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Momentum-resolved electron dynamics in a strange metal
No full textSubmission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo termsThe student, Xuefei Guo, accepted the attached license on 2025-07-09 at 16:58.The student, Xuefei Guo, submitted this Dissertation for approval on 2025-07-09 at 17:01.This Dissertation was approved for publication on 2025-07-11 at 13:06.DSpace SAF Submission Ingestion Package generated from Vireo submission #22468 on 2025-10-20 at 16:57:36The strange metal phase, characterized by its simple linear-in-temperature resistivity, challenges the conventional quasiparticle paradigm. This anomalous behavior, associated with Planckian dissipation, suggests a minimal relaxation timescale and a maximally entangled many-body quantum state. Despite decades of investigation, this strongly interacting electronic phase remains one of the most enduring puzzles in condensed matter physics. This thesis uses advanced scattering and spectroscopy techniques to investigate the strange metal phase in Bi2Sr2CaCu2O8+x (Bi-2212), aiming to shed new light on its underlying dynamics. In the pseudogap regime, putative broken symmetries are considered essential to understanding the emergence of the strange metal state within the framework of quantum criticality. Using resonant soft x-ray scattering at the Cu L3 edge, signatures of a Q ~ 0 order are observed in optimally doped Bi-2212, indicated by the appearance of the nominally forbidden (0, 0, 3) Bragg peak under circularly polarized light within the pseudogap regime. In contrast, this peak remains absent under linear polarization or at temperatures outside the pseudogap regime. These results suggest the presence of a spatially uniform valence band order involving higher-order multipole moments of charge or spin distribution around the copper sites. In the strange metal regime, momentum-resolved electron energy-loss spectroscopy (M-EELS) reveals that the low-energy charge fluctuations in Bi-2212 exhibit w/T scaling invariance. The dynamic charge response is well captured by the Glauber relaxational model, indicating predominantly relaxational dynamics with negligible diffusive contribution. The extracted relaxation rate is consistent with Planckian dissipation. Moreover, the momentum-independent nature of the response suggests that the charge dynamics are local. Strikingly, the data are well described by a conformal field theory with a conformal dimension of 0.05, significantly deviating from the marginal Fermi liquid hypothesis, which predicts a conformal dimension of 0.5. These findings indicate that the charge fluctuations in the strange metal phase of Bi-2212 exhibit conformal invariance, suggesting a connection to holographic descriptions of strange metals. Recent advances in electron detector technology have prompted the development of a new time-of-flight approach for M-EELS measurements, expected to significantly improve the efficiency of the current scheme. As an initial step, a thermally enhanced photocathode was developed using a conventional LaB6 filament illuminated by a 392 nm ultrafast UV laser. Increasing the filament temperature leads to a higher photoemission current, but also introduces a higher continuous thermal background. An optimal operating temperature is identified to maximize the signal-to-noise ratio. Additionally, higher filament temperatures improve the stability of the cathode, which is advantageous for M-EELS measurements with low count rates
High temperature, oxidation resistant, silicon nitride, ignition-assisted devices in multifuel aviation engines
No full textSubmission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo termsThe student, Prapassorn Numkiatsakul, accepted the attached license on 2025-07-11 at 14:04.The student, Prapassorn Numkiatsakul, submitted this Dissertation for approval on 2025-07-11 at 14:16.This Dissertation was approved for publication on 2025-07-14 at 14:22.DSpace SAF Submission Ingestion Package generated from Vireo submission #22519 on 2025-10-20 at 16:57:49Recent advancements in aviation engine design have increasingly emphasized the use of lower-quality alternative fuels to diversify fuel sources, particularly for aircraft operating in remote or fuel-limited environments. However, many of these fuels exhibit low autoignition reactivity, requiring supplemental thermal energy to initiate and sustain stable combustion. As a result, the development of multi-fuel engine technology has created a demand for robust ceramic heaters or Ignition Assisted (IA) devices capable of delivering consistent thermal input while withstanding the extreme conditions of high-temperature combustion environments. Silicon nitride-based glow plugs, commonly used as heaters in diesel automotive engines, were investigated as potential candidates for this application. These devices could rapidly reach surface temperatures of up to 1350 °C. However, they were originally developed for short-term operation in ground vehicles, primarily to assist