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Articles 121 - 150 of 69087

Full-Text Articles in Physical Sciences and Mathematics

Gradients Of Abandonment, William Tatman Jul 2026

Gradients Of Abandonment, William Tatman

Geography ETDs

As urban-rural disparities drive depopulation in rural areas worldwide, local strategies emerge as pathways for resilience. Research on Ojika, a Japanese island that has lost 75% of its population since the 1960s, reveals an Abandonment Gradient: a nuanced pattern of disuse adapted to modern polycrises. Extending the concept of "lying fallow" to homes and infrastructure, this thesis focuses on abandonment practices that reflect complex realities of labor, capital, and climate uncertainty. Rather than viewing depopulating communities as passive victims of out-migration, this paper argues they are critical sites for generating crisis response. Communally crafted attitudes toward unused space and more-than-human …

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The Uncertainty Principles, Lee Michael Felicetti Jul 2026

The Uncertainty Principles, Lee Michael Felicetti

Mathematics & Statistics ETDs

The Heisenberg uncertainty principle is a central aspect of quantum mechanics, but also illustrates an essential quality of the Fourier transform. After Heisenberg, a variety of uncertainty inequalities emerged in the fields of physics and mathematics. In this thesis we will analyze the Heisenberg uncertainty principle in both the setting of quantum mechanics and Fourier analysis. We will then look at how the work of Heisenberg has been expanded upon in both physics and mathematics. Particularity, we will see how uncertainty principles can be applied to signal recovery and explore current research in this field.

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Boundary Integral Method For A Modified Mullins–Sekerka System, Ly Le Jul 2026

Boundary Integral Method For A Modified Mullins–Sekerka System, Ly Le

Mathematics & Statistics ETDs

This thesis develops a boundary integral method for a modified Mullins–Sekerka system arising as the sharp-interface limit of a nonreciprocal Cahn–Hilliard model. Nonreciprocal coupling changes the classical Cahn–Hilliard structure by introducing an additional conserved field, leading to coupled elliptic and parabolic dynamics at the interface. Using matched asymptotic expansions, we formally derive the modified Mullins–Sekerka model and then apply the boundary integral method to rewrite it on the moving interface. The elliptic component is represented using the periodic Green’s function for the Laplace equation, while the parabolic component is represented using the periodic heat kernel. This method reduces the bulk …

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Nerve Constructions And Mapper, Alexander Bram Fritschi Jul 2026

Nerve Constructions And Mapper, Alexander Bram Fritschi

Mathematics & Statistics ETDs

Mapper is a data visualization tool commonly used in topological data analysis to study large, often high-dimensional datasets. Mapper operates through the selection of a lens function, a clustering algorithm, and a cover. The Mapper graph is constructed using the nerve of the cover after the clustering algorithm is performed; it is therefore useful to study nerves to better understand Mapper. In this thesis, we will utilize the properties of nerves to find the minimal point set that produces a given graph. We will then extend this to Mapper to determine what Mapper graphs may be constructed over a given …

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Timelines Over Tokens: Summarization, Prompting, And Explainable Fine-Tuning For User-Level Suicide Risk Detection, Aditya Tekale Jul 2026

Timelines Over Tokens: Summarization, Prompting, And Explainable Fine-Tuning For User-Level Suicide Risk Detection, Aditya Tekale

Master's Theses

This research presents a two-stage pipeline for user-level suicide risk detection from Reddit: first, inference-only prompting with summarization; second, fine-tuned encoder classification with explainability and expert validation. The data are user-level: each of the 500 C-SSRS Reddit items is one user’s chronologically concatenated posts and comments (a user timeline), annotated by psychiatrists. Stage one: six prompting strategies zero-shot, few-shot, chain-of-thought, tree-of-thought, least-to-most, and self-consistency are evaluated across six LLMs on multi-class and binary formulations; simple zero-shot achieves the highest balanced accuracy (0.53 multi-class). Error analysis shows longer inputs associate with misclassification (p = 0.002); domain-specific summarization (timelines >2,000 tokens) reduces …

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Elucidation Of Spin-Hamiltonian Parameters Via Spectroscopy, Magnetization, And Computation, Joshua C. Mengell Jul 2026

Elucidation Of Spin-Hamiltonian Parameters Via Spectroscopy, Magnetization, And Computation, Joshua C. Mengell

