Physical Sciences and Mathematics Commons^™

Circle Actions On Oriented 4-Manifolds, Donghoon Jang, Oleg R. Musin

School of Mathematical & Statistical Sciences Faculty Publications

In this present paper, we consider an action of the circle group on a compact oriented 4-manifold. We derive the Atiyah–Hirzebruch formula for the manifold, and associate a graph in terms of data on the fixed point set. We show in the case of isolated fixed points that if an abstract graph satisfies the Atiyah–Hirzebruch formula, then there exists a corresponding 4-dimensional oriented S1-manifold.

Hyena: An Observing System Simulation Experiment For Hypothetical Energetic Neutral Atom Imagers, Joel Tibbetts, Amy Keesee, Matina Gkioulidou, Robert Demajistre, Viacheslav Merkin

Faculty Publications

Mesoscale plasma sheet flows are widely understood to be a critical component of the overall picture of energy, particle, and magnetic flux transport during periods of geomagnetic activity. Without simultaneous measurements with true global coverage, the short lifetime (~10 min) and localized spatial extents (~1–3 R_E in azimuth) of these structures make obtaining a global picture of their contributions to stormtime magnetosphere dynamics difficult to characterize. Energetic neutral atom (ENA) imaging can enable remote mapping of plasma energization in the magnetosphere; however, its line-of-sight integrated nature, coupled with the challenging-to-characterize attributes of the target physical phenomena, means that numerous …

Workshop Outcomes Report: 2nd International Workshop On Seismic Resilience Of Arctic Infrastructure And Social Systems, Majid Ghayoomi, Daniela Morganti

Faculty Publications

The report provides an overview of the second international workshop on Seismic Resilience of Arctic Infrastructure and Social Systems. The report discusses agenda, workshop activities, interdisciplinary working groups, and results. It ends with several strategic questions and investigation plans that were developed as part of the workshop activities.

Factors Influencing Eastern Wild Turkey (Meleagris Gallopavo Silvestris) Productivity And Nesting Chronology In West Virginia, Kirstin Palumbo

Graduate Theses, Dissertations, and Problem Reports (ETD)

Identifying drivers of variation in the timing of breeding behaviors, such as courtship activities and nesting chronology, is important for the effective management of avian species. Likewise, productivity is an important component of game bird population dynamics and can be broken up into multiple components such as the probability of nesting, clutch size, and nest success. One species that experiences a relatively long reproductive season is the Eastern wild turkey (Meleagris gallopavo silvestris). Contemporary research in the southeastern United States has raised concerns regarding declines in both wild turkey populations and overall productivity. West Virginia, however, is unique …

Multi-Timescale Monitoring And Modeling For Resilient Smart Grids: Pmu Anomaly Detection And Battery Digital Twins, Muhammad Imran Hossain

Graduate Theses, Dissertations, and Problem Reports (ETD)

Modern power systems face failures at very different timescales. Cyber-physical disturbances may emerge within seconds, while battery degradation develops over hundreds of operating cycles. Both monitoring problems share the same underlying difficulty: power systems produce measurement data in abundance, but reliably labeled examples of abnormal or degraded operation are scarce. Rare grid events are difficult to label, and battery degradation data are heterogeneous across cells, cycling protocols, and chemistries. This thesis addresses these challenges through two complementary domain-informed learning frameworks that constrain representation learning using information specific to each physical problem.

First, at the system level, T-BiGAN, a Transformer-augmented bidirectional …

Dataless Neural Networks For Boolean Satisfiability And Network Optimization, Andrew Evan Gautier

Graduate Theses, Dissertations, and Problem Reports (ETD)

Combinatorial optimization problems (COPs) require searching over a finite solution space subject to constraints, with the goal of satisfying an objective function. They arise in operations research, scheduling, resource allocation, circuit design, and many other fields. Many problems in combinatorial optimization (including satisfiability and network design) are NP-hard. Traditionally, researchers have built approximate solvers that return near- optimal solutions efficiently by developing increasingly sophisticated heuristics and meta- heuristics. Deep learning has provided new opportunities for improving combinatorial solvers by leveraging neural guidance to prune the search space. Traditional neural networks have distinct drawbacks in this context: separate training and …

Comparing Unet And Hrnet For Geomorphic Feature Extraction From Digital Terrain Model-Derived Land Surface Parameters, Behnam Solouki

Graduate Theses, Dissertations, and Problem Reports (ETD)