combustion during cold starts. In contrast, ignition-assisted devices for multi-fuel aviation engines were required to operate continuously throughout an entire flight and maintain surface temperatures above 1100 °C, even under high-altitude cooling effects. No commercial device existed that fulfilled these requirements, which prompted the work presented in this dissertation. The core challenge in developing a reliable IA device was identified as a materials limitation. Specifically, the focus was placed on understanding the performance constraints and failure modes of silicon nitride-based systems (Si₃N₄), which serve as the primary structural ceramic in glow plug components. This research was divided into two parts. The first part involved a systematic characterization of commercial off-the-shelf glow plugs to evaluate their structural design, material composition, and failure behavior under engine-relevant conditions. Multiple degradation mechanisms were identified, including thermal cracking, interfacial delamination, sintering aid migration, and progressive oxidation. Glow plugs with U-shaped designs were particularly prone to delamination caused by thermal stress and electric-field-induced ion migration. Co-annular glow plug architectures, on the other hand, were more susceptible to oxidation-related degradation due to direct exposure of the heating elements to high-temperature oxidative environments. The second part of the study focused on addressing these degradation mechanisms - particularly oxidation - by developing improved ceramic materials. Three strategies were explored. The first approach involved incorporating aluminum nitride (AlN) as a bulk additive, which enhanced oxidation resistance by forming dense, protective, oxide layers. However, this approach introduced challenges related to reduced thermal conductivity and poor sinterability. The second strategy applied CaO surface treatments to sintered Si₃N₄ pellets, which promoted the formation of crystalline Ca-Mg-silicate phases to stabilize the oxidation front. These stable surface layers reduced oxygen ingress without altering the bulk microstructure. The third and most comprehensive strategy involved designing adjacent material systems, specifically O-SiAlON ceramics, synthesized via reaction sintering. These materials exhibited superior oxidation resistance when fabricated under carefully controlled conditions. Detailed analysis of O-SiAlON microstructure and composition provided insights into oxidation kinetics in sintered ceramics containing additives. The study revealed that oxidation resistance was governed by kinetics and oxygen transport through the microstructure. Samples with optimized grain structure and stable glassy phase composition showed the highest oxidation resistance. Phase evolution and oxidation behavior of O-SiAlON were found to depend strongly on sintering temperature and Al-O substitution level (x-value). Samples with moderate substitution levels (x = 0.1-0.2), sintered at 1550 °C, developed fine-grained, dense microstructures and stable protective phases with minimal glass volatilization, resulting in excellent oxidation performance. Overall, this dissertation presented a critical evaluation of the limitations of current IA ceramic materials and outlined promising strategies for improvement. The findings supported the potential of tailored silicon nitride-based compositions, surface engineering techniques, and alternative systems such as O-SiAlON to enable the development of reliable materials for ignition-assisted devices operating in multi-fuel, high-temperature combustion environments
Simple and practical algorithms in computational geometry
Get PDFSubmission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo termsThe student, Eliot Robson, accepted the attached license on 2025-07-14 at 09:47.The student, Eliot Robson, submitted this Dissertation for approval on 2025-07-14 at 10:02.This Dissertation was approved for publication on 2025-07-14 at 11:36.DSpace SAF Submission Ingestion Package generated from Vireo submission #22542 on 2025-10-20 at 16:57:54Geometric data is everywhere, and the sheer size of modern datasets motivates the development of efficient geometric algorithms. This thesis investigates several such algorithms – striving for near linear time and practical simplicity. The specific problems studied in this thesis include: 1. No-dimensional Tverberg partitions: We study a relaxation of the classical Tverberg theorem, where the intersection requirement is weakened, and the dependence on the dimension is replaced by other parameters. We present simple linear-time algorithms for computing such partitions, improving over known results that were either existential, or yield worse partitions. 2. Constructing a reliable spanner for disk graphs: We present a near-linear time algorithm for computing connectivity-preserving “spanners” for disk intersection graphs that can withstand catastrophic failures, where a large fraction of disks fail/disappear. 