https://aurora.auburn.edu/handle/11200/44211 2026-04-18T04:16:40Z 2026-04-18T04:16:40Z https://aurora.auburn.edu/handle/11200/50696 2025-07-14T14:48:32Z

Gestalt-ing a Diagram Using ideas from Gestalt psychology about how humans may perceive diagrams, we consider, and offer alternative representations of, a popular mathematics education diagram: the ‘egg’ model of mathematical knowledge for teaching (Ball, Thames, & Phelps, 2008; Hill, Ball, & Schilling, 2008).

https://aurora.auburn.edu/handle/11200/50639 2024-04-06T08:30:11Z

Stellar Blend Image Classification Using Computationally Efficient Gaussian Processes (MuyGPs) Stellar blends are a challenge in visualizing celestial bodies and are typically disambiguated through expensive methods. To address this, we propose an automated pipeline to distinguish single stars and blended stars in low resolution images. We apply different normalizations to the data, which are passed as inputs into machine learning methods and to a computationally efficient Gaussian process model (MuyGPs). MuyGPs with 𝑁𝑡 ℎ root local min-max normalization achieves 86% accuracy (i.e. 12% above the second-best). Moreover, MuyGPs outperforms the benchmarked models significantly on limited training data. Further, MuyGPs low confidence predictions can be redirected to a specialist for human-assisted labeling.

https://aurora.auburn.edu/handle/11200/50637 2024-04-05T08:30:11Z

Optimal Upscaling with Transport Maps Partial differential equation models often involve space-dependent parameters, such as diffusion coefficients and advection fields, that cannot be measured explicitly and are therefore uncertain. Midpoint (MP), spatial averaging (SA), shape function (SF) and series expansion (SE) methods have long existed in the stochastic simulation community and are well known for their computational hurdles. In this work, we compute efficient, spatially adaptive, lower-dimensional approximations of these fields, using transport maps. Such parsimonious representations of the parameter space would greatly improve the efficiency of the resulting stochastic simulations, allow for more targeted use of reduced order models, and aid in the related design of interventions. Numerical examples demonstrate our theoretical results

https://aurora.auburn.edu/handle/11200/50636 2024-04-05T08:30:10Z

Show Me a Function: More Than Meets the Eye Mathematics is a fascinating subject used to understand functions' properties and behavior. From simple precalculus to challenging graduate-level courses, there is an intricate web of functions to explore. Unfortunately, functions that arise from real life problems are elusive, hard to characterize and can often only be approximated. In this talk, we will discuss practical methods used to uncover valuable functions in a variety of applications