Automated extraction of geomorphic features from high spatial resolution terrain data is important for environmental monitoring, geohazard assessment, and landscape change analysis. This study compares two convolutional neural network architectures, UNet and High-Resolution Network (HRNet), for semantic segmentation of mine benches and sinkholes from lidar-derived digital terrain models and land surface parameters. Mine benches represent anthropogenic, elongated, stepped landforms associated with historic surface mining, whereas sinkholes are natural, compact depressions common in karst terrain. Three terrain-derived input layers were used: square-root-transformed slope, broad-scale topographic position index, and fine-scale annulus topographic position index. Models were trained using five training sample sizes, …

Multimodal Representation Learning For Face Understanding: From Caption Supervision To Foundation Model Adaptation, Md Mahedi Hasan

Graduate Theses, Dissertations, and Problem Reports (ETD)

The rapid advancement of intelligent surveillance systems and the increasing demand for reliable biometric identification in border security, public safety, and digital forensics require robust face understanding under unconstrained conditions, including low resolution, pose variation, and occlusion. While Vision Transformer (ViT)-based foundation models have greatly improved visual representation learning, their patch-based tokenization and lack of spatial inductive bias limit their ability to capture fine-grained details in low-resolution inputs. This dissertation investigates multimodal representation learning for face understanding through natural language supervision, large-scale face-caption pre-training, and parameter-efficient foundation model adaptation. It hypothesizes that textual supervision provides complementary semantic cues that improve …

Does Diverse Seeding Adoption Reduce Production Costs? The Case Of Diverse Forage Seeding Strategies In West Virginia., Ivan Andres Wong

Graduate Theses, Dissertations, and Problem Reports (ETD)

Feed and harvested forage represent a major share of production costs in Appalachian cow-calf systems, where a pronounced summer forage gap forces producers to rely on purchased hay. This thesis evaluates whether adopting diverse forage seeding strategies reduces production costs relative to the existing pasture management practice, accounting for the spatial heterogeneity of West Virginia’s production environments. The analysis proceeds in two steps. First, an unsupervised K-means clustering of 14 farms enrolled in the NRCS Conservation Innovation Grant field trial groups the farms into two agroclimatic clusters, Highland-Cool and LowlandWarm, using elevation, growing-season Growing Degree Days, growing-season precipitation, and soil …

Dielectrophoretic Biomarkers For Cancer Detection And Cell Analysis: Integrating Microfluidics And Ai, Raphael Olumide Oladokun

Graduate Theses, Dissertations, and Problem Reports (ETD)

Pancreatic ductal adenocarcinoma (PDAC) carries a five-year survival rate of 13%, driven largely by late-stage diagnosis and the absence of sensitive noninvasive screening tools. Current diagnostic methods lack the sensitivity to detect disease-associated systemic changes at early and precancerous stages, representing a critical clinical gap. This dissertation addresses the central hypothesis that PDAC and its pathological subtypes induce measurable, disease-associated electrophysiological changes in circulating PBMCs that can serve as correlative liquid-biopsy biomarkers. To test this hypothesis, this work asks: can dielectrophoresis (DEP), impedance and zeta potential analysis with AI-assisted classification distinguish benign pancreatic conditions (non-malignant control), precancerous lesions (primarily IPMNs), …

Energy Partition And Heating Mechanisms In Asymmetric Antiparallel Magnetic Reconnection, Aleksandra Abova-Volkova

Graduate Theses, Dissertations, and Problem Reports (ETD)

Magnetic reconnection is a fundamental plasma physics process whereby a change in magnetic field connectivity drives the conversion of magnetic energy into energy of the surrounding plasma, often explosively. One of the many settings where it occurs is at the dayside magnetopause of Earth and other planets, where the magnetic field, number density, and/or temperature in the plasmas on the two sides upstream of the reconnection site are asymmetric. How the incoming magnetic energy gets partitioned into outgoing energies during asymmetric reconnection remains an outstanding question; of special interest is the fraction that gets converted into internal energy of ions …

Timing, Spectral, And Single-Pulse Properties Of Radio Pulsars, Evan Francis Lewis

Graduate Theses, Dissertations, and Problem Reports (ETD)

Radio pulsars are highly magnetized, rapidly rotating neutron stars which emit beams of radio waves from their magnetic poles. Their incredible rotational stability allows for their use in a variety of high-energy astrophysical studies, though the details of their internal structure and emission mechanisms are still unknown. We use observations of a cross-section of the pulsar population in order to investigate the nature of their evolution, their emission properties, and their environments.