3. Fault-tolerant k-center. We consider a robust variant of k-center clustering where some centers could fail. This is done by measuring the distance for each client to the αth closest center (instead of the closest). We establish an analogous connection between this (k, α)- center problem and the α-distance permutation, similar to the established link between the traditional k-center problem and the greedy permutation. We provide efficient approximation algorithms for computing this clustering and its associated α-distance permutation. 4. Practical Fr´echet distance. We present simple algorithms for the Fr´echet distance, a metric that quantifies the similarity between two polygonal curves. Combining simplification, approximation, and a new variant of the Fr´echet distance, we present new algorithms for computing the almost-exact Fr´echet distance between curves, that in practice seems to run in near linear time. The new implementation is faster than the current state-of-the-art. We provide open-source implementations both in Julia and Python
Studies on increasing resilience in dairy and crossbred calves
Get PDFSubmission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo termsThe student, Meghan Pister, accepted the attached license on 2025-07-14 at 12:09.The student, Meghan Pister, submitted this Dissertation for approval on 2025-07-14 at 12:20.This Dissertation was approved for publication on 2025-07-17 at 21:01.DSpace SAF Submission Ingestion Package generated from Vireo submission #22548 on 2025-10-20 at 16:57:58Intestinal health is critical for the overall growth and well-being of young dairy calves. Despite advancements in calf management, diarrhea remains the leading cause of morbidity and mortality in this population. While infectious pathogens are often responsible, nutritional factors—particularly diet composition—can also contribute to diarrhea. One such factor is the concentration of total solids (TS) in milk replacer (MR). Feeding MR with high TS levels (e.g., 18%) can enhance nutrient delivery; however, the resulting increase in osmolality may lead to digestive upset and diarrhea. Nutritional strategies—including the addition of electrolytes, fiber sources, and casein protein—may help mitigate these effects. To evaluate these approaches, four experiments were conducted to determine whether high-TS feeding induces diarrhea and whether specific dietary manipulations can reduce its incidence. Results indicated that calves fed high-TS MR experienced a greater incidence of diarrhea and had lower fecal dry matter compared to non-diarrheic calves. Among the interventions tested, the inclusion of casein and psyllium fiber showed promise in reducing diarrhea incidence in one of three trials. This suggests potential benefits, though further research is warranted to confirm consistency across different settings. In addition to managing diarrhea, optimizing vitamin intake is essential, particularly B vitamins, which preweaned calves cannot synthesize independently. Despite their importance, research on ideal supplementation levels remains limited. An experiment was conducted to assess the health and growth outcomes of feeding B vitamins (thiamine, niacin, pyridoxine, and cobalamin) at levels above both the basal diet and the 2021 NASEM recommendations. The results showed that calves receiving only the basal MR diet exhibited fewer cases of ocular discharge, while the basal diet calves tended toward reduced respiratory issues compared to those supplemented above basal levels. No significant differences were observed in body weight or growth parameters between treatment groups. However, analysis of plasma metabolites and hepatic gene expression revealed some distinctions. For example, genes associated with stress response (GR), pyridoxine metabolism (PNPO), and lipid metabolism (ATGL/PNPLA2) showed differential expression, suggesting potential metabolic effects of B vitamin supplementation. These findings indicate that while B vitamin supplementation may influence metabolism, its impact on growth and health outcomes is less clear, and further research with defined dosing is needed. Another area of interest is mitigating heat stress and improving early disease detection in calves. Elevated body temperature is a key indicator of both heat stress and illness, yet measuring rectal temperature (RT) on large-scale farms is time-consuming. Infrared thermography (IRT) offers a non-invasive alternative and has shown promise in detecting illness in livestock. A study was conducted to determine whether IRT could reliably detect elevated body temperature in calves and correlate with RT. Heat stress conditions were defined using a temperature-humidity index (THI). Findings indicated only a weak correlation between infrared surface temperatures and RT. While RT remained relatively stable, IRT readings varied significantly with ambient conditions. Although heat-stressed calves did exhibit elevated internal temperatures compared to their non-stressed counterparts, IRT did not accurately detect fever under the tested conditions. Thus, current