Chemistry and Chemical Biology ETDs

Molecular Quantum Information Science (QIS) is fundamentally concerned with using spin-systems as quantum bits (qubits) or as sensors. Prerequisite to using molecular systems for QIS applications, it must be understood how one can design molecules with bespoke magnetic characteristics. Herein we study various paramagnetic molecular compounds, describing their complex magnetic characteristics using a spin-Hamiltonian formalism. We utilize various (sometimes novel) methods for determining these spin-Hamiltonian parameters. Many of these molecules possess magnetic characteristics, which make them attractive as qubits or for sensing applications. These characteristics include higher total spin-states (qudits—ST>1/2), forbidden interstate electronic transitions, systems of spatially distant …

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Exploring The Nature And Role Of Local Cation Ordering In Disordered Rock Salt Cathodes For Li- And Na-Ion Batteries, You Wang Jul 2026

Exploring The Nature And Role Of Local Cation Ordering In Disordered Rock Salt Cathodes For Li- And Na-Ion Batteries, You Wang

Chemistry and Chemical Biology ETDs

Cation-disordered rock-salt (DRX) cathodes provide a highly tunable platform for next-generation Li- and Na-ion batteries, but their electrochemical behavior is strongly influenced by local structural features hidden in average crystal structures. This dissertation systematically investigates local cation ordering in Li- and Na-based DRX cathodes to understand its effects on Li+/Na+ transport, redox activity, structural evolution, and electrochemical performance. In Li-based systems, Raman spectroscopy and electrochemical analysis reveal that local layered cation ordering in Mn- and Fe-based DRX cathodes is closely correlated with electrochemical behavior. Over-stoichiometric Li-based DRX oxyfluorides further demonstrate that excess Li can regulate local cation ordering, improve Li+ …

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Mapping And Modeling Threat-Evoked Brain States After Early Life Adversity, Taylor W. Uselman Jul 2026

Mapping And Modeling Threat-Evoked Brain States After Early Life Adversity, Taylor W. Uselman

Biomedical Sciences ETDs

Early life adversity (ELA) increases lifelong neuropsychiatric vulnerability. Yet how ELA reorganizes brain-wide activity and circuit coordination across later experience remains unclear. This dissertation tests the hypothesis that ELA alters adult brain-wide activity and responses to threat through disrupted coordination among neural systems that regulate emotional experience, including prefrontal-limbic and monoaminergic systems. Longitudinal manganese-enhanced MRI of adult mice exposed to standard or fragmented early care, combined with computational processing and statistical modeling, quantified brain states before, during, and long after innate predator threat. These studies established that acute threat evokes large-scale, distributed brain activity that evolves over time. ELA potentiates …

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Multiscale Network Modeling Of Native And Modified Photosynthetic Light-Harvesting Complexes, Zane E. Armijo Jul 2026

Multiscale Network Modeling Of Native And Modified Photosynthetic Light-Harvesting Complexes, Zane E. Armijo

Chemical and Biological Engineering ETDs

Photosynthetic light-harvesting complexes harvest solar energy and direct electronic excitations toward reaction centers with exceptional efficiency. This dissertation models the Fenna--Matthews--Olson complex of green sulfur bacteria, coupled to the PscA1 reaction center, as a chromophoric network. Forster resonance energy transfer theory, validated against numerically exact hierarchical equations of motion, was implemented in kinetic Monte Carlo simulations to resolve fine-grained excitation-transport pathways. The predicted charge-transfer efficiency of 77\% agrees with experiment, with the FMO2 monomer and its gateway pigment governing interfacial transfer. Systematic single, multi, and symmetry-preserving site removals, interpreted through Mobius inversion, identify critical pigments and show that cooperative effects …

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Wildfire Impacts On Fluvial Hydrology From Watershed To National Scales, Paige G. Tunby Jul 2026

Wildfire Impacts On Fluvial Hydrology From Watershed To National Scales, Paige G. Tunby

Civil Engineering ETDs

Wildfires alter the water quantity and quality in downstream river networks. Fires promote biodiversity, maintain habitat, and provide many ecosystem services in a fire-adapted landscape. However, changes in the natural fire regimes can alter ecosystem function and threaten the water security of impacted downstream communities. The magnitude, timing, and persistence of these impacts are difficult to predict due to the lack of high-resolution datasets with adequate coverage to evaluate spatiotemporal trends after a fire. This dissertation moves us beyond the status quo to evaluate post-fire fluvial responses across scales, from the event-scale impacts after the Hermit’s Peak-Calf Canyon wildfire in …

