http://hdl.handle.net/10150/129652 2026-06-14T22:44:36Z http://hdl.handle.net/10150/680934 New Dynamical Probes of Dark Matter Physics in the Era of Precision Astrometry Foote, Hayden Multiple lines of astrophysical evidence support that roughly 80% of the Universe’s mass is composed of invisible dark matter (DM). However, the nature of the DM particle is still unknown. Efforts to directly detect DM particles with Earth-based experiments rely on direction from local astrophysical probes that can predict the composition and distribution of DM in our Galaxy and, in turn, our Solar System. The era of Gaia precision astrometry has opened new pathways for studying DM in the Milky Way (MW) by unveiling the motions of stars and satellite galaxies orbiting within the gravitational potential of the MW’s DM halo. In this dissertation, I develop three novel theoretical frameworks for utilizing the observed dynamics of the MW’s stellar halo and satellite galaxies to constrain the nature of DM. I begin by introducing the first known collision between an ultrafaint dwarf satellite of the MW, Segue 2, and a stellar stream, Cetus-Palca. This interaction is a promising test bed for modeling the effects of the MW's DM substructure on stellar streams. Additionally, Segue 2’s impact on Cetus-Palca offers a novel method for understanding the structure of the smallest known DM halos. Second, I construct and discuss results from a suite of windtunnel-style N-body simulations of the interaction between the MW and its largest satellite, the LMC, assuming two DM particle candidates, cold and fuzzy DM. I demonstrate that observations of the LMC’s wake in the MW’s stellar halo can be used to confirm the existence of DM and discriminate between cold and fuzzy DM models. Finally, I present a framework for quantifying how the MW’s two largest satellites, the LMC and SMC, shape each other’s DM halos during their ~6 Gyr interaction history. Dynamical studies of the LMC-SMC system must take their time-dependent, asymmetric DM distributions into account. The perturbations to both galaxies’ halos bear similarities to those predicted and observed in the LMC-MW interaction, suggesting the LMC-SMC binary can be used as a powerful DM laboratory. As current and upcoming surveys continue to increase the availability of kinematic data for the MW system, the frameworks I establish in this dissertation offer a promising path forward for understanding the local composition and distribution of DM. 2026-01-01T00:00:00Z http://hdl.handle.net/10150/680933 Towards Stable Adversarial Training with Stochastic Attention Schwartz, David A new attack surface emerges as neural networks increasingly permeate safety critical applications (e.g., autonomous vehicle control, autonomous surgery, and medical diagnostics). Therefore, due to the potentially life-threatening consequences of successful attacks at these networks' interfaces, the development of principles and methods that robustify vulnerable models is a major interest of the ML community. One factor stymieing these endeavors is the dataset-dependent trade-off typically observed between neural network performance on benign and adversarially altered data. Consequently, there is no clear consensus on how the optimization algorithms and network architectures should navigate this tradeoff. Further exacerbating the dilemma, defending ML models typically increase the overall computational burden at training and/or testing time. As a result, which network architectures and learning algorithms are optimal depends on the user's budgets and constraints on computational power, energy consumption, and time. Hence, light-weight defense techniques that do not prohibitively inflate training time, model footprint, and evaluation time are highly desirable. To that end, this thesis proposes two novel defense techniques that have been empirically demonstrated to improve adversarial accuracy without significant degradation in benign accuracy. In the first method, robustness is enhanced by adding to the loss a regularization term that directly penalizes differences in latent representations evoked throughout a network by adversarial perturbation of the input. The novelty of the second approach is an alteration of the neural network architecture itself. Specifically, to form the algorithm dubbed Data Dependent Stochastic Resonance (DDSR), each hidden attentional layer is augmented with a mechanism that integrates information from earlier layers in a manner reminiscent of Resnet's residual connections, controlling the locations and intensity with which random noise is added to the latent neural representations and the original attentional weights as a function of the earlier layers' activations. This dissertation outlines results from prior work before evaluating some relevant defense methodologies and state-of-the-art techniques to assess the true impacts of the novel ones. These experiments are designed to inform an understanding of adversarial defenses' limits, and their ability to defend against previously unseen attacks, where the adversary holds the adaptive advantage. The ensuing results include a demonstration that despite approaching or matching similarly constrained