IRT methods may not be sufficient for standalone fever detection in calves. Finally, the weaning and immediate post-weaning period present unique challenges for calves, as they transition to solid feed and often face added stress from transport or commingling. During this period, calves may become more susceptible to disease. Plasma protein supplementation has demonstrated health and growth benefits in other species and in calves during the preweaning phase when added to MR, but its efficacy post-weaning is less studied. A study was conducted to evaluate whether including plasma protein in grower feed could improve health and performance in newly weaned calves. Results showed no significant differences in health metrics, growth performance, or plasma cortisol levels between treatment groups. These findings suggest that while plasma protein may offer preweaning benefits, its impact post-weaning requires further investigation, especially with clearly defined stress biomarkers such as cortisol. Together, these studies suggest that targeted nutritional interventions—such as managing TS concentration, optimizing B vitamin supplementation, and using functional feed additives—may have the potential to support calf health and growth. However, the evidence highlights the need for further research to define effective inclusion rates, validate novel diagnostic tools, and refine nutritional strategies for both pre- and post-weaning phases
Unconventional superconductivity in topological insulator and magnetic Josephson junctions
No full textSubmission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo termsThe student, Alexander Beach, accepted the attached license on 2025-07-14 at 23:55.The student, Alexander Beach, submitted this Dissertation for approval on 2025-07-15 at 00:27.This Dissertation was approved for publication on 2025-07-16 at 09:47.DSpace SAF Submission Ingestion Package generated from Vireo submission #22572 on 2025-10-20 at 16:57:59In its century-long history, superconductivity has been applied in a host of technologies, including in medical devices, power grids, mag-lev trains, particle accelerators, incredibly sensitive quantum detectors, and many more areas. More recently, research has increasingly focused on unconventional forms of superconductivity that are not explained by the standard BCS theory. The potential applications of these unconventional forms of superconductivity are many, and so my research focuses on exploring and understanding superconductivity in different materials. I present experiments I have performed on unconventional superconductivity in Josephson junctions made with Bi2Se3 and Josephson junctions made with Cr1/3NbS2. Bi2Se3 is a 3D topological insulator, which means it has an insulating bulk, but conducting surface states. Cr1/3NbS2 is a chiral helimagnet, which means it has a magnetization that rotates in a helix. In both experiments the junction interlayers are made from mechanically exfoliated flakes of the materials. The primary measurements of the Bi2Se3 junctions are Fraunhofer patterns that measure the critical current of the junction under a changing magnetic field. These patterns have considerable deviations from the standard Fraunhofer form, showing asymmetry in magnetic field, offsets from zero field, aperiodicity, and lifted nodes. Simulations of junctions with geometric disorder in the form of flake thickness jumps also show these phenomena. Atomic force microscopy scans of the Bi2Se3 flakes in the junctions show that the surface of the flakes is very rough, with jumps in height that are linked to the observed features of the measured Fraunhofer patterns. The measurements of Cr1/3NbS2 junctions are also mostly Fraunhofer patterns, but with an emphasis on asymmetry in current. The positive critical current and negative critical current of the junctions are not the same magnitude, + ≠ − , and this is called the superconducting/Josephson diode effect. This effect is explained by the chiral nature of Cr1/3NbS2 with the additional presence of a small out-of-plane magnetic field. There is also an anomalous magnetic hysteresis in the junction that could be explained by the presence of one or more Abrikosov vortices in the junction, which themselves may also be caused by a small out-of-plane field. Whether an out-of-plane field comes from a conical spin configuration in the Cr1/3NbS2, flux focusing effects, or another source is unknown. I also briefly describe three secondary experiments that have not yet produced published results. The first of these experiments is the creation of Josephson junctions with the topological crystalline insulator SnTe. In SnTe the topological surface states are protected by crystalline symmetries, rather than time-reversal symmetry, meaning the surface states will appear and disappear under different conditions than in a 3D topological insulator. The SnTe junctions I fabricated did not show any Josephson behavior, but did show weak superconductivity at very low temperatures. The second experiment consists of capacitance and leakage current measurements of La2O3 thin films. The measurements are used to determine the dielectric quality of several thicknesses of the La2O3 and the efficacy of a forming gas annealing process. The final experiment attempts to observe a superconducting transition in Co thin films. Co is ferromagnetic and does not superconduct under standard conditions, but is predicted to do so when under strain. Resistance measurements show some transition in response to temperature changes and current changes, while measurements with applied magnetic fields are more ambiguous. The temperature transition also shows an anomalous hysteresis