First we derive timing solutions for three pulsars discovered through their sporadic single pulses. It was possible to obtain timing solutions through a set of single-pulse times of …

Sedimentological And Geochemical Investigation Of The Origin Of Upper Pennsylvanian Black Shales, East-Central Appalachian Basin, Tyler Hickey

Graduate Theses, Dissertations, and Problem Reports (ETD)

In the east-central Allegheny foreland basin, laminated black shales overlying Upper Pennsylvanian Glenshaw Fm. coal seams record paleoenvironmental conditions associated with the termination of peat swamp deposition before, during, and after the Carboniferous Coal Forest Collapse (CCFC), a major paleobotanical evolutionary event during the Late Paleozoic Ice Age (LPIA) that contributed to extinction of lepidodendrons near the Desmoinesian-Missourian boundary (~306 Ma). Previous investigations of the CCFC commonly implicate an episode of aridification during intensification of LPIA glaciation that stressed the lepidodendrons beyond their ecological tipping point; however, the cause of this aridification is unclear. An investigation of Glenshaw Fm. black …

Deposition And Diagenesis Of Permo-Triassic Gypsum From Wyoming And Texas: Saline Lake And Groundwater Systems Of Equatorial Pangea, Maya Yamei Bradford

Graduate Theses, Dissertations, and Problem Reports (ETD)

Knowledge of gypsum textures and the processes that yield them is important for interpreting the history of environments, climates, and life on Earth. This is because gypsum textures are products of specific environmental, microbiological, and diagenetic processes, and because gypsum is relatively common in the Earth’s sedimentary record. Despite this significance, gypsum is relatively understudied. The fundamental goal of this dissertation is to advance our understanding of gypsum textures by presenting detailed, petrography-based investigations of Permo-Triassic gypsum from the continental interior of Pangea.

Gypsum is typical in the Permo-Triassic sedimentary record of tropical Pangea, where it is associated with red …

Adventures In Black Hole Binary Waveform Modeling, Siddharth Mahesh

Graduate Theses, Dissertations, and Problem Reports (ETD)

The modeling of black hole binaries requires accurate descriptions of both their relativistic vacuum dynamics and their interaction with surrounding astrophysical environments. Although these problems are often treated separately, this dissertation develops a unified view: key observables of black hole binary systems can be understood by identifying the dynamical instabilities that control their evolution. In the vacuum problem, the relevant unstable structure is associated with the remnant spacetime and its role in shaping the merger-ringdown gravitational waveform. In the environmental problem, the relevant instability is the epicyclic instability of orbits in the binary potential, which controls the location and evolution …

High-Resolution Laser Diagnostics For Ion Measurements In Magnetized Plasmas, Katey Stevenson

Graduate Theses, Dissertations, and Problem Reports (ETD)

In this work, we investigate ion heating in two plasma systems (helicon plasmas and flux rope plasmas) using the PHAse Space MApping (PHASMA) experiment. Our studies rely on high-resolution laser diagnostics, specifically laser-induced fluorescence (LIF), to measure ion velocity distribution functions (IVDFs). The temperature and bulk flow of each species are inferred from their respective VDFs. This dissertation is organized into three main parts: the study of ion heating in helicon plasmas, pulsed LIF modeling and diagnostic development, and the study of ion heating in flux rope plasmas. Helicon plasma sources efficiently generate high-density plasmas and are widely used to …

Studies On The Depth Formula And On Reducing Dimensions, Brian Mccourt Laverty

Graduate Theses, Dissertations, and Problem Reports (ETD)

This dissertation presents the author’s recent research, conducted under the supervision of Professor Olgur Celikbas, and based on two articles—one published and one in progress. These works develop two closely related research directions in commutative algebra. Together, they contribute to the subject by addressing aspects of existing conjectures, establishing new results, and introducing methods for studying homological invariants.

The first research direction concerns the depth formula, namely the equality \[ \depth_R(M)+\depth_R(N)=\depth(R)+\depth_R(M\otimes_RN) \] where $M$ and $N$ are finitely generated $R$-modules. A classical result of Auslander \cite{Aus} shows that the depth formula holds provided that either $M$ or $N$ has finite …

A Digital Calibration Source For 21 Cm Cosmology Telescopes, Kalyani Balkrishna Bhopi

Graduate Theses, Dissertations, and Problem Reports (ETD)

Precise calibration of radio telescope beams and gains is a central requirement for 21 cm intensity mapping experiments, which aim to measure large scale cosmological structure through the redshifted emission line of neutral hydrogen. Bright astrophysical foregrounds dominate the sky at these frequencies, and separating them from the cosmological signal demands precise control over instrumental systematics, particularly the telescope beam and its frequency-dependent response. Existing aerial calibration sources are incoherent broadband emitters, detectable only as total power. They provide no direct phase information and suffer from poor sensitivity in low signal-to-noise regimes.