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Surveyception: An Exploration Of Deceptive Survey Forms, Muhammad Danish Jul 2026

Surveyception: An Exploration Of Deceptive Survey Forms, Muhammad Danish

Computer Science ETDs

Survey platforms such as Google Forms and Microsoft Forms are widely used for feedback, data collection, and engagement, but scammers increasingly exploit them to distribute phishing and deceptive attacks. This thesis presents a large-scale study of survey-form abuse across ten major providers. We collected 140,000 forms from three sources: public posts on X, search-engine results, and web pages from the top 10 million DomCop-ranked domains. Using automated filtering and manual qualitative review, we identified 2,645 forms requesting sensitive information and classified 566 as scams. These forms used techniques including phishing, private-secret theft, account and personal-data harvesting, financial deception, and psychological …

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New Distance Distributions Of Asymptotic Giant Branch Stars And Their Role In Tracing Galactic Structure, Rajorshi Bhattacharya Jul 2026

New Distance Distributions Of Asymptotic Giant Branch Stars And Their Role In Tracing Galactic Structure, Rajorshi Bhattacharya

Physics & Astronomy ETDs

Asymptotic giant branch (AGB) stars are among the final evolutionary stages of low- and intermediate-mass stars and among the most luminous cool stellar populations in the Milky Way (MW). Their strong infrared emission allows them to be observed through regions of high interstellar extinction, making them useful tracers of the inner MW. However, their use is limited by unreliable distances because many are dust-obscured and variable, while geometric parallaxes are often unavailable or uncertain. This thesis develops statistical distance-estimation methods for large samples of oxygen-rich AGB stars. The resulting distances broadly agree with literature estimates, supporting their statistical reliability for …

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Extending The Discovery Space Of Tess: Probing Underexplored Exoplanet Populations, Mallory L. Harris Jul 2026

Extending The Discovery Space Of Tess: Probing Underexplored Exoplanet Populations, Mallory L. Harris

Physics & Astronomy ETDs

This dissertation investigates how cold exoplanets can be identified despite the strong observational bias of exoplanet surveys toward short-period systems. Planets at wider orbital separations remain comparatively poorly constrained, limiting tests of planetary-system formation and the prevalence of outer architectures beyond compact systems. To address this gap, I use two complementary approaches. First, I develop a transit-search pipeline for TESS Full-Frame Images that identifies both isolated and repeated transit-like signals around nearby M dwarfs and characterizes the dominant false-positive classes that limit sensitivity in this regime. I then present TOI-904 c, the coldest planet discovered by TESS around an M …

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An Investigation Of Tess M&Ms And The Occurrence Rate Of Transiting Circumbinary Planets, Dominic Oddo Jul 2026

An Investigation Of Tess M&Ms And The Occurrence Rate Of Transiting Circumbinary Planets, Dominic Oddo

Physics & Astronomy ETDs

Circumbinary planets (CBPs) are worlds which orbit two stars simultaneously. CBPs are excellent tests of the tenacity of planet formation, but are difficult to detect. The space-based NASA Transiting Exoplanet Survey Satellite (TESS) mission is a nearly all-sky survey designed to detect exoplanets transiting nearby stars. In this dissertation, I analyze the performance of TESS by comparing to the photometric precision of the ESA CHEOPS mission. Then, I define a catalog of low-mass eclipsing binaries (M&Ms), which are the best sources to search for CBPs. I describe my custom transit search methodology and apply it to the M&M catalog. I …

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Simulating Quantum Field Theories On Fault-Tolerant Quantum Computers, Mason L. Rhodes Jul 2026

Simulating Quantum Field Theories On Fault-Tolerant Quantum Computers, Mason L. Rhodes

Physics & Astronomy ETDs

Quantum field theories are an essential framework in modeling fundamental interactions in nature, yet reliable simulations consume large portions of the world's most powerful supercomputers. In this Dissertation, we explore an alternative simulation paradigm on fault-tolerant quantum hardware, discussing both algorithmic and model advancements. In the former, we construct state-of-the-art algorithmic subroutines that take advantage of useful properties of the Hamiltonian describing the theory to achieve an exponential improvement in resources over prior quantum algorithms. In the latter, we simplify the structure of the Hamiltonian, making it more amenable to quantum simulation. First, we present an improved regularization of the …

