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University of South Carolina

Theses and Dissertations

2017

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Topics In Group Testing With Multiple Infections, Peijie Hou May 2017

Topics In Group Testing With Multiple Infections, Peijie Hou

Theses and Dissertations

Group testing, dating back to the early 1940s, was first proposed to screen for syphilis among US inductees during World War II (Dorfman, 1943). Since then, the benefits of reducing testing costs by employing group testing have been demonstrated in many areas, such as drug discovery, genetics, and infectious disease testing. Traditionally, statistical research in group testing has largely been motivated by applications involving a single infection. With the recent development of multiplex assays that can diagnose multiple infections simultaneously, generalizing the existing group testing literature to incorporate multiple infections is a natural and necessary next step. This dissertation consists …


Characterization Of Sufs And Sufe Of Suf Pathway For Fe-S Cluster Assembly In Escherichia Coli, Guangchao Dong May 2017

Characterization Of Sufs And Sufe Of Suf Pathway For Fe-S Cluster Assembly In Escherichia Coli, Guangchao Dong

Theses and Dissertations

Fe-S clusters are one major type of the sulfur-containing cofactors, which conduct essential functions in organisms. The Suf pathway is one of the three main pathways for the biosynthesis of Fe-S clusters. In E. coli, the Suf pathway is utilized under iron limitation and oxidative stress. This ability is important for pathogens to survive. Also, the Suf pathway is found to be exclusive in bacteria, so it is a good target for novel antibiotic design. SufS is a cysteine desulfurase in the Suf pathway to extract sulfur from L-cysteine. It needs the enhancement of SufE. To better understand the catalytic …


On The Existence Of Non-Free Totally Reflexive Modules, J. Cameron Atkins May 2017

On The Existence Of Non-Free Totally Reflexive Modules, J. Cameron Atkins

Theses and Dissertations

For a standard graded Cohen-Macaulay ring R, if the quotient R/(x) admits nonfree totally reflexive modules, where x is a system of parameters consisting of elements of degree one, then so does the ring R. A non-constructive proof of this statement was given in [16]. We give an explicit construction of the totally reflexive modules over R obtained from those over R/(x).

We consider the question of which Stanley-Reisner rings of graphs admit nonfree totally reflexive modules and discuss some examples. For an Artinian local ring (R,m) with m3 = 0 and containing the complex numbers, we describe an explicit …


Bird's Eye View: Cooperative Exploration By Ugv And Uav, Shannon Hood May 2017

Bird's Eye View: Cooperative Exploration By Ugv And Uav, Shannon Hood

Theses and Dissertations

This paper proposes a solution to the problem of cooperative exploration using an Unmanned Ground Vehicle (UGV) and an Unmanned Aerial Vehicle (UAV). More specifically, the UGV navigates through the free space, and the UAV provides enhanced situational awareness via its higher vantage point. The motivating application is search and rescue in a damaged building. A camera atop the UGV is used to track a fiducial tag on the underside of the UAV, allowing the UAV to maintain a fixed pose relative to the UGV. Furthermore, the UAV uses its front facing camera to provide a birds-eye-view to the remote …


Electroproduction Of W Mesons Off Protons In The Third Resonance Region And Beyond, Evan Phelps May 2017

Electroproduction Of W Mesons Off Protons In The Third Resonance Region And Beyond, Evan Phelps

Theses and Dissertations

Exclusive electroproduction of ω(782) mesons in the reaction ep → epω → epπ+π−π0 was studied from the production threshold, through the third resonance region, and beyond. With electron beam energies close to 6 GeV, the kinematic range covers W = [1.72, 2.60) GeV and Q2 = [1.85, 5.15) GeV2. By combining two sets of data collected by the Thomas Jefferson National Accelerator Facility’s wide-acceptance spectrometer (CLAS), the largest set of resonance-region differential cross sections, d2σh dΩ∗ , for ω electroproduction have been produced. Response functions RT + LRL, RTT , and RTL were extracted to provide a view of how …


Bayesian Flexible Modeling Of Interval-Censored Failure Time Data, Sheng-Yang Wang May 2017

Bayesian Flexible Modeling Of Interval-Censored Failure Time Data, Sheng-Yang Wang

Theses and Dissertations

Interval-censored data are a special type of survival data, in which the survival time is not accurately observed but known to fall within a specific time interval. Interval censored data commonly arise in real-life epidemiological and medical studies that involve periodic examinations. In this dissertation, several semi-parametric regression models are investigated to provide flexible modeling and robust inference for interval censored data from Bayesian perspectives.

