Physical Sciences and Mathematics Commons^™

Interstructure Lattices And Types Of Peano Arithmetic, Athar Abdul-Quader

Dissertations, Theses, and Capstone Projects

The collection of elementary substructures of a model of PA forms a lattice, and is referred to as the substructure lattice of the model. In this thesis, we study substructure and interstructure lattices of models of PA. We apply techniques used in studying these lattices to other problems in the model theory of PA.

In Chapter 2, we study a problem that had its origin in Simpson, who used arithmetic forcing to show that every countable model of PA has an expansion to PA^∗ that is pointwise definable. Enayat later showed that there are 2^ℵ₀ models with …

Asymptotic Counting Formulas For Markoff-Hurwitz Tuples, Ryan Ronan

Dissertations, Theses, and Capstone Projects

The Markoff equation is a Diophantine equation in 3 variables first studied in Markoff's celebrated work on indefinite binary quadratic forms. We study the growth of solutions to an n variable generalization of the Markoff equation, which we refer to as the Markoff-Hurwitz equation. We prove explicit asymptotic formulas counting solutions to this generalized equation with and without a congruence restriction. After normalizing and linearizing the equation, we show that all but finitely many solutions appear in the orbit of a certain semigroup of maps acting on finitely many root solutions. We then pass to an accelerated subsemigroup of maps …

Some Results In Combinatorial Number Theory, Karl Levy

Dissertations, Theses, and Capstone Projects

The first chapter establishes results concerning equidistributed sequences of numbers. For a given $d\in\mathbb{N}$, $s(d)$ is the largest $N\in\mathbb{N}$ for which there is an $N$-regular sequence with $d$ irregularities. We compute lower bounds for $s(d)$ for $d\leq 10000$ and then demonstrate lower and upper bounds $\left\lfloor\sqrt{4d+895}+1\right\rfloor\leq s(d)< 24801d^{3} + 942d^{2} + 3$ for all $d\geq 1$. In the second chapter we ask if $Q(x)\in\mathbb{R}[x]$ is a degree $d$ polynomial such that for $x\in[x_k]=\{x_1,\cdots,x_k\}$ we have $|Q(x)|\leq 1$, then how big can its lead coefficient be? We prove that there is a unique polynomial, which we call $L_{d,[x_k]}(x)$, with maximum lead coefficient under these constraints and construct an algorithm that generates $L_{d,[x_k]}(x)$.

Detecting Majorana Fermion Induced Crossed Andreev Reflection, Lei Fang

Dissertations, Theses, and Capstone Projects

This dissertation is devoted to a study of detecting the Majorana fermion induced crossed Andreev reflection.

Majorana fermions are particles that constitute their own antiparticles. In condensed matter physics, Majorana fermions are zero energy modes that reside at edges or around vortices of topological superconductors. The special properties of Majorana fermions result in their potential to conduct topological quantum computation, which has been attracting a lot of current research. One of the most important issues in the field of the Majorana fermion physics now is to detect their existence in realistic systems. Among many classes of detecting methods, a transport …

Exploring The Internal Statistics: Single Image Super-Resolution, Completion And Captioning, Yang Xian

Dissertations, Theses, and Capstone Projects

Image enhancement has drawn increasingly attention in improving image quality or interpretability. It aims to modify images to achieve a better perception for human visual system or a more suitable representation for further analysis in a variety of applications such as medical imaging, remote sensing, and video surveillance. Based on different attributes of the given input images, enhancement tasks vary, e.g., noise removal, deblurring, resolution enhancement, prediction of missing pixels, etc. The latter two are usually referred to as image super-resolution and image inpainting (or completion).