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Strategies For Large Dynamic Range, Entanglement-Enhanced Quantum Metrology With Experimentally Demonstrated Resources, Tyler G. Thurtell Jul 2026

Strategies For Large Dynamic Range, Entanglement-Enhanced Quantum Metrology With Experimentally Demonstrated Resources, Tyler G. Thurtell

Physics & Astronomy ETDs

Quantum metrology studies the use of quantum mechanical systems as measurement devices or sensors. Surprisingly, preparing a sensor in an entangled state can enhance measurement precision. The simplest protocols for entanglement enhancement sense only small changes in a quantity. The range of values over which a measurement protocol works is called its dynamic range. For many types of sensors we require end-to-end protocols that describe how to use entanglement to achieve enhanced precision over a large dynamic range. In this dissertation, we describe two approaches to achieving entanglement-enhanced sensing over a large dynamic range. The first approach uses entangling resources …

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Quantum Control Of Qubits And Qudits In Neutral Atom Systems, Sri Datta Vikas Buchemmavari Jul 2026

Quantum Control Of Qubits And Qudits In Neutral Atom Systems, Sri Datta Vikas Buchemmavari

Physics & Astronomy ETDs

This dissertation explores control of neutral atom quantum systems across multiple levels of abstraction, from atomic physics to system-level fault tolerance, using optimal control to improve performance. First, we propose a Rydberg entangling gate based on dressing with only the qubit control field; an interaction energy near the Rabi frequency benefits both gate speed and Rydberg decay. Second, with Sandia National Laboratories, we show that leakage errors in neutral atom systems can be converted to atom loss errors and detected using two entangling gates with an auxiliary atom, where a SWAP-based leakage detection unit outperforms the standard design. Next, we …

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Understanding The Long-Run Effect Of Historical Redlining Practices, Yujian Lu Jul 2026

Understanding The Long-Run Effect Of Historical Redlining Practices, Yujian Lu

Geography ETDs

Historical redlining practices initiated by Home Owners’ Loan Corporation (HOLC) in the 1930s have produced enduring persistent socioeconomic and environmental disparities in U.S. cities. This dissertation examines their long-term impacts on social vulnerability, urban flood risk, along with public discourse about redlining practices. Results indicate that neighborhoods with HOLC grade A (greenlined) exhibit the lowest overall social vulnerability, while those graded D (redlined) face the highest across U.S. cities. In Chicago, associations between redlining practices and flood risk disparities are stronger than in Los Angeles, reflecting place-specific characteristics among environmental, socioeconomic, and demographic factors shaping flood risk disparities in long …

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How Forest Structure And Climate Influence Snowpack For Water Resources In The Southwestern United States, Lindsey L. Rotche Jul 2026

How Forest Structure And Climate Influence Snowpack For Water Resources In The Southwestern United States, Lindsey L. Rotche

Geography ETDs

Climate change, declining snowpack, and increasing wildfire risk have profound impacts on water availability in the southwestern United States. Because the southwestern United States is a global hotspot for freshwater vulnerability, and snowpack provides much of the region’s freshwater, understanding how climate and forest structure influence snowpack dynamics is increasingly important. In this dissertation I aim to better understand and communicate these dynamics through empirical data collection and the development of a simple vegetation driven temperature-index snow model: SNOW-17(VEG). I then implement the model at a watershed scale using remotely sensed imagery to create vegetation zones and climate simulations to …

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Reading The Martian Surface: Impact Crater Distributions And Geochemical Signatures In Gale Crater As Recorded By The Curiosity Rover, Megan E. Hoffman Jul 2026

Reading The Martian Surface: Impact Crater Distributions And Geochemical Signatures In Gale Crater As Recorded By The Curiosity Rover, Megan E. Hoffman

Earth and Planetary Sciences ETDs

The Curiosity rover has been exploring Gale crater, a large impact basin near the Mars equator since 2012. This mission has greatly improved our ability to explore the surface of Mars with a suite of geologic tools and cameras and has revealed that Mars likely once resembled present-day Earth. In this dissertation, I utilize measurements and data taken by Curiosity to analyze the distribution and preservation of small impact craters at meter scales, I quantify the formation characteristics of a small impact crater cluster, and I examine the presence of barium in a geologic unit with high-Si to constrain sediment …