Chapter 1 provides a detailed description about interval-censored data and gives several examples. Existing models and methods for analyzing such interval-censored data are reviewed as well. Chapter 2 develops a unified Bayesian estimation approach under …


Advances In Chemistry, Part I: Noise, Calibration, And Educational Advances In Analytical Chemistry. Part Ii: Safety Oversight In Chemical Journals, Lauren E. Grabowski May 2017

Advances In Chemistry, Part I: Noise, Calibration, And Educational Advances In Analytical Chemistry. Part Ii: Safety Oversight In Chemical Journals, Lauren E. Grabowski

Theses and Dissertations

Part I:

The accuracy and precision of the results of any chemical analysis depends on the calibration graph and its associated systematic and random errors. Least squares regression generally treats all data with equal weights. A weighted least-squares fit is an improvement but requires knowledge of the imprecision in each point of the calibration graph. The imprecision is not easy to estimate with high confidence because of the large number of replicates needed.

The imprecision depends on the types and magnitudes of the sources of noise. We characterized the noise sources in ICP-OES and UV/Vis and developed a model that …


Antimicrobial Biomaterials And Sustainable Polymers From Renewable Biomass, Mitra Shiran Ganewatta May 2017

Antimicrobial Biomaterials And Sustainable Polymers From Renewable Biomass, Mitra Shiran Ganewatta

Theses and Dissertations

In this dissertation, development of antimicrobial biomaterials and sustainable polymers from renewable biomass is described. In Chapter 1, an overview and recent development about sustainable polymers from renewable biomass, antimicrobial biomaterials and polymerization methods are given. Afterwards, the major research objectives of this doctoral research work are described.

Innovative cationic polymers containing pine resin sourced abietic acid is discussed in Chapter 2. The preparation of cationic compounds is conversed via a combination of Diels-Alder, catalytic esterification, quaternization and subsequent decoration of polycaprolactone that was prepared via ring-opening polymerization (ROP). Furthermore, the antimicrobial activity against a range of bacteria, biocompatibility with …


Shaping Metallic Nanoparticles Toward Integrated Plasmonics And Catalysis, Qingfeng Zhang May 2017

Shaping Metallic Nanoparticles Toward Integrated Plasmonics And Catalysis, Qingfeng Zhang

Theses and Dissertations

Noble metal nanoparticles have been of tremendous interest because of their intriguing size- and shape-dependent plasmonic and catalytic properties. The combination of tunable plasmon resonances with superior catalytic activities on the same nanoparticle, however, has long been challenging because plasmonics and catalysis require nanoparticles in two drastically different size regimes. Tunable plasmon resonances is a unique feature of sub-wavelength metallic nanoparticles, whereas heterogeneous catalysis requires the use of sub-5 nm nanoparticles as the catalysts. In this dissertation, I firstly found a unique way to bridge this size gap between nanoplasmonics and nanocatalysis. I demonstrated that desired plasmonic and catalytic properties …


A Family Of Simple Codimension Two Singularities With Infinite Cohen-Macaulay Representation Type, Tyler Lewis May 2017

A Family Of Simple Codimension Two Singularities With Infinite Cohen-Macaulay Representation Type, Tyler Lewis

Theses and Dissertations

A celebrated theorem of Buchweitz, Greuel, Knörrer, and Schreyer is that the hypersurface singularities of finite representation type, i.e. the hypersurface singularities admitting only finitely many indecomposable maximal Cohen-Macaulay modules, are exactly the ADE singularities. The codimension 2 singularities that are the analogs of the ADE singularities have been classified by Frühbis-Krühger and Neumer, and it is natural to expect an analogous result holds for these singularities. In this paper, I will present a proof that, in contrast to hypersurfaces, Frühbis-Krühger and Neumer’s singularities include a subset of singularities of infinite representation type.


