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Computational Problems on Depth Measures Combining Combinatorics and Geometry
No full textA fundamental concept in statistics is the measure of the "centrality" of a point relative to a multidimensional point set. This generalizes the one-dimensional concept of the median and has been modeled in statistics through depth functions. Such a function assigns each point in space a numeric value that increases with the point's degree of centrality. This topic has been extensively studied in statistics, and numerous depth functions have been proposed and analyzed.
Broadly speaking, depth functions can be classified into two groups: those that are based on geometric properties, such as distances, and those that are based on combinatorial properties, such as counts. In this dissertation, we introduce two new depth functions that combine both of these elements. We explore these functions from both a mathematical and computational perspective.
The first depth function is called the Shapley-value depth. This is based on a classical concept from game theory, called the Shapley value, which measures the contribution of each player, when working in a cooperative setting. In our case, the points serve as players, and contributions are measured geometrically in terms of volume, area, or mean width.
The second depth function is called the projective halfspace metric depth. This adapts the well-known Tukey depth by including a component based on distances (rather than counts) of points to a hyperplane. This depth function can be interpreted as the minimum total distance that points in a point set need to be moved so that the query point is exposed to the exterior of the convex hull.
We show that both functions possess nice mathematical properties, and we present efficient algorithms and data structures to compute or approximate them. We also study a recently proposed depth function, called the hyperplane distance depth. We develop a space-efficient data structure that can answer approximation queries to this function
Quantum Algorithms for Thermal State Preparation and the Suppression of Gauge Drift
No full textThe study of quantum computers and quantum algorithms has captured the attention of physics globally in recent decades. While some researchers are working towards constructing fault-tolerant large-scale quantum computers, others are theorizing about the capabilities of these new computers and developing quantum algorithms to leverage their increased abilities. This dissertation engages with the second area of research concerning quantum algorithms.
The first part of this dissertation discusses quantum algorithms for state preparation, with a focus on thermal state preparation. A selection of other state preparation methods is briefly summarized before a novel method of thermal state preparation is laid out wherein a so-called heat pump is employed in a technique of active cooling.
The second part of this dissertation discusses quantum algorithms that aim to address the problem of gauge violation during the simulation of lattice gauge theories. The problem of gauge violation in both quantum analog and digital simulations is presented before two related methods are delineated. These methods leverage the quantum Zeno effect with frequent measurements on a system's physical subspace to keep the system's state physical throughout the course of a simulation. Furthermore, the properties of gauge transformations are utilized to help curtail the growth of unwanted unphysical amplitudes
THE IMPACT OF RESISTANCE EXERCISE ON PERIPHERAL VASCULAR AND CEREBROVASCULAR FUNCTION IN RESISTANCE EXERCISE TRAINED AND UNTRAINED MIDDLE-AGED WOMEN
No full textIn middle-age, women experience an increased risk for hypertension and resultant vascular dementia, partially due to concomitant aging and the loss of endogenous estrogen production with menopause. Vascular dysfunction, arterial stiffening, and cerebrovascular dysfunction contribute to heightened hypertension and vascular dementia risk. Aging and menopause concurrently increase the risk for these aberrant physiologies while exercise dampens the risk. More specifically, resistance exercise training (RET) improves vascular health, particularly in aging women, making RET critical in the context of hypertension and vascular dementia. The vascular health benefits of RET stem from adaptations to large oscillations in blood pressure and blood flow experienced during acute resistance exercise (RE). Further, an acute hypertensive challenge, such as acute RE, is a systemic physiological stressor that can be utilized to understand the cardiovascular implications of inactivity or long-term RET engagement. However, there are limited studies investigating vascular health, RET, and acute RE in middle-aged women. In young women, RET preserves carotid artery compliance and central arterial stiffness while also improving peripheral vascular function responses to an acute hypertensive stimulus (acute RE). However, the effect of RET on cerebrovascular function is largely uncharacterized, particularly in women. Taken together, understanding the effect of acute RE and RET on central and carotid artery stiffness, peripheral vascular function, and