The development of novel aqueous cross-coupling strategies has emerged as a rapidly expanding area of research within organic synthesis. However, many of these cross-coupling reactions require the pre-formation of an organohalide substrate, which often involves toxic halogenating reagents and harsh reaction conditions. This work details the development of a tandem halogenation/cross-coupling procedure in which an electron-rich arene or heteroarene is brominated through an enzymatic halogenation reaction catalyzed by a vanadium dependent haloperoxidase (VHPO) and then used without workup in a subsequent aqueous Suzuki cross-coupling reaction. This sequential process allows the arylated product to be accessed in a single pot from the unfunctionalized substrate via the brominated intermediate. Optimization of the enzymatic halogenation step was performed for three different substrates, resulting in the discovery of conditions for the bromination of 2,3-dihydrobenzofuran, chromane, and anisole in high yield (>95%). The scope of the reaction was then investigated for a range of electron-rich arene and heteroarene substrates. Next, Suzuki cross-coupling conditions were developed in a reaction mixture of pH 5 citrate buffer and acetonitrile and applied to the arylation of 2,3-dihydrobenzofuran utilizing an array of arylboronic acid coupling partners. Finally, the two procedures were combined to perform a tandem enzymatic halogenation/aqueous Suzuki cross-coupling of 2,3-dihydrobenzofuran to give the arylated product in 74% yield.

The classical double copy maps exact solutions of general relativity to exact solutions of U(1) Yang-Mills theory and suggests a hitherto unknown connection between gravity and gauge theory. In this thesis I study three problems using the Kerr-Schild and Weyl formulations of the classical double copy. Using the Kerr-Schild double copy, I analyze the single copy of a rotating nonsingular black hole and analyze its horizon structure to probe the relationship between the presence of horizons on the gravity side and the single copy field on the gauge theory side. In the second problem I describe the mapping between the surface gravity of static spherically symmetric black holes and the force on a test particle due to the single copy field of the black hole. I also describe potential routes to extending this map to rotating black holes. Finally, inspired by the extended Weyl double copy for spacetimes possessing sources, I reinterpret the single copy of the Taub- NUT metric as being comprised of two terms each being sourced by a separate parameter (the mass and the NUT charge).

The focus of my honors thesis is to find ways to use deep learning in tandem with tools in statistical mechanics to derive new ways to solve problems in biophysics. More specifically, I’ve been interested in finding transition pathways between two known states of a biomolecule. This is because understanding the mechanisms in which proteins fold and ligands bind is crucial to creating new medicines and understanding biological processes. In this thesis, I work with individuals in the Singharoy lab to develop a formulation to utilize reinforcement learning and sampling-based robotics planning to derive low free energy transition pathways between two known states. Our formulation uses Jarzynski’s equality and the stiff-spring approximation to obtain point estimates of energy, and construct an informed path search with atomistic resolution. At the core of this framework, is our first ever attempt we use a policy driven adaptive steered molecular dynamics (SMD) to control our molecular dynamics simulations. We show that both the reinforcement learning (RL) and robotics planning realization of the RL-guided framework can solve for pathways on toy analytical surfaces and alanine dipeptide.

For my Honors Thesis, I decided to create an Artificial Intelligence Project to predict Fantasy NFL Football Points of players and team's defense. I created a Tensorflow Keras AI Regression model and created a Flask API that holds the AI model, and a Django Try-It Page for the user to use the model. These services are hosted on ASU's AWS service. In my Flask API, it actively gathers data from Pro-Football-Reference, then calculates the fantasy points. Let’s say the current year is 2022, then the model analyzes each player and trains on all data from available from 2000 to 2020 data, tests the data on 2021 data, and predicts for 2022 year. The Django Website asks the user to input the current year, then the user clicks the submit button runs the AI model, and the process explained earlier. Next, the user enters the player's name for the point prediction and the website predicts the last 5 rows with 4 being the previous fantasy points and the 5th row being the prediction.

This document is a guide that can be used by undergraduate physics students alongside Richard J. Jacob and Professor Emeritus’s Tutorials in the Mathematical Methods of Physics to aid in their understanding of the key mathematical concepts from PHY201 and PHY302. This guide can stand on its own and be used in other upper division physics courses as a handbook for common special functions. Additionally, we have created several Mathematica notebooks that showcase and visualize some of the topics discussed (available from the GitHub link in the introduction of the guide).