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Pebble Accretion: Compositions And Water Origins Of Terrestrial Planets, Susmita Garai Jul 2026

Pebble Accretion: Compositions And Water Origins Of Terrestrial Planets, Susmita Garai

Earth and Planetary Sciences ETDs

Two leading models of planet formation invoke either stochastic collisions among km-sized planetesimals, or pebble accretion of sub-mm-cm solids regulated by gas drag. While collision based models typically require tens to hundreds of millions of years to assemble terrestrial planets, pebble accretion can produce Mars to Jupiter-mass bodies within the lifetime of the protoplanetary disk. Although widely accepted for the rapid growth of giant planet cores, the role of pebble accretion in forming terrestrial planets, including Earth, remains debated. Here, we investigate the consequences of pebble accretion for Earth’s origin. Here, I combine numerical models and laboratory experiments to find …

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Algorithmic Sculpting Of Complex Fused Silica Surfaces For Nondestructive, Mode-Matched Cavity Quantum Electrodynamics: Adaptive Co2 Milling And Simulation-Guided Ultrafast Inscription, From Fiber Fabry-Perot Cavities To Monolithic Architectures, Meagan E. Parker Jul 2026

Algorithmic Sculpting Of Complex Fused Silica Surfaces For Nondestructive, Mode-Matched Cavity Quantum Electrodynamics: Adaptive Co2 Milling And Simulation-Guided Ultrafast Inscription, From Fiber Fabry-Perot Cavities To Monolithic Architectures, Meagan E. Parker

Optical Science and Engineering ETDs

Quantum sensors achieve exceptional measurement sensitivity through coherent, well-isolated quantum systems, but practical deployment is hindered by destructive readouts that require repeated state preparation and create long system dead times. Optical cavities enable continuous, nondestructive measurements with minimal back-action, yet integrating high-finesse cavities into scalable quantum devices remains limited by existing fabrication methods. To overcome these constraints, an adaptive CO₂ laser-milling platform was developed. Guided by glass thermodynamics and melt dynamics, this closed-loop system uses in-situ phase-shifting interferometry to sculpt complex fused-silica surfaces with sub-nanometer root-mean-square roughness. The platform was validated by fabricating extended-length fiber Fabry–Pérot cavities and monolithic micro-cavity …

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Non-Traditional Rare-Earth-Doped Oxide Glass As A Gain Medium, Jared S. Tolliver Jul 2026

Non-Traditional Rare-Earth-Doped Oxide Glass As A Gain Medium, Jared S. Tolliver

Optical Science and Engineering ETDs

There is a need for mid-infrared(MIR) lasers in defense, medical, and environmental monitoring. A large part of this technological development is the study of gain media. One class of materials of special interest is glasses with a low maximum phonon energy. These have the fiberization and broad spectral features of glass, whereas glasses with high maximum phonon energy exhibit higher rates of multi-phonon relaxation and can be opaque in the MIR, both of which are detrimental to laser operation. Recent advances in container-less processing have allowed for the study of new glasses that aren’t possible with conventional fabrication techniques. One …

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Interpretable Case-Control Inference Through Log-Linear General Location Models, Zacharia Stuart Jul 2026

Interpretable Case-Control Inference Through Log-Linear General Location Models, Zacharia Stuart

Mathematics & Statistics ETDs

This dissertation analyzes one of the few publicly available NFL injury datasets to study field type and non-contact lower-limb injuries. Field type is studied jointly with other risk factors to understand how these factors interact to affect injury risk. The data were gathered through a case-control sampling scheme, which limits direct inference on absolute injury probabilities. While not the most common approach for case-control data, this dissertation models the retrospective distribution directly through Log-Linear General Location Models (Log-Linear GLOMs). Through a log-linear structure placed on a log-odds-ratio reparameterization, the model provides directly interpretable marginal and interaction contributions to injury log-odds …

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Measurements And Studies For Rare Event Searches Using Directional Detectors, Elizabeth Tilly Jul 2026

Measurements And Studies For Rare Event Searches Using Directional Detectors, Elizabeth Tilly