Semiparametric Estimation And Inference In Causal Inference And Measurement Error Models, Jianxuan Liu Apr 2017

Semiparametric Estimation And Inference In Causal Inference And Measurement Error Models, Jianxuan Liu

Theses and Dissertations

This dissertation research has focused on theoretical and practical developments of semiparametric modeling and statistical inference for high dimensional data and measurement error data. In causal inference framework, when evaluating the effectiveness of medical treatments or social intervention policies, the average treatment effect becomes fundamentally important. We focus on propensity score modelling in treatment effect problems and develop new robust tools to overcome the curse of dimensionality. Furthermore, estimating and testing the effect of covariates of interest while accommodating many other covariates is an important problem in many scientific practices, including but not limited to empirical economics, public health and …


Chemical Sensing In Harsh Environments By Multivariate Optical Computing, Christopher Michael Jones Jan 2017

Chemical Sensing In Harsh Environments By Multivariate Optical Computing, Christopher Michael Jones

Theses and Dissertations

Multivariate optical computing (MOC) is a compressive sensing technique for which an analyte concentration is detected in an interfering mixture by direct detector output. The detector measures the dot product of a linear regression vector with a sample spectrum, as an analog optical computation. The computation is accomplished with the multivariate optical element (MOE), to which the optical regression vector is encoded as a transmission pattern. As a spectrum of light emanates from a sample and passes through the MOE, the dot product naturally occurs when light strikes the detector. The MOC platform allows a simple, robust, and direct measurement …


High Resolution Gravity, Helicopter Magnetic, And Electromagnetic Study, Haile Gold Mine, South Carolina, Saad Saud Alarifi Jan 2017

High Resolution Gravity, Helicopter Magnetic, And Electromagnetic Study, Haile Gold Mine, South Carolina, Saad Saud Alarifi

Theses and Dissertations

The goal of this research was to calibrate and test geophysical methods for the detection of disseminated sulfides in the area of the Haile Gold Mine, South Carolina. The work focused on the calibration of high resolution gravity, and helicopter electromagnetic (EM) and magnetic data provided by OceanaGold. While high resolution potential field data (gravity and magnetics) has not been proven to be effective at small scales in exploration for disseminated sulfides, there is a strong regional correlation between high amplitude gravity and magnetic anomalies and the most productive gold mines in the Carolina terrane. Helicopter EM methods have been …


Robustness Evaluation For Phylogenetic Reconstruction Methods And Evolutionary Models Reconstruction Of Tumor Progression, Jun Zhou Jan 2017

Robustness Evaluation For Phylogenetic Reconstruction Methods And Evolutionary Models Reconstruction Of Tumor Progression, Jun Zhou

Theses and Dissertations

During evolutionary history, genomes evolve by DNA mutation, genome rearrangement, duplication and gene loss events. There has been endless effort to the phylogenetic and ancestral genome inference study. Due to the great development of various technology, the information about genomes is exponentially increasing, which make it possible figure the problem out. The problem has been shown so interesting that a great number of algorithms have been developed rigorously over the past decades in attempts to tackle these problems following different kind of principles. However, difficulties and limits in performance and capacity, and also low consistency largely prevent us from confidently …


Polarization Observables In Double Pion Photo-Production With Circularly Polarized Photons Off Transversely Polarized Protons, Lelia Aneta Net Jan 2017

Polarization Observables In Double Pion Photo-Production With Circularly Polarized Photons Off Transversely Polarized Protons, Lelia Aneta Net

Theses and Dissertations

The study of excited states of the nucleon facilitates the understanding of the nucleon structure and its underlying symmetry and couplings. A main goal of the NL program at the Thomas Jefferson National Accelerator Facility is to investigate the excitation and decays of the baryon resonances and assist in identifying the “missing” nucleon resonances that are predicted by theoretical models. One way to study the nucleon resonances is by extracting polarization observables, which provide more information than the unpolarized cross-section studies, e.g. access to the transition amplitudes of the reaction. Double-pion photoproduction contributes strongly to the total cross section …


The Summerville Formation: Evidence For A Sub-Horizontal Stratigraphic Sequence Below The Post-Rift Unconformity In The Middleton Place Summerville Seismic Zone, Joseph Edward Getz Jan 2017

The Summerville Formation: Evidence For A Sub-Horizontal Stratigraphic Sequence Below The Post-Rift Unconformity In The Middleton Place Summerville Seismic Zone, Joseph Edward Getz

