methods based on the use of density functional theory (DFT) calculations are developed and applied to calculate linear and non-linear elastic constants of materials at zero and finite temperature. These methods rely on finite difference techniques and are designed to be general, numerically accurate, and suitable to investigate the thermoelastic properties of anharmonic materials. A first method was developed to compute the third-order elastic constants of crystalline materials at zero temperature, a task that is numerically challenging and is currently undertaken by using approaches typically applicable to cubic and hexagonal crystalline systems. This method relies on numerical differentiation of …

Understanding Atmospheres Across The Stellar-Substellar Boundary, Eileen C. Gonzales

Dissertations, Theses, and Capstone Projects

Complexities in the atmospheres of sources that straddle the boundary between low-mass stars and planets drive the spectral features we observe and the fundamental parameters that we derive. In an effort to understand the underlying cause of these spectral features, this work examines low-mass stars and brown dwarfs using two approaches: distance-calibrated spectral energy distributions (SEDs) and atmospheric retrievals. SEDs allow for the determination of semi-empirical fundamental parameters, while atmospheric retrievals allow us to derive the atmospheric structure and composition, as well as extrapolated fundamental parameters for a source. Low-metallicity and high surface gravity sources, known as subdwarfs, are the …

Peo-Ppo-Peo Surfactant Mixtures As Templates For Silicas With Very Large Cylindrical Mesopores At Ambient Temperature And With Helical Mesopores At Sub-Ambient Temperature, Laurance Beaton

Dissertations, Theses, and Capstone Projects

The original research described herein concerns the synthesis of mesoporous silicas through a surfactant-templating method. The approach taken involved the use of a mixed surfactant system of two poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) surfactants, with one of the copolymers containing a much larger percentage of hydrophobic (PPO) blocks than the employed co-surfactant. Systematic adjustments of experimental parameters initially enabled the preparation of 2-D hexagonally ordered mesoporous silicas (SBA-15) of uncommonly large pore diameter at ambient temperature. Comparable silica was synthesized with and without temperature control. Additional adjustments to experimental parameters, including reduction of the relative amount of framework precursor used in …

Averages And Nonvanishing Of Central Values Of Triple Product L-Functions Via The Relative Trace Formula, Bin Guan

Dissertations, Theses, and Capstone Projects

Harris and Kudla (2004) proved a conjecture of Jacquet, that the central value of a triple product L-function does not vanish if and only if there exists a quaternion algebra over which a period integral of three corresponding automorphic forms does not vanish. Moreover, Gross and Kudla (1992) established an explicit identity relating central L-values and period integrals (which are finite sums in their case), when the cusp forms are of prime levels and weight 2. Böcherer, Schulze-Pillot (1996) and Watson (2002) generalized this identity to more general levels and weights, and Ichino (2008) proved an adelic period formula which …

Structural Studies Of Peptide Toxins And Their Binding Properties Towards The Voltage Sensing Domain Of Nav1.7, Ryan Schroder

Dissertations, Theses, and Capstone Projects

Voltage gated sodium channels (VGSCs) are essential to the propagation of nerve cell impulses and thus communication in the nervous system. VGSCs are comprised of four repeating units of six transmembrane helices. Of the six transmembrane helices, the first four (called S1-S4) comprise the voltage sensing domain (VSD) and the last two (S5-S6) comprise the pore domain (PD)¹. The Human voltage-gated sodium channel Na_V1.7 has been shown to play a vital role in the nerve pathways that induce pain response². Many of the currently available pain therapeutic drugs are opiates, derivative molecules of opium. …

Model Theory Of Groups And Monoids, Laura M. Lopez Cruz

Dissertations, Theses, and Capstone Projects

We first show that arithmetic is bi-interpretable (with parameters) with the free monoid and with partially commutative monoids with trivial center. This bi-interpretability implies that these monoids have the QFA property and that finitely generated submonoids of these monoids are definable. Moreover, we show that any recursively enumerable language in a finite alphabet X with two or more generators is definable in the free monoid. We also show that for metabelian Baumslag-Solitar groups and for a family of metabelian restricted wreath products, the Diophantine Problem is decidable. That is, we provide an algorithm that decides whether or not a given …

Translation Distance And Fibered 3-Manifolds, Alexander J. Stas

Dissertations, Theses, and Capstone Projects

A 3-manifold is said to be fibered if it is homeomorphic to a surface bundle over the circle. For a cusped, hyperbolic, fibered 3-manifold M, we study an invariant of the mapping class of a surface homeomorphism called the translation distance in the arc complex and its relation with essential surfaces in M. We prove that the translation distance of the monodromy of M can be bounded above by the Euler characteristic of an essential surface. For one-cusped, hyperbolic, fibered 3-manifolds, the monodromy can also be bounded above by a linear function of the genus of an essential …