We present the Precision Emitter for 21cm Array …

Evaluation Of Potential Factors Limiting The Expansion Of Invasive Carp (Hypophthalmichthys Spp.) In The Ohio River Basin, Erin Shepta

Graduate Theses, Dissertations, and Problem Reports (ETD)

The introduction of aquatic invasive species is one of the greatest threats to freshwater biodiversity around the world. Two species of invasive carp, bighead carp (Hypophthalmichthys nobilis) and silver carp (H. molitrix) have spread throughout much of the Mississippi River Basin, resulting in serious ecological impacts to native communities. Their spread in the Ohio River, a major tributary of the Mississippi River, appears to have slowed, with limited evidence of upstream advancements. Here, we investigated abiotic and biotic factors that may be contributing to the reduced spread of invasive carp in the Ohio River Basin. Generally, …

A New Parsimony-Based Method For Reconstructing Sequences Of Developmental Events And Estimating Rates Of Intraspecific Variation, With Applications To Trilobites, Alexander Benjamin Bradley

Graduate Theses, Dissertations, and Problem Reports (ETD)

Ontogenetic Sequence Analysis (OSA) is a method for reconstructing multiple sequences of abrupt phenotypic transformations (developmental events) for sampled populations of any kind of organism. It makes use of cladistic parsimony software to produce a network, or graph, whose vertices represent unique phenotypes at different stages of maturity (“semaphoronts”) and whose edges describe the developmental events occurring between semaphoronts. It is a powerful tool for constraining the range of developmental variation possible for a given species and generating sample statistics capable of identifying both the most common and the outlier ontogenetic sequences. However, OSA has seen little use since its …

Development Of Novel Methods For Investigative Leads In Firearm And Explosive Related Incidents, Addio Joseph Fiordigigli Jr.

Graduate Theses, Dissertations, and Problem Reports (ETD)

Criminal outbreaks and gun violence persist as a multifaceted global crisis, marked by escalating rates of homicide, suicide, and terrorism that destabilize communities and strain public resources. The proliferation of illicit firearms and homemade explosive devices, along with the complexity of modern criminal networks, necessitates innovative scientific tools to strengthen preventive intelligence operations and ensure that the legal process is grounded in physical evidence. More efficient detection of traces left behind at a crime scene can help prevent further harm or injury from follow-up attacks. This study aims to develop and evaluate new triage methods for characterizing gunshot residues (GSR) …

Optimization Of The Cmc Algorithm, Christopher Joseph Moner

Graduate Theses, Dissertations, and Problem Reports (ETD)

Cartridge cases recovered from discharged firearms contain tool marks produced by the internal mechanisms of said firearm. Firearm and tool mark examiners com pare these marks to determine whether two cartridge cases originated from the same firearm. Traditional comparison methods have been criticized for their subjective nature and reliance on examiner interpretation rather than objective decision thresholds. The Congruent Matching Cells (CMC) algorithm was developed as a quantitative, objective method for tool mark comparison. CMC is a surface topography correlation algorithm that partitions a tool mark into small regions, or cells, and evaluates their similarity using the areal cross-correlation function …

New Fossil Mygalomorph Spiders (?Idiopidae, Pycnothelidae) From The Lower Cretaceous Crato Formation Of Brazil, Elis Maria Gomes Santana

Graduate Theses, Dissertations, and Problem Reports (ETD)

The infraorder Mygalomorphae represents one of the earliest-diverging lineages of spiders, but its fossil record remains sparse relative to the modern diversity of the group. This is a reflection of both ecological and preservational biases, such as the predominantly fossorial habits of many mygalomorphs and the strong bias of the spider fossil record toward amber deposits. Compression fossils from rock deposits are therefore especially important for documenting the evolutionary history of the group. Here, two new mygalomorph fossils from the Lower Cretaceous Crato Formation, Araripe Basin (Brazil) are described. The first specimen is tentatively referred to ?Idiopidae based on male …

Geospatial Analysis Of Sinkhole Density And Characteristics In West Virginia, Marissa Shannon Loftus

Graduate Theses, Dissertations, and Problem Reports (ETD)