Theses and Dissertations

The Middleton Place Summerville Seismic Zone (MPSSZ) near Summerville, South Carolina was the site of renewed extensive investigation, beginning in the 1970’s, for the source of the 1886 Charleston earthquake. Reactivation of faults associated with a putative fault-bounded Triassic rift basin through analysis of seismic reflection, seismic refraction, and well data has since become the favored interpretation for the source of MPSSZ seismicity. Critical to this interpretation is the association of continental redbed sedimentary rocks in Triassic basins throughout the North American Atlantic margin. Reanalysis of 18 seismic reflection profiles and 25 seismic refraction profiles within the MPSSZ suggests that …


Mechanistic Studies Of Nucleic Acid Chaperone Activities Of Retroviral Nucleocapsid Protein, Lichao Sun Jan 2017

Mechanistic Studies Of Nucleic Acid Chaperone Activities Of Retroviral Nucleocapsid Protein, Lichao Sun

Theses and Dissertations

In this dissertation, I have used single molecule Fluorescence Resonance Energy Transfer (sm-FRET), as a nanoscale spectroscopic ruler to gain quantitative, molecular-level understanding about the kinetics and mechanism of NC-chaperoned TAR sequence rearrangements. Firstly, I have resolved the complex kinetics and underlying reaction pathways of TAR sequence annealing in the presence of HIV-1 NC over a broad NC concentration by performing the time-resolved sm-FRET measurements in a unique aggregation-free environment. I have further gained the insights that the NC-induced secondary structural changed of TAR hairpins modulate the annealing pathways and consequently affect the overall kinetics of the TAR sequence annealing. …


Sanitary Sewer Overflows In Columbia, South Carolina And Their Impact On Mercury And Metal Cycling, Alison Emmons Jan 2017

Sanitary Sewer Overflows In Columbia, South Carolina And Their Impact On Mercury And Metal Cycling, Alison Emmons

Theses and Dissertations

Objectives. Microbial pathogens and their threat to human health have been the primary concern of sanitary sewer overflows (SSO); however, SSOs may also be a source of metals, including methylmercury, to local waterways. We hypothesized that SSOs had elevated concentrations of metals compared to nearby reference creeks.

Methods. Unfiltered and filtered (0.2 μm) surface water samples were collected monthly between November 2015 and March 2016 from three sewage-impacted creeks in Columbia, South Carolina. During this period, three sewage events were captured including an active SSO, a ruptured force main sewer pipe, and one site downstream from SSOs. In October 2016 …


Utilizing Structure-From-Motion Photogrammetry And Unmanned Aerial Vehicles To Characterize Variability In Fluvial Deposits From The Salt Wash Member Of The Morrison Formation, East-Central Utah, John Chesley Jan 2017

Utilizing Structure-From-Motion Photogrammetry And Unmanned Aerial Vehicles To Characterize Variability In Fluvial Deposits From The Salt Wash Member Of The Morrison Formation, East-Central Utah, John Chesley

Theses and Dissertations

Modern fluvial systems are highly variable, often containing the entire spectrum of fluvial styles (e.g., braided to meandering). This variability is difficult to capture in ancient fluvial deposits due to limited 1- and 2-dimesional exposures, which provide only a snapshot of the depositional history at one location. As a result, researchers are forced to interpolate between exposures and develop regional scale models that often underestimate the complexity and variability seen in modern environments. Outcrops of the Upper Jurassic Salt Wash Member of the Morrison Formation in east-central Utah, USA provide a relatively unique opportunity to examine ancient fluvial sandstone bodies …


Drivers Of Sediment Accumulation And Nutrient Burial In Coastal South Carolina Residential Stormwater Detention Ponds, William Schroer Jan 2017

Drivers Of Sediment Accumulation And Nutrient Burial In Coastal South Carolina Residential Stormwater Detention Ponds, William Schroer

Theses and Dissertations

Stormwater detention ponds are widely utilized as control structures to manage runoff waters during storm events. These sediments also represent significant sites of organic carbon and nutrient burial. Here, carbon (C) and nutrient sources and burial rates were determined in 14 residential stormwater detention ponds throughout coastal counties of South Carolina. Bulk sediment accumulation was directly correlated with catchment impervious surface coverage (R2 = 0.90) with sediment accumulation rates ranging from 0.06 to 0.50 cm y-1. These rates of sediment accumulation and subsequent pond volume loss are lower than expected indicating that required maintenance dredging schedules be reassessed. Strong, positive …