Image super-resolution and completion are numerically ill-posed problems. Multi-frame-based approaches make use of the …

Toxic Gas Sensing On Nanoporous Carbons, Nikolina-Eleni Travlou

Dissertations, Theses, and Capstone Projects

Activated carbons, either synthetic, developed in our laboratory, or commercial, were prepared or further modified, in order to introduce specific heteroatoms such as oxygen, nitrogen and sulfur to their matrices. Chips coated with thin layers of the carbon samples were used for the sensing of gaseous ammonia. They were exposed to continuous cycles of various ammonia concentrations (10-500 ppm), and changes in normalized resistance were analyzed. In all cases linear responses were recorded and the chips reached sensitivities as high as 31%, which are comparable to those of modified graphene-based sensors. The applied specific surface chemical modifications were an effective …

Involute Analysis: Virtual Discourse, Memory Systems And Archive In The Involutes Of Thomas De Quincey, Kimberley A. Garcia

Dissertations, Theses, and Capstone Projects

Thomas De Quincey’s involutes inform metaphysical thought on memory and language, particularly concerning multiplicity and the virtual, repetition and difference. When co-opting the mathematic and mechanic involute in Suspiria de Profundis, De Quincey generates an interdisciplinary matrix for the semiotics underpinning his philosophy of language and theory of memory and experience. Involutes entangle and reproduce. De Quincey’s involute exposes the concrete and actual through which all experience accesses the abstract or virtual. The materiality of their informatics and technics provides a literary model and theoretical precursor to a combination of archive and systems theory. The textuality of involute system(s)—both …

A Partial Nonlinear Extension Of Lax-Richtmyer Approximation Theory, Aradhana Kumari

Dissertations, Theses, and Capstone Projects

Lax and Richtmyer developed a theory of algorithms for linear initial value problems that guarantees, under certain circumstances, the convergence to numerical solution of initial value problem. The assumptions are first that the difference equations (algorithms) approx- imate the differential equations under study (this is called consistency) and, secondly, that the initial value problem be well-posed (which means that the solutions exist, are unique and depend continuously on initial data). Under these assumptions the stability condition (which requires that errors in the algorithm do not accumulate nor increase as one iter- ates the algorithm) is necessary and sufficient for convergence …

Nonlinear Optical Studies Of Defects And Domain Structures In Perovskite-Type Dielectric Ceramics, David J. Ascienzo

Dissertations, Theses, and Capstone Projects

In order to improve future generations of dielectric capacitors a deeper understanding of voltage-induced dielectric breakdown and electrical energy storage limitations is required. This dissertation presents the use of far-field optical second harmonic generation (SHG) polarimetry for probing structural defects and polar domains in linear and nonlinear perovskite dielectric ceramics. We investigated the formation of electric field-induced structural distortions at pristine Fe-doped SrTiO₃ (Fe:STO) electrode interfaces, structural defect and strain formation due to oxygen vacancy migration in electrodegraded Fe:STO single crystals, and mixed tetragonal and rhombohedral phase domains in ferroelectric Zr-doped BaTiO₃ (BZT) films exhibiting excellent …

Approximation Algorithms For Effective Team Formation, George Rabanca

Dissertations, Theses, and Capstone Projects

This dissertation investigates the problem of creating multiple disjoint teams of maximum efficacy from a fixed set of workers. We identify three parameters which directly correlate to the team effectiveness — team expertise, team cohesion and team size — and propose efficient algorithms for optimizing each in various settings. We show that under standard assumptions the problems we explore are not optimally solvable in polynomial time, and thus we focus on developing efficient algorithms with guaranteed worst case approximation bounds. First, we investigate maximizing team expertise in a setting where each worker has different expertise for each job and each …

Secure And Efficient Delegation Of A Single And Multiple Exponentiations To A Single Malicious Server, Matluba Khodjaeva

Dissertations, Theses, and Capstone Projects

Group exponentiation is an important operation used in many cryptographic protocols, specifically public-key cryptosystems such as RSA, Diffie Hellman, ElGamal, etc. To expand the applicability of group exponentiation to computationally weaker devices, procedures were established by which to delegate this operation from a computationally weaker client to a computationally stronger server. However, solving this problem with a single, possibly malicious, server, has remained open since a formal cryptographic model was introduced by Hohenberger and Lysyanskaya in 2005. Several later attempts either failed to achieve privacy or only achieved constant security probability.

In this dissertation, we study and solve this problem …

Machine Learning Algorithms For Automated Satellite Snow And Sea Ice Detection, George Bonev

Dissertations, Theses, and Capstone Projects

The continuous mapping of snow and ice cover, particularly in the arctic and poles, are critical to understanding the earth and atmospheric science. Much of the world's sea ice and snow covers the most inhospitable places, making measurements from satellite-based remote sensors essential. Despite the wealth of data from these instruments many challenges remain. For instance, remote sensing instruments reside on-board different satellites and observe the earth at different portions of the electromagnetic spectrum with different spatial footprints. Integrating and fusing this information to make estimates of the surface is a subject of active research.

