Umpires play a critical role in baseball by enforcing rules and making judgment calls, particularly in pitch-calling, which significantly affects game flow and results. Given the subjective nature of these decisions, umpires are susceptible to cognitive biases that may consciously or unconsciously influence their calls.

This ongoing study provides an initial examination into a few dimensions of umpire bias.

PurrCare is a smart cat health monitoring gadget for busy tech-savvy cat owners who prefer to feel safe from a distance when they’re not around. The smart collar and smartphone app monitor physical movement, vital signs, and moods of a cat in real time. With remote voice control and health reminders added, PurrCare allows owners to be proactively involved in nursing their pets—over distance. It is particularly appealing to city workers who already wear health monitors on themselves and will pay for top-of-the-line preventive care on their pets.

We aim to implement The Zipper Algorithm, an elementary procedure to develop a conformal map between particular regions, in such a way to minimize error. The Zipper Algorithm repeatedly applies various transformations to the complex plane, which can result in loss of precision in points that are close together and greater distance between faraway points. This project will implement each step of the map into its elementary transformations as described in Marshall and Rohde’s paper Convergence of a Variant of The Zipper Algorithm for Conformal Mapping. A function is said to be poorly conditioned if a small perturbation in the inputs results in a large change in outputs. We aim to conduct the entire mapping within the unit disc in attempts to eliminate some of the poorly conditioned steps, and in doing so provide bounds on the error that may be introduced in such a mapping.

Spin glasses are disordered systems in statistical physics with randomly interacting particles; the Sherrington-Kirkpatrick (SK) model is a widely studied idealization that represents such systems using ±1-valued “spins” and random couplings. These random interactions create “frustration,” a phenomenon where conflicting constraints prevent spins from all aligning optimally. This results in a complex energy landscape with many local minima, making global optimization both computationally challenging and theoretically rich. A central focus of this project is the study of universality: whether algorithmic behaviors are determined solely by broad statistical features of the system or if they depend on finer distributional details. By analyzing algorithms that interpolate between greedy and reluctant local updates, we examine the geometry and complexity of optimizing the SK model. Since many NP-hard problems, such as Max-Cut and Vertex Cover, can be reformulated as spin glass systems, understanding these dynamics offers broader insights into designing effective heuristics for complex optimization problems.