A Study Of Two Digital Hydrological Networks In South Carolina And An Assessment Of Site Reconnaissance Results From The Sc Department Of Health And Environmental Control Probability Survey For Streams And Rivers, Caitlin Smith Jan 2017

A Study Of Two Digital Hydrological Networks In South Carolina And An Assessment Of Site Reconnaissance Results From The Sc Department Of Health And Environmental Control Probability Survey For Streams And Rivers, Caitlin Smith

Theses and Dissertations

The South Carolina Department of Health and Environmental Control (SCDHEC), Surface Water Monitoring Section utilizes a probability survey to assess water quality conditions of streams and rivers in the state. The Generalized Random-Tessellation Stratified survey design prioritizes specific stream order (size) subpopulations and spatial distribution in the generation of potential sample sites, and is intended to survey only perennial stream reaches. Site reconnaissance is conducted to assess site suitability and accessibility. The stream characteristics associated with accepted and rejected sites have been recorded since the late 1990s/early 2000s. Data from 2001-2016 was analyzed to assess apparent trends in both rejected …


On Slowly Rotating Supercompact Schwarzschild Stars, Nelson Camilo Posada-Aguirre Jan 2017

On Slowly Rotating Supercompact Schwarzschild Stars, Nelson Camilo Posada-Aguirre

Theses and Dissertations

In this Ph.D thesis, I will present results concerning to my doctoral research project submitted to the Department of Physics and Astronomy at the University of South Carolina. The thesis belongs to the area of Theoretical Physics, particularly, in the framework of Einstein’s Theory of General Relativity.

The project is the study of integral and surface properties of slowly rotating homogeneous masses in the gravastar limit R ! Rs, where Rs is the Schwarzschild radius. For this purpose we followed the perturbative method proposed by Hartle in 1967. In this model, the relativistic equations of structure for a slowly rotating …


Development Of An Electrochemical Method To Study Real-Time In Vivo Neurotransmitter Modulation, Srimal Aminda Samaranayake Jan 2017

Development Of An Electrochemical Method To Study Real-Time In Vivo Neurotransmitter Modulation, Srimal Aminda Samaranayake

Theses and Dissertations

Histamine and serotonin are important biogenic amines that regulate vital brain functions. These two transmitters are thoughts to be involved in neurodegenerative diseases such as Parkinson’s and Alzheimer’s and affective disorders including depression. Histamine and serotonin are believed to regulate each other but their fundamental neuromodulation mechanisms are not well understood. This lack of understanding makes brain disorders implicating these two transmitters difficult to diagnose and treat. Our lab extensively investigates the serotonergic system to understand serotonin’s neurochemistry in the brain. However, histamine is relatively understudied with respect to other biogenic amines because of an absence of suitable analytical tools. …


Synthesis, Characterization And Application Of Polymer-Grafted Nanoparticles, Yang Zheng Jan 2017

Synthesis, Characterization And Application Of Polymer-Grafted Nanoparticles, Yang Zheng

Theses and Dissertations

This work focused on the synthesis and characterization of polymer-grafted nanoparticles for various applications including drug-delivery, directed self-assembly and mechanical reinforcement applications. The surfaces of inorganic particles were modified with polymers of different composition, chain length, graft density and polymer architecture depending on the specific needs of each project. The surface modifications were mainly achieved by surface-initiated reversible addition fragmentation chain transfer (RAFT) polymerization, which is a very versatile technique to prepare nanocomposites with desired properties.

The first part of this work (Chapters 2 & 3) focused on novel self-assembly techniques. Chapter 2 described the design and characterization of a …


Glacial To Holocene Changes In Eastern Equatorial Pacific Deep-Water Chemistry And Circulation, Natalie E. Umling Jan 2017

Glacial To Holocene Changes In Eastern Equatorial Pacific Deep-Water Chemistry And Circulation, Natalie E. Umling

Theses and Dissertations

It has been hypothesized that the oceans store CO2 during glacial periods and then release it to the atmosphere, causing the onset of warm interglacial periods (Sigman and Boyle, 2000). Documenting this past transfer of CO2 between the oceans and atmosphere is of utmost importance for better understanding the impact that anthropogenic CO2 has and will have on Earth’s climate. The last deglaciation is a good analogue to modern increases in CO2 and temperature and is recent enough to be studied using radiocarbon. This period provides important insights into the nature of climate changes during the transition from glacial to …


Silylation-Based Kinetic Resolution Of 2-Arylcyclohexanols And Understanding Internal Chirality Transmission Via Circular Dichroism, Li Wang Jan 2017

Silylation-Based Kinetic Resolution Of 2-Arylcyclohexanols And Understanding Internal Chirality Transmission Via Circular Dichroism, Li Wang

Theses and Dissertations

This work described herein focuses on the silylation-based kinetic resolution methodology developed by the Wiskur group in 2011. It is a powerful method for the separation of a single enantiomer from a mixture of racemic secondary alcohols. Chapter one is a summary of the background and related works of this methodology.