state-of-the-art (SOTA) defenses' robust accuracy, DDSR retains or recovers benign accuracy at levels matching or exceeding those of the standard (i.e., undefended) instance. With similar budgets for computer hardware or time, combining the defense techniques documented here with present SOTA training techniques, including immense quantities of additional data (i.e., samples not included in the original benchmark datasets) may find evaluations competitive with top results on the RobustBench leaderboard. The impacts of these outcomes are two-fold: firstly by offering engineers deploying neural networks a relatively inexpensive method to improve adversarial robustness without noticeably sacrificing their original objective, and secondly, by elucidating the extent to which information learned to defend against one attack transfers to others, we clarify what computational budget is required to develop acceptable robustness. 2026-01-01T00:00:00Z http://hdl.handle.net/10150/680928 Statistical Normalization and Measures Development in the Biological Sciences Allred, Serena Precedent, practicality, comparative studies, and newly developed methods often leave researchers wondering which measurement method or normalization approach is optimal for a particular study. While there is no single widely accepted method for comparing measurement methods, sensitivity, as defined by Mandel and Stiehler (1954), is an important quantity that holds promise in this regard. Sensitivity is the slope of a calibration curve divided by the measurement error standard deviation of a response. As we will show, it is also the reciprocal of prediction error; thus, high sensitivity corresponds to low prediction error, clearly desirable criteria for measurement. Mandel (1984) also developed relative sensitivity for the comparison of measurement methods within the context of analytical chemistry. The objective of this work is to apply statistical methods to Mandel's metric, making it more useful in the biological sciences. We accomplish this objective by developing Bayesian statistical models for relative sensitivity estimation, applying our estimation model in linear and nonlinear settings, and identifying important distributional features for normalization using covariates. We develop estimation methods for relative sensitivity when the values of the measurand are either known or unknown by applying what we call direct and indirect models, respectively. Using MCMC for inference, direct and indirect models show good agreement in both simulations and a total protein measurement. Particularly when it is impossible or impractical to obtain known analyte concentrations, our Bayesian method of estimating relative sensitivity may prove useful for researchers considering multiple methods of measurement, while simultaneously providing concentration approximation. In the nonlinear example of relative sensitivity estimation, this method also provides vital uncertainty information for determining whether MTS or xCELLigence is the superior cell viability response over portions of the concentration range; we implement a four-parameter log-logistic mean model with proportional variance. When covariates are included in normalization, we find that bias is a non-ignorable component that relative sensitivity does not recognize. Another key finding that sensitivity is inversely related to prediction error leads us to propose the mean squared prediction error (MSPE) for the comparison of normalizations with covariates. MSPE effectively compares an unadjusted, division-based, and regression-based normalization with both variance and bias, identifying several issues with the division-based method. Additionally, we have derived general analytical expressions for the expectation and variance of each normalization method, which may help determine which of several potential normalization approaches has the lowest prediction error. 2026-01-01T00:00:00Z http://hdl.handle.net/10150/680929 Taming Tongues: Developing a Culturally Concious and Sustaining Education for Primary Emergent Bilinguals Elias, Karina Isabelle There has been rampant growth in the language-minority population in public education, pressuring schools and teachers to maintain or improve test scores, implement adequate programs and services, and to employ effective teachers to support these students. This pressure forces many language-minority students to face experiences with individuals who have deficit-based perspectives (Huckle, 2024; Menken & Solorza, 2014). This case study examines the narratives of five primary teachers who work with emergent bilingual (EB) students to understand how they access, recognize, and use funds of knowledge in their classrooms. Semi-structured interviews with the participants provided insight into the resources, tools, and strategies used to support EB students. Specifically, participants revealed how they used their funds of knowledge to better understand their students and maintain a culturally conscious and sustaining education for all their students. This study has implications for teachers, school leaders, and state and federal level policy who work with primary EB students in public education. 2026-01-01T00:00:00Z