cerebrovascular function in middle-aged women is critical yet largely understudied. Therefore, the aims of the present dissertation were (1) to investigate the effects of an acute hypertensive stimulus (acute RE) on aortic and carotid artery stiffness, macrovascular and microvascular function, and cerebrovascular function in untrained and long-term resistance-trained middle-aged women, (2) to assess the effect of 8-week RET on resting and post-hypertensive stimulus (acute RE) vascular function in initially untrained middle-aged women, and (3) to compare the efficacy of 8-week RET versus long-term RET in the context of vascular responses to an acute hypertensive stimulus in middle-aged women. The present dissertation included gold-standard measurements (blood pressure, flow-mediated dilation, pulse wave velocity) and critical, understudied measurements (carotid artery wave reflection, middle cerebral artery velocity, and cerebrovascular reactivity). It was hypothesized long-term resistance-trained middle-aged women would exhibit beneficial arterial stiffness and vascular function responses to acute RE, as indicated by preserved aortic and carotid artery stiffness, improved or preserved peripheral vascular function, preserved cerebral blood velocity, and increased cerebrovascular reactivity. It was also hypothesized initially untrained middle-aged women would exhibit deleterious responses to acute RE (elevated aortic and carotid artery stiffness, impaired peripheral vascular function, impaired cerebral blood velocity and cerebrovascular reactivity), and post-acute RE responses would improve after 8-week RET. The overall conclusions are (1) long-term RET does not negatively impact central aortic stiffness and confers positive macrovascular, microvascular, and cerebrovascular responses to acute RE in middle-aged women, (2) 8-week RET induces beneficial macrovascular responses to acute RE in middle-aged women, and (3) in middle-aged women, 8-week RET confers similarly beneficial vascular responses to acute RE when compared to long-term RET
MISSING TEETH: The Holes In Our Communities
No full textThe events of hurricane Helene in September 2024 brought to the front pages an area of the country that is often forgotten despite being so close to the populated east coast. According to the Appalachian Regional Commission, there were 26.4 million people living in the region known as Appalachia in 2022.Many places in Appalachia could be described as “under-resourced.” The overall poverty rate is 14.3% compared to the US national average of 12.1%, and spikes upwards of 30% or more in areas like eastern Kentucky or Southwest Virginia (fig 1). Additionally, Appalachia experiences a specific set of problems: environmental issues related to the mining industries and an increased frequency of 100 year storms, and depopulation instead of gentrification. The shrinking coal industry can no longer provide enough jobs, disastrous floods destroy current buildings, and these diminishing resources drive younger people out who would otherwise be a resource to support an aging population. While the combination of issues could be unique to this area, they apply to many types of under-resourced communities.
But this is not the whole picture: many people of Appalachia are characterized by strong connections to their land, history, and each other. Together they have laid the groundwork to retain talent, rebuild after floods, and obtain new resources. Buildings are a resource that can house people, create opportunities for social organizing, and attract visitors and revenue. By building in the community’s "missing teeth"--empty storefronts, large parking lots, streetfront gaps where floods have taken structures away–we can help reknit the town fabric and give the community a resource that can support their continuous efforts: a main street that the town can feel proud of.
This thesis uses a mixed-methodology approach, including literature and statistical review, morphological study, and firsthand ethnographic research
COMSOL models for working-electrode/solid-electrolyte under mechanical loadings
No full textThe attached COMSOL models simulate the mechanical state of a working-electrode/solid-electrolyte system under the following loading conditions.
* Scenario I - working electrode under out-of-plane uniaxial compression
* Scenario II - solid electrolyte under in-plane uniaxial compression
* Scenario III - solid electrolyte under pure shearThis work was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under grant DE-SC0021070. The views expressed in this work do not necessarily represent the views of the US Department of Energy or the United States Government
Josephson Effects in the Iron-Based Superconductor FeTeSe
No full textThe iron-based superconductor FeTeSe has emerged as a promising platform for combining superconductivity and topology in a single system, for the realization of topological quantum computing. Besides this, FeTeSe hosts rich physical phenomena such as S superconductivity, Majorana bound states, and higher-order topological superconductivity, among others. Despite the interest in superconducting devices based on FeTeSe, there have been relatively few demonstrations of Josephson junctions in FeTeSe-based systems.