Beyond words: investigating emotional expression and change talk in motivational interviewing for substance use treatment
Get PDFSubmission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo termsThe student, Corey Campbell, accepted the attached license on 2025-07-16 at 08:20.The student, Corey Campbell, submitted this Dissertation for approval on 2025-07-16 at 08:28.This Dissertation was approved for publication on 2025-07-17 at 18:36.DSpace SAF Submission Ingestion Package generated from Vireo submission #22595 on 2025-10-20 at 16:58:35Background: Motivational Interviewing (MI) is an evidence-based counseling approach for substance use treatment that emphasizes client-centered dialogue and the resolution of ambivalence. While prior research has extensively examined verbal content—particularly "change talk"—the role of emotional expression, especially as conveyed nonverbally through facial behavior, remains underexplored. Objective: This study investigated the temporal relationship between client emotional expressions and subsequent change talk in MI sessions with emerging adults engaged in substance use treatment. Specifically, it examined whether facial expressions coded as positive, negative, or ambivalent predicted varying levels of change talk intensity. Methods: Nineteen audio-video recorded MI sessions were analyzed using the Facial Action Coding System (FACS) to classify client emotional expressions and the Motivational Interviewing Skill Code (MISC) to assess motivational language. Emotional expressions were coded during therapist speaking turns, and client utterances were categorized into low, medium, or high change talk. Sequential analysis techniques were employed to evaluate lag +1 transitions from emotional display to motivational speech. Results: Ambivalent expressions were the most commonly observed, followed by negative and then positive expressions. Positive facial expressions—particularly Duchenne smiles (AU6+12)—were significantly more likely to precede high-intensity change talk. In contrast, negative expressions were most frequently followed by low-intensity change talk. Ambivalent expressions tended to precede medium-intensity change talk, suggesting a motivational tension reflective of internal conflict. Conclusions: These findings highlight the relevance of nonverbal emotional expression in MI and suggest that emotion may serve as a dynamic and observable precursor to motivational engagement. Clinicians may benefit from greater attention to client affective cues—particularly facial expressions—as signals of readiness to change. Implications for emotion-informed MI practice, therapist training, and future research on the integration of affect in behavior change models are discussed
Analysis of tidal dynamics of binary neutron stars and properties of gravitational collapse beyond general relativity
Get PDFSubmission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo termsThe student, Abhishek Hegade Kumbale Raveesha, accepted the attached license on 2025-06-12 at 21:38.The student, Abhishek Hegade Kumbale Raveesha, submitted this Dissertation for approval on 2025-06-12 at 21:45.This Dissertation was approved for publication on 2025-06-24 at 10:45.DSpace SAF Submission Ingestion Package generated from Vireo submission #22338 on 2025-10-20 at 20:14:47Gravitational wave emission from compact binary sources has the potential to probe the dynamics of matter and gravity in extremely compact regions of spacetime. In this thesis, we explore the ability of gravitational wave observations to probe the internal nature of neutron stars and understand the nature of gravitational collapse in theories beyond general relativity. In Part I of this dissertation, we will examine the ability of gravitational wave observations to understand the dynamical tidal excitations in a binary neutron star system, probe the internal viscous process inside a neutron star, and measure the Hubble constant. We first build models of time-dependent tidal dynamics of neutron star binary systems using tools from relativistic fluid perturbation theory and post-Newtonian theory. To obtain the dynamical and dissipative tidal response of a non-rotating neutron star, we treat the fluid and gravitational perturbations inside a neutron star exactly and re-sum the external gravitational solution obtained in a small frequency approximation to consistently match to a post-Newtonian