In response to these challenges, …

Nuclear Magnetic Resonance Studies Of Electrode And Electrolyte Materials For Li-Ion Batteries, Lisa Cirrincione

Dissertations, Theses, and Capstone Projects

In this thesis, Nuclear Magnetic Resonance (NMR) spectroscopic techniques are used to study lithium electrode and electrolyte materials for advanced rechargeable lithium ion batteries. Three projects are described in this thesis. The first involves ²³Na and ³⁷Al static and magic angle spinning NMR studies of NaAlH₄/C anode materials for advanced rechargeable batteries. The second project is a study of paramagnetic lithium transition-metal phosphate cathode materials for Li-ion batteries, where ⁷Li, and ³¹P single crystal NMR was used in order to obtain detailed information on the local electronic and magnetic environments. The third project investigates …

Characterization Of Hydrophobic Interactions Of Polymers With Water And Phospholipid Membranes Using Molecular Dynamics Simulations, Mihaela Drenscko

Dissertations, Theses, and Capstone Projects

Polymers and lipid membranes are both essential soft materials. The structure and hydrophobicity/hydrophilicity of polymers, as well as the solvent they are embedded in, ultimately determines their size and shape. Understating the variation of shape of the polymer as well as its interactions with model biological membranes can assist in understanding the biocompatibility of the polymer itself. Computer simulations, in particular molecular dynamics, can aid in characterization of the interaction of polymers with solvent, as well as polymers with model membranes. In this thesis, molecular dynamics serve to describe polymer interactions with a solvent (water) and with a lipid membrane. …

Control Of Light-Matter Interaction In 2d Semiconductors, Zheng Sun

Dissertations, Theses, and Capstone Projects

In this thesis we discuss the control of light matter interaction in low dimensional nanostructure cavity light confining structures. These structures have controllable dispersion properties through design which can be exploited to modify the interaction of light and matter. We will discuss two different types of light confining microcavities: a dielectric cavity and a metal cavity. The specific design of the cavity gives rise to the confinement of the electric field in the center where the nano-materials are placed. In this work, the main material was on the new class of two- dimensional semiconductors of transition metal dichalcogenides (TMDs). Due …

A Combinatorial Framework For Multiple Rna Interaction Prediction, Syed Ali Ahmed

Dissertations, Theses, and Capstone Projects

The interaction of two RNA molecules involves a complex interplay between folding and binding that warranted recent developments in RNA-RNA interaction algorithms. However, biological mechanisms in which more than two RNAs take part in an interaction also exist.

A typical algorithmic approach to such problems is to find the minimum energy structure. Often the computationally optimal solution does not represent the biologically correct structure of the interaction. In addition, different biological structures may be observed, depending on several factors. Furthermore, scoring techniques often miss critical details about dependencies within different parts of the structure, which typically leads to lower scores …

Morphogenesis And Growth Driven By Selection Of Dynamical Properties, Yuri Cantor

Dissertations, Theses, and Capstone Projects

Organisms are understood to be complex adaptive systems that evolved to thrive in hostile environments. Though widely studied, the phenomena of organism development and growth, and their relationship to organism dynamics is not well understood. Indeed, the large number of components, their interconnectivity, and complex system interactions all obscure our ability to see, describe, and understand the functioning of biological organisms.

Here we take a synthetic and computational approach to the problem, abstracting the organism as a cellular automaton. Such systems are discrete digital models of real-world environments, making them more accessible and easier to study then their physical world …

Heterojunction Engineering For Next Generation Hybrid Ii-Vi Materials, Thor Garcia

Dissertations, Theses, and Capstone Projects

Molecular Beam Epitaxy(MBE) is a versatile thin film growth technique with monolayer control of crystallization. The flexibility and precision afforded by the technique allows for unique control of interfaces and electronic structure of the films grown. This facilitates the realization of novel devices and structures within a research environment normally only achieved though complex industrial processes. In the past, the control of each interface in MBE has been explored to great benefit. In this work, we study the control of these interfaces so as to increase the performance of novel devices material systems. This dissertation focuses on two main areas …