In this dissertation we measured Josephson effects in a FeTeSe-based device and found three signatures of unconventional Josephson junction behavior. This first signature was the existence of two distinct Josephson diffraction patterns under applied RF irradiation, which likely arises from flux flow and a phase slip line in FeTeSe. The second signature was the emergence of sudden jumps in the DC current at which Shapiro steps arise, as a function of applied RF power. This was measured by mapping vs DC current and RF power. We provide two potential explanations for this phenomenon based on non-equilibrium superconductivity. The third signature is a minimum critical current at zero magnetic field when RF irradiation is present which resembles the -Josephson junctions formed as a consequence of multiband superconductivity
GENOMIC AND MICROBIOME ANALYSIS TO IMPROVE FILLET YIELD AND QUALITY TRAITS IN RAINBOW TROUT
No full textRainbow trout is the most widely farmed cool- and cold-water freshwater fish species in the United States. It is primarily cultivated for its fillets, rich in protein and essential fatty acids. As interest grows in enhancing the productive efficiency of rainbow trout, most breeding programs still rely heavily on traditional, pedigree-based selection. Incorporating genomic information holds promise for accelerating genetic gains, particularly for complex or lethally measured traits such as fillet yield and quality. However, even with the availability of genomic data, a substantial portion of phenotypic variation remains unexplained—an issue commonly referred to as “missing heritability.” Recently, the gut microbiome has emerged as a potential contributor to phenotypic variation through host–microbiome interactions. Some microbiome features may be heritable, which could help account for portions of the missing heritability. In this study, we investigated the genomic and microbiome architecture of rainbow trout families from USDA breeding programs, aiming to improve fillet yield and quality traits. Fillet color, a key quality attribute influencing consumer preferences, was a major focus. Using genome-wide association studies (GWAS) and RNA-Seq, we characterized the genetic basis of variation in fillet yield and quality traits. GWAS identified SNPs within genes involved in carotenoid metabolism (e.g., β,β-carotene 15,15-dioxygenase, retinol dehydrogenase), myoglobin regulation (ATP5F1B), and structural maintenance of muscle tissue (klh41b, COL28A1, CTSK). RNA-Seq further highlighted genes involved in lipid/carotenoid metabolism, ribosomal function, mitochondrial activity, and stress response as contributors to fillet color variation. We also integrated expression quantitative trait loci (eQTL) mapping to connect genetic variants with gene expression and phenotypic outcomes. A total of 6,275 cis-eQTLs were identified near promoter regions influencing gene expression. Notable candidate genes included GABRR1-like, AZIN1, and ATP6V1 for body weight; TNNI2, PDLIM3, CDK5, and CYP3A27 for tissue robustness; and GATD3A, PPP2R1BB, and USP6NL for muscle development. A specific A-A-C eQTL haplotype was strongly associated with elevated expression of ATP6V1. These eQTLs overlapped with regions enriched for active enhancers, making them strong candidates for inclusion in genomic selection strategies. To assess the role of the gut microbiome, we employed both 16S rRNA gene sequencing and shotgun metagenomics to identify taxa and pathways predictive of fillet color. Fish with red fillets were enriched (LDA score > 1.5) for Leuconostoc lactis, Corynebacterium variabile, Jeotgalicoccus halotolerans, and Leucobacter chromiireducens—bacterial species with known probiotic functions and carotenoid biosynthesis capabilities. These fish also exhibited enrichment of the Methylerythritol Phosphate (MEP) pathway, which is involved in carotenoid production. Microbiome-wide association studies (MWAS) revealed microbial taxa and metabolic pathways associated with growth traits. These included pathways such as fatty acid elongation, fatty acid oxidation II, pyruvate fermentation to isobutanol, glyoxylate cycle, mixed acid fermentation, superpathway of branched chain amino acid biosynthesis, and peptidoglycan biosynthesis II —all of which may influence growth performance in rainbow trout. Lastly, we demonstrated the feasibility of combining low-coverage whole-genome sequencing (1x WGS) with genotype imputation and microbiome data for genomic prediction. Our findings show that combining 1x WGS with pedigree data provides predictive power that outperforms the pedigree-only-based models. Moreover, incorporating microbiome data improved prediction accuracy for body weight and muscle yield by 7.2%, and 8.6%, respectively, offering potential for substantial cumulative gains across generations. In conclusion, this study identifies key genetic and microbiome contributors to variation in fish growth, fillet yield and quality traits in rainbow trout. Our results highlight the potential of integrating genomic and microbiome information to enhance selective breeding strategies, promote sustainable aquaculture, improve protein security, and deliver economic benefits to the U.S. aquaculture industry
Necessary and Sufficient Conditions for the Transfer of Kinetic Energy at Asymptotically Large Reynolds Numbers
No full textAt high Reynolds numbers, an incompressible fluid will become turbulent --- a phenomenon where the fluid is sensitive to external noise, develops chaotic time dynamics, and can develop eddy-type structures which break apart into smaller and smaller versions of themselves to dissipate energy as heat. In the field of mathematical physics, turbulent flows are typically modeled using stochastic partial differential equations to model the apparent randomness of the turbulent flow. Moreover, from a physics perspective, this method accounts for external noise on the system, such as the vibrations of the table holding the cup of coffee. Parameterizing these solutions by the viscosity (or the inverse of the Reynolds number) we can then study the behavior of the flow in the inviscid limit --- or as the viscosity decreases toward 0.