Creation of a sinkhole map of West Virginia provides useful data to help identify areas susceptible to sinkhole related hazards, as well as allowing for detailed analysis of factors controlling karst development. Newly available, statewide LiDAR-derived digital elevation data have made mapping sinkholes over larger spatial extents feasible. For this study, sinkholes were mapped for all areas of West Virginia that are underlain by carbonate rocks; then the distribution and characteristics were evaluated overall and in four focus areas (Berkeley and Jefferson counties, Pendleton County, Greenbrier County, and Monroe County). These areas correspond to broader physiographic regions, with Berkeley, Jefferson, …

Eigenvalue Spacing Distributions And The Weak Disorder Limit For Random Schrodinger Operators, Kyle E. Hammer

Theses and Dissertations--Mathematics

We study a collection of discrete Schrodinger Operators with random potentials through the lens of global and local eigenvalue spacings. We discuss the three models: the standard scaled disorder Anderson Model, the Anderson-Bernoulli Polymer Model, and the Discrete Fractional Laplacian Anderson Model. First, we discuss the scaled disorder case using the invariant measure and its application to the density of states in the weak disorder limit. We also prove the limit of the local and global eigenvalue spacings in the non random case, and demonstrate numerically how randomness affects the eigenvalue spacings. We then discuss a special family of random …

Spectral Properties And The Behavior Of The Current-Current Correlation Measure For The Luttinger-Sy Model, Jonathan Benoit

Theses and Dissertations--Mathematics

The Luttinger-Sy Model, sometimes referred to as the Pieces Model, is a Random Schrodinger Operator on L²(R) which is characterized in part by "pieces" whose endpoints are chosen by a Poisson Point Process. The Hamiltonian in this setting is then given as a direct sum of Laplacians with Dirchlet boundary conditions on each piece. In this work, we show several spectral properties of the Luttinger-Sy Model, including proving the deterministic spectrum is [0,infinity) and that a Wegner-type and Minami-type estimate both hold. Additionally, we show that the finite-volume Current-Current Correlation Measure is singular continuous with respect …

Student Conceptions Of Summation And Limits In The Definite Integral Following Quantitatively Focused Instruction, Caleb Daniel Holloway

2026 Scholarly Teaching Conference: Concurrent Session Papers

Recent studies have examined how students form productive conceptions of the definite integral and discussed techniques for promoting such conceptions. In this paper I present findings from interviews held with six students enrolled in second-semester calculus, four of whom had received quantitatively focused instruction on the definite integral. All six were chosen for their observed use of summation conceptions on definite integral problems, and here their conceptions are explored further. Additionally, we gain insight on their thinking regarding limits as related to the definite integral. The findings presented here add to our understanding of student thinking regarding the integral and …

Test Retakes In Introductory Math Courses, John Hird, Chris Mcclain

2026 Scholarly Teaching Conference: Poster Session Papers

In this poster, we describe the implementation of an exam retake model using specifications grading for math courses taken by non-STEM majors. This system was implemented by two faculty members over three years in two sequential courses. During that time, we tried several versions of allowed retakes, with varying restrictions on partial credit. Some of the challenges that we faced were scaling the system for use by different faculty members and with different courses, managing faculty workload on writing and grading multiple exams, and managing student expectations.

Techniques For Inclusive College Mathematics Classrooms, Christopher Anderson Davis, Josh Hiller, Anil Venkatesh

Journal of Mathematics and Science: Collaborative Explorations

Creating a welcoming and inclusive mathematics classroom is an important responsibility for all college mathematics faculty. But where do we begin? In this paper we present several techniques based on White’s (2024) building inclusive classrooms strategies framework, which the authors have found to be successful in making their own classrooms more inclusive. The techniques include the inclusion of contemporary diverse voices, exploring the history of applications of mathematical concepts, elevating the diverse intellectual history of mathematics, bringing diverse guest speakers into the classroom, and mentoring students as they engage in doing research. For each strategy we provide narrative comments based …

Connections Between Mathematics And Chemistry: An Interdisciplinary Undergraduate Curricular Initiative, George Ashline, Bret Findley

Journal of Mathematics and Science: Collaborative Explorations

In this article, we describe an undergraduate curricular initiative involving mathematics and chemistry faculty and students. Supported by a grant from the National Science Foundation Scholarships in Science, Technology, Engineering, and Mathematics Program, a program designed to encourage the study of and connections between quantitative fields and life sciences, this interdisciplinary collaboration features undergraduate student research and involves the development of curricular connections between mathematics and chemistry. Through this initiative, we have created activities for calculus courses featuring chemistry applications as well as activities for chemistry courses showcasing mathematical concepts. After the implementation of these curricular enhancements, we gathered student …