metric. The resummation procedure allows one to calculate the dynamical tidal response during the late inspiral of a binary neutron star system. Next, we use post-Newtonian theory techniques to calculate the gravitational waveform due to dissipative tidal interactions, which is accurate to 1 post-Newtonian order. The gravitational waveform obtained from this analysis is used to place the first constraint on the dissipative tidal deformability of a neutron star from GW170817 data. We also use binary-love relations to understand how well we can constrain the Hubble constant using third-generation detectors. Our analysis reveals that third-generation detectors with detections could allow one to constrain the Hubble constant to percent-level precision. In Part II, we understand the theoretical properties of gravitational collapse in theories beyond general relativity. In the decoupling limit, we show analytically and numerically that the scalar radiation resulting from the formation of the horizon leads to the loss of monopole and dipole hair in Einstein scalar Gauss-Bonnet gravity and dynamical Chern-Simons theory. We then understand the breakdown of hyperbolicity in Einstein scalar Gauss-Bonnet theory. We show that the breakdown of hyperbolicity is linked to the growth of strong gradients during gravitational collapse and provide sufficient criteria for the breakdown of hyperbolicity during spherical collapse. Using the insights from the analytical result, we numerically explore the process of scalarization of black holes in Einstein scalar Gauss-Bonnet gravity and show that a fine-tuning of initial data is required to achieve scalarization without breaking hyperbolicity
Enhancing multi-label object recognition in complex images via region-based continual learning
Get PDFSubmission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo termsThe student, Elen Chatikyan, accepted the attached license on 2025-07-15 at 16:48.The student, Elen Chatikyan, submitted this Thesis for approval on 2025-07-15 at 17:01.This Thesis was approved for publication on 2025-07-18 at 14:56.DSpace SAF Submission Ingestion Package generated from Vireo submission #22404 on 2025-10-20 at 20:14:55This thesis explores a region-based continual learning approach for multi-label object recognition in complex, multi-object scenes, designed to facilitate efficient learning from limited region-level supervision. We build on the AnytimeCL framework [1] by adapting it to a region-aware, multi-label setting. Our approach supports fine-grained learning with limited supervision by training on object-level regions from a controlled, balanced subset of the COCO dataset (14,000 images). Rather than emphasizing extremely low-shot scenarios at this stage, we focus on validating the effectiveness of region-based learning in improving multi-label object detection under moderate supervision. Investigating whether similar gains hold in extremely low-shot settings (e.g., 15–20 examples per class) is left for future work. To improve region-level predictions, we incorporate value-projected features from the final layers of transformer models, following the method proposed by Xiao et al. in their TextRegion work [2], which enhances class-specific region alignment. Our system combines vision-language features from CLIP and DINOv2, utilizing binary cross-entropy loss to support multi-label classification. To strengthen learning under limited supervision, we incorporate negative sampling at both the region and label levels. Areas corresponding to background or unrelated objects are treated as negatives, while unannotated classes are treated as negative labels. Annotated classes are ignored outside their corresponding regions. As a result, the model focuses on fine-grained object representations without requiring dense annotations. At inference time, we employ the Segment Anything Model (SAM)~\cite{kirillov2023segment} with a filtering layer to propose candidate object regions in unannotated images. This enables scalable, region-level predictions without requiring inference-time annotations. We evaluate our approach on a subset of the COCO dataset~\cite{lin2014microsoft}, using both region-level and image-level metrics, including Top-1 accuracy, F1 score, mean average precision (mAP), and subset accuracy. Our findings highlight the effectiveness of combining region-level learning with negative sampling for scalable, fine-grained multi-label recognition under limited supervision
Uniform bounds in D-minimal structures