One striking feature of three-dimensional turbulence is the presence of anomalous dissipation, or that the mean rate of energy dissipation is bounded below by a positive number in the inviscid limit. This is thought to be due to the convective acceleration acting in part like a dissipation mechanism instead of a pure transport mechanism at asymptotically large Reynold's numbers (i.e. in the inviscid limit). Moreover the amount of anomalous dissipation dictates how fast the various eddy structures in the flow can break apart into smaller and smaller versions of themselves known as an energy cascade. In 1941, Kolmogorov predicted the rate of the energy cascade to be where is the size of the eddy structure and is the amount of anomalous dissipation. Kolmogorov's work has been experimentally verified and simulated in numerous studies, but has faced serious mathematical obstacles in its analysis. In the first part of this dissertation we focus on finding necessary and sufficient conditions for Kolmogorov's flux laws on the movement of kinetic energy. We complete this over a torus in both two and three dimensions and discusses both the physical and mathematical differences encountered due to the dimension.
In the second part of this dissertation we examine the anomalous dissipation assumption itself. Here we consider the case of a bounded domain, subject to the Navier slip condition and show that the existence of (global) anomalous dissipation --- anomalous dissipation over the entire domain --- can be caused in a linear problem through lack of control over the tangential component of the velocity at the boundary
"The Eye Is The Window for the Soul:" Essays on the American Anti-Comics Movement
No full textFor almost twenty years, from the advent of superhero comics in 1939 to the end of the 1950s, comic books were a profound cultural phenomenon in midcentury America. Millions of Americans read comics, child and adult alike, but comics retained a perception as a medium consumed primarily by children. A powerful anti-comic book movement arose to combat their influence because of perceived threats to the wellbeing and development of children, its members arguing at once for their regulation, restriction, and elimination. In modern historical memory, the movement often reduces to a “classical phase” that foregrounds only the sensationalist critiques of Dr. Fredric Wertham, a German-American psychiatrist, and the governmental investigation of comic books by the Senate Subcommittee on Juvenile Delinquency in 1954. Though Wertham was undoubtedly the most prominent critic of comic books and the hearings were the high-water mark of the anti-comics movement, this dissertation contends that reducing the entire movement to these two points obscures both the longer antidemocratic origins of the midcentury “decency” movements and marginalizes other perspectives and critiques of the anti-comics movement that demonstrate that views of comics at midcentury were hardly monolithic.
This dissertation argues overall that the primary driver of the anti-comics movement was a deep-seated fear of images and iconocentric culture among a generation raised primarily on the written word -- Americans who feared that the epistemological shifts occurring in the production and consumption of culture would threaten their legitimacy as parents, teachers, ministers, and politicians. These shifts dovetailed with the ramped-up antidemocratic tendencies of the Cold War, whose logic came to define the actions of the movement during its later years. This study also argues that the anti-comics movement was a clear and important aspect of domestic Cold War culture. Through primary source investigations of organized right-wing Catholic censorship organizations, local-level civic decency groups, government documents and legal materials, the writings of public intellectuals, and nonprofit organizations, this study aims to present an expanded portrait of an often-misremembered period of repression in American history
Toward Integrating Intelligence Into Everything Around Us
No full textThe vision of ambient intelligence promises a world where computational capabilities seamlessly integrate into everyday objects and environments, creating systems that sense, learn, and adapt to human needs while remaining invisible to users. Despite significant advances in miniaturization and low-power computing, true ambient intelligence has remained elusive, hindered by a fundamental challenge: current intelligent systems require substantial energy, complex hardware, and frequent maintenance, making widespread deployment impractical. We introduce a paradigm shift in how we create intelligent systems by fundamentally reimagining sensing and computing architectures from first principles for extreme resource constraints.
This thesis centers on encoding intelligence directly into the physical domain through novel hardware-software co-design, where passive structures perform initial signal transformations without consuming power. Through novel architectures across acoustic, radio frequency, and optical domains, we demonstrate systems that achieve spatial perception, global positioning, and environmental monitoring with orders of magnitude less power than conventional approaches. These innovations enable intelligence in previously impossible contexts: insect-scale robots that navigate complex environments, sticker-sized tags that provide GPS-like tracking for years on a single battery, and wireless sensors that monitor food quality throughout global supply chains. By bridging the gap between what intelligent systems can do and what resource-constrained platforms can support, this work establishes a foundation for truly pervasive intelligence that operates sustainably at large scale