Some Metric Properties Of The Teichmüller Space Of A Closed Set In The Riemann Sphere, Nishan Chatterjee

Dissertations, Theses, and Capstone Projects

Let E be an infinite closed set in the Riemann sphere, and let T(E) denote its Teichmüller space. In this dissertation we study some metric properties of T(E). We prove Earle's form of Teichmüller contraction for T(E), holomorphic isometries from the open unit disk into T(E), extend Earle's form of Schwarz's lemma for classical Teichmüller spaces to T(E), and finally study complex geodesics and unique extremality for T(E).

Stereospecific Electrophilic Fluorination Of Alkylcarbastannatrane Reagents, Xinghua Ma

Dissertations, Theses, and Capstone Projects

The introduction of fluorine atoms into organic molecules significantly changes their physical, chemical, and biological properties. Fluorinated organic compounds are used as pharmaceuticals, agrochemicals, materials, and tracers for positron emission tomography (PET). For example, the site-specific fluorination of drugs can block sites of phase I metabolism by cytochrome P450 enzymes as well as improve target-binding affinities. In view of the unique features of fluorine-containing compounds, there has been increasing interest in the development of novel methods for the synthesis of fluorinated molecules, especially the site-specific monofluorination of complex molecules. Herein, we present the enantiospecific conversion of chiral secondary alkylcarbastannatranes into …

Walking As Ontological Shifter: Thoughts In The Key Of Life, Bibi (Silvina) Calderaro

Dissertations, Theses, and Capstone Projects

With walking as ontological shifter I pursue an alternative to the dominant modernist episteme that offers either/or onto-epistemologies of opposition and their reifying engagements. I propose this type of walking is an intentional turning towards a set of radical positions that, as integrative aesthetic and therapeutic practice, brings multiplicity and synchronicity to experience and being in an expanded sociality. This practice facilitates the conditions of possibility for recurring points of contact between the interiority perceived as ‘body’ and the exteriority perceived as ‘world.’ While making evident the self’s at once incoherence with it-self, it opens to a space beyond the …

A Realization Of Modernity: Case Studies In Connectivity And Time, Mari Gorman

Dissertations, Theses, and Capstone Projects

My stated goal in applying to The Graduate Center was to explore my previous research in diverse fields of study. This research, the result of a formal investigation of acting, was and still is centrally focused on the subject of relationship itself, relationships being what actors create. In pursuit of a greater understanding of the essential nature of relationship in practical terms, a self-organizing complex system that constitutes universal relationship was unexpectedly discovered. As such, this system has been shown to offer solutions to many outstanding problems in diverse areas of study. The Liberal Studies program track, Approaches to Modernity …

Continuum Electrostatics Analysis Of The Kok Cycle Of Photosystem Ii, Witold Szejgis

Dissertations, Theses, and Capstone Projects

The Kok cycle is catalytic process by which the oxygen-evolving complex (OEC) of photosystem II (PSII) oxidizes two water molecules forming oxygen. Four OEC oxidation states (S₀ to S₃) in the Kok cycle precede the final product formation in the S₄ state. Here a semi-empirical classical electrostatics analysis is applied to S₀ to S₃ states of the OEC is used to estimate the electrochemical midpoints for each S-state transition and the proton loss coupled to oxidation. To account for geometrical rearrangement within the cluster during Kok cycle optimized QM/MM geometries are used for each …

Machine Learning Approach To Retrieving Physical Variables From Remotely Sensed Data, Fazlul Shahriar

Dissertations, Theses, and Capstone Projects

Scientists from all over the world make use of remotely sensed data from hundreds of satellites to better understand the Earth. However, physical measurements from an instrument is sometimes missing either because the instrument hasn't been launched yet or the design of the instrument omitted a particular spectral band. Measurements received from the instrument may also be corrupt due to malfunction in the detectors on the instrument. Fortunately, there are machine learning techniques to estimate the missing or corrupt data. Using these techniques we can make use of the available data to its full potential.