Get PDFSubmission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo termsThe student, Madie Farris, accepted the attached license on 2025-07-07 at 09:52.The student, Madie Farris, submitted this Dissertation for approval on 2025-07-07 at 09:58.This Dissertation was approved for publication on 2025-07-08 at 13:32.DSpace SAF Submission Ingestion Package generated from Vireo submission #22423 on 2025-10-20 at 20:15:04O-minimality as a classification of the topological tameness of a structure has been extensively studied since its introduction in 1982. Many generalizations and variations of o-minimality have since been introduced and studied as well. In this thesis we focus on one particular generalization: d-minimality. We establish some of the first results on d-minimality that truly mirror those of o-minimality. The most central of which is the equivalence of d-minimality and strong d-minimality. In the process of proving this equivalence we develop a d-minimal version of cell decomposition, one of the most important results in o-minimality. In Chapter 1 we discuss the overarching project of tame topology, and situate d-minimality within this context. We define a grid, the object that we will use to decompose sets in d-minimal structures, and our main results, including the aforementioned decomposition theorem. Chapter 2 is spent establishing some preliminary facts that are used throughout this thesis. In Chapter 3 we motivate our choice of definition for grids by working through an example of a grid decomposition, and compare this decomposition to a previously known result for strongly d-minimal structures. We develop the theory of grids (and cells and stacks which are used to build grids) in Chapter 4. We put all of these pieces together in Chapter 5 where we prove our main results. In Chapter 6 we extend these results to a more general setting. Lastly, we discuss future applications of our main results in Chapter 7
Learning to share: Bayesian approaches to sparsity and transfer
Get PDFSubmission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo termsThe student, Anwesha Chakravarti, accepted the attached license on 2025-07-08 at 12:43.The student, Anwesha Chakravarti, submitted this Dissertation for approval on 2025-07-08 at 12:57.This Dissertation was approved for publication on 2025-07-11 at 15:01.DSpace SAF Submission Ingestion Package generated from Vireo submission #22439 on 2025-10-20 at 20:15:05In an age of increasingly complex, high-dimensional, and scarce data, sharing information across variables, tasks, and datasets, is critical to building models that are effective. This thesis explores Bayesian approaches to sparsity and transfer learning that utilize information present within different aspects of available data to construct models that are more efficient and interpretable. We utilize the Bayesian framework's inherent ability to integrate prior knowledge with new data, enabling information sharing to get informed posterior distributions. Our first contribution pertains to high-dimensional settings, where both the number of responses and covariates is substantial, and the responses themselves are interdependent. In such scenarios, we introduce a novel Bayesian methodology for simultaneous variable selection and sparse precision matrix estimation using high-dimensional Gaussian graphical models. Our approach provides sparse estimates for three distinct structures: the regression coefficient matrix, the conditional dependency structure among responses, and the relationships between responses and covariates. Together, these parameters offer a complete picture of the relationship between the responses and the covariates. Our second contribution involves collaboration with Mosquito Abatement Districts (MADs) in the Chicago metropolitan area and its suburbs to develop efficient models for West Nile Virus (WNV) surveillance. First, we propose a three-phase framework to identify optimal locations for mosquito traps, which can then inform about the risk of infection. This framework assists the MADs in reducing the number of traps required while making each individual trap more efficient. Next, we focus on predicting the human risk of WNV using trap-derived data. We illustrate that predicting the Vector Index (VI), a commonly used measure of WNV risk, is insufficient by itself. Instead, accurately predicting VI's underlying components—abundance and infection rates—simultaneously provides a clearer basis for targeted interventions. We employ the Bayesian framework developed earlier to obtain improved predictions of these components, thereby enabling mosquito prevention programs to make better-informed decisions. Our final contribution focuses on sharing information between models. Specifically, we propose a semi-supervised, source-free transfer learning approach based on power priors. By generating pseudo-labeled source data from a black-box model and combining it with a small labeled target dataset, we derive a posterior update that allows adaptive transfer without requiring direct access to source data or internal parameters of pre-existing models. Overall, this thesis integrates theoretical advancements with practical statistical applications. Collaborations with public health organizations illustrate the practical effectiveness of our information-sharing methodologies, demonstrating significant improvements in statistical modeling. Ultimately, this work underscores the importance of adopting information sharing as a fundamental statistical principle to better handle increasingly complex and rich datasets