In chapter two, the silylation-based kinetic resolution of various trans 2-arylcyclohexanols will be discussed by employing a p-isopropyl triphenylsilyl chloride as the derivatizing reagent with (-)-benzotetramisole as the catalyst. The diastereoselective and enantioselective of trans alcohols over the cis will be investigated and a facial one-pot reaction sequence will …


Serpentinization And Synthesis: Searching For Abiotic And Biotic Non-Volatile Organic Molecules In The Subsurface Of The Atlantis Massif, Katherine A. Hickok Jan 2017

Serpentinization And Synthesis: Searching For Abiotic And Biotic Non-Volatile Organic Molecules In The Subsurface Of The Atlantis Massif, Katherine A. Hickok

Theses and Dissertations

High concentrations of hydrogen created during serpentinization can promote the formation of abiotic organic carbon molecules such as methane, formate, and short chain hydrocarbons and, in laboratory experiments, larger molecules containing up to 32 carbon atoms. Subsurface archaeal and bacterial communities can use these reduced compounds for metabolic energy. International Ocean Discovery Project Expedition 357 drilled 17 boreholes into the Atlantis Massif with the goals of investigating carbon cycling and the presence of life in a zone of active serpentinization. The expedition recovered multiple lithologies including gabbros, basalts, carbonate sands, and serpentinites. A subset of contrasting lithologies were analyzed for …


Geometric Influence On Electronic Properties: Graphene With Antidots, Two-Dimensional Electron Gas And Three-Dimensional Carbon Nanostructures, Lei Wang Jan 2017

Geometric Influence On Electronic Properties: Graphene With Antidots, Two-Dimensional Electron Gas And Three-Dimensional Carbon Nanostructures, Lei Wang

Theses and Dissertations

Geometric influence on electrical and magneto transport properties has been investigated in three types of systems: (i) Graphene, a single layer of carbon atoms; (ii) Two-dimensional electron gas (2DEG) in AlInN/GaN heterostructure; and (iii) 3D carbon nanostructures, a special type of three-dimensional materials with spherical voids. Due to unique structures and energy dispersion relations, these three systems demonstrate distinct physical properties.

AlInN is the newest and amongst the widest band gap semiconductors. The 2DEG in AlInN/GaN heterostucture displays long transport lifetime along with conventional behaviors, including Shubnikov-de Haas (SdH) oscillation and weak localization. From SdH oscillation, the effective mass of …


Statistical Methods For Multivariate And Correlated Data, Xinling Xu Jan 2017

Statistical Methods For Multivariate And Correlated Data, Xinling Xu

Theses and Dissertations

A commonly encountered data type in real life is count data, especially in selfreported behavioral studies. One issue of the self-reported count data is the inaccuracy. In the first part of the dissertation, we are going to address one specific type of inaccuracy in bivariate count data–heaping. Copula functions are used for the formulation of the bivariate distribution. Using copula functions for solving data inaccuracy problems is still a new area, which we are going to explore in this dissertation.

We also discuss the methods for variable selection when the explanatory variables are highly correlated. In particular, our method is …


Covering Subsets Of The Integers And A Result On Digits Of Fibonacci Numbers, Wilson Andrew Harvey Jan 2017

Covering Subsets Of The Integers And A Result On Digits Of Fibonacci Numbers, Wilson Andrew Harvey

Theses and Dissertations

A covering system of the integers is a finite system of congruences where each integer satisfies at least one of the congruences. Two questions in covering systems have been of particular interest in the mathematical literature. First is the minimum modulus problem, whether the minimum modulus of a covering system of the integers with distinct moduli can be arbitrarily large, and the second is the odd covering problem, whether a covering system of the integers with distinct moduli can be constructed with all moduli odd. We consider these and similar questions for subsets of the integers, such as the set …