We present work on four …

The Formation Of Fine-Grained Chondrule Rims In Unequilibrated Ordinary Chondrites, John Bigolski

Dissertations, Theses, and Capstone Projects

Fine-grained rims are ubiquitous, non-igneous, features that completely or partially envelope the majority of chondrules within the least equilibrated of the unequilibrated ordinary chondrites (UOCs). A detailed examination of such rims in 4 UOC samples less than petrologic type 3.2 was conducted in order to 1) characterize the relative distribution of rims within chondrite samples, 2) inspect differences between fine-grained rims and adjacent matrix material, 3) petrologically analyze the rims and their relationships with chondrule cores, 4) characterize an ungrouped UOC, Northwest Africa 5717, 5) conduct a microanalytical investigation of rim / matrix boundaries to discern relative chronologies of fine-grained …

Synthesis And Evaluation Of Tetrahydroprotoberberines As Dopamine Receptor Ligands, Satishkumar V. Gadhiya

Dissertations, Theses, and Capstone Projects

Dopamine (DA) receptors belong to the G-protein coupled receptors (GPCRs) family, divided in to two groups based on their high homology transmembrane domains; D1-like DA receptors (D1, D5) and D2-like DA receptors (D2-D4). DA receptor specific ligands have been exploited as a means for studying the prognosis and curing several CNS disorders. Though several efforts have been devoted to discover selective and potent DA receptor ligands, complete selectivity within the DA receptor subtypes remains a challenge.

Tetrahydroprotoberberines (THPBs) are a group of naturally occurring tetracyclic alkaloids that belong to the tetrahydroisoquinoline family. A wide range of biological activities are associated …

Computational Investigation Of The Pore Formation Mechanism Of Beta-Hairpin Antimicrobial Peptides, Richard Lipkin

Dissertations, Theses, and Capstone Projects

β-hairpin antimicrobial peptides (AMPs) are small, usually cationic peptides that provide innate biological defenses against multiple agents. They have been proposed as the basis for novel antibiotics, but their pore formation has not been directly observed on a molecular level. We review previous computational studies of peptide-induced membrane pore formation and report several new molecular dynamics simulations of β-hairpin AMPs to elucidate their pore formation mechanism. We simulated β-barrels of various AMPs in anionic implicit membranes, finding that most of the AMPs’ β-barrels were not as stable as those of protegrin. We also performed an optimization study of protegrin β-barrels …

Travel Mode Identification With Smartphone Sensors, Xing Su

Dissertations, Theses, and Capstone Projects

Personal trips in a modern urban society typically involve multiple travel modes. Recognizing a traveller's transportation mode is not only critical to personal context-awareness in related applications, but also essential to urban traffic operations, transportation planning, and facility design. While the state of the art in travel mode recognition mainly relies on large-scale infrastructure-based fixed sensors or on individuals' GPS devices, the emergence of the smartphone provides a promising alternative with its ever-growing computing, networking, and sensing powers. In this thesis, we propose new algorithms for travel mode identification using smartphone sensors. The prototype system is built upon the latest …

Counting Rational Points, Integral Points, Fields, And Hypersurfaces, Joseph Gunther

Dissertations, Theses, and Capstone Projects

This thesis comes in four parts, which can be read independently of each other.

In the first chapter, we prove a generalization of Poonen's finite field Bertini theorem, and use this to show that the obvious obstruction to embedding a curve in some smooth surface is the only obstruction over perfect fields, extending a result of Altman and Kleiman. We also prove a conjecture of Vakil and Wood on the asymptotic probability of hypersurface sections having a prescribed number of singularities.

In the second chapter, for a fixed base curve over a finite field of characteristic at least 5, we …

Turaev Surfaces And Toroidally Alternating Knots, Seungwon Kim

Dissertations, Theses, and Capstone Projects

In this thesis, we study knots and links via their alternating diagrams on closed orientable surfaces. Every knot or link has such a diagram by a construction of Turaev, which is called the Turaev surface of the link. Links that have an alternating diagram on a torus were defined by Adams as toroidally alternating. For a toroidally alternating link, the minimal genus of its Turaev surface may be greater than one. Hence, these surfaces provide different topological measures of how far a link is from being alternating.

First, we classify link diagrams with Turaev genus one and two in terms …