Physics & Astronomy ETDs

Measuring topology and initial direction of low-energy (keV-MeV) particle tracks is interesting to rare-event searches. While directional dark matter searches have been one of the largest drivers for R&D for low-energy directional detectors, this work is interested in its application to Migdal searches. The Migdal effect—a nuclear recoil and an electron recoil sharing a vertex—has been used as a detection channel for low-mass dark matter but has only recently been measured. Low-energy directional detectors are ideal to measure the canonic Migdal topology. This dissertation discusses 3D reconstruction algorithms developed for the Migdal In Galactic Dark mAtter expLoration (MIGDAL) experiment and …

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Exploring The Role Of A Mushy, Crustal Compliant Region In Volcano Deformation, Grant A. Block Jul 2026

Exploring The Role Of A Mushy, Crustal Compliant Region In Volcano Deformation, Grant A. Block

Physics & Astronomy ETDs

Volcanoes are both creative and destructive forces that have shaped and continue to shape our world from early geologic time to the present day. Continued study of volcanic processes not only better prepares us for monitoring volcanic hazards but also allows us to better understand processes fundamental to Earth as we know it, such as the generation of the atmosphere and accretion of the continents. This dissertation focuses on an integral part of volcanic processes: the trans-crustal magmatic transport system. Specifically, we investigate regions of these transport systems where magma pools in melt-rich lenses within broader regions of low melt-fraction, …

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Spatial Heterogeneity And Temporal Trends Of California Extreme Heat Using High-Resolution Earth System Model Simulations, Eleni Konstantelos Jul 2026

Spatial Heterogeneity And Temporal Trends Of California Extreme Heat Using High-Resolution Earth System Model Simulations, Eleni Konstantelos

Master's Theses

Extreme heat threatens California’s diverse landscapes and populations through intensifying and geographically shifting patterns. This study examined the temporal trend and spatial heterogeneities of California’s extreme heat for 1994–2015. The analysis was based on the fully coupled Energy Exascale Earth System Model version 2 (E3SMv2), specifically its 25-km regionally refined configuration. While the Desert/Inland region exhibited the highest number of days ≥ 35 °C and the highest heatwave severity, Central Valley showed the fastest increase in the number of days ≥ 35 °C and heatwave events, as well as the fastest increases of days exceeding various heat index thresholds over …

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Error-Tolerant Metric Dimension, Leander Ten Hoff Jul 2026

Error-Tolerant Metric Dimension, Leander Ten Hoff

Master's Theses

Metric dimension is a graph parameter that measures the smallest distance-based unique coordinate system on a graph. Fault-tolerant metric dimension is a variant that requires redundancy. Inspired by this idea, we propose and investigate a new variant we call error-tolerant metric dimension. We first prove some fundamental results to gain familiarity with this more complex variant. Then, we use these tools to study relative behaviors of error-tolerant metric dimension. We prove explicit computations for simple graph families, including bipartite complete graphs and paths. Finally, we extend extremal results from previous papers on metric dimension, including a full correction of an …

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Probabilistic Metric Dimension, Kyle Worley Jul 2026

Probabilistic Metric Dimension, Kyle Worley

Master's Theses

The metric dimension of a graph G is the smallest number of unique vertices (often called “marked vertices” or “landmarks”) such that each vertex has a unique distance to the marked vertices. If a set of vertices S ⊆ V (G) when marked gives all vertices unique distances, it is called a resolving set. Hence if G is a graph with a resolving set S, then for all v, u ∈ V (G) there exists s ∈ S such that d(v, s) ̸= d(u, s). The metric dimension dim(G) = min(|S|). Two widely studied variants exist, one where edges are …

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The Relationship Between Foliations Of The Plane, Kaplan Diagrams, And Non-Hausdorff 1-Manifolds, Monique Justine Howe Jul 2026

The Relationship Between Foliations Of The Plane, Kaplan Diagrams, And Non-Hausdorff 1-Manifolds, Monique Justine Howe

Master's Theses

In this paper we seek to explain the relationship between foliations of the plane, Kaplan diagrams, and simply connected non-Hausdorff 1-manifolds with countable basis that are orientable with an ordering on branch points. We will walk the reader through the definitions of all of these objects, and provide examples with a focus on the motivating example of the Reeb foliation. This paper will describe and define the known bijection from the set of foliations of the plane, F, to the set of Kaplan diagrams, K, its inverse, and the one-to-one map from F to the set of simply connected non-Hausdorff …

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