Jessica (Jesse) Dohmann is currently pursuing two bachelor of science degrees at the University of Texas at Austin, one in physics with an emphasis on radiation and health physics, and another in mathematics with an emphasis on statistics and data analysis. She was first introduced to scientific research through the Freshmen Research Initiative program at UT Austin, working in an astronomy lab that specializes in white dwarf stars, specifically looking at the theoretical framework of stellar evolution simulations. She has also done numerous mathematical projects on elliptic PDEs, Monte Carlo methods, and Poisson processes.
In her free time, she does a lot of science outreach in the city of Austin and writes about mathematics and technology on her blog. She also enjoys going out to listen to the best blues music Austin has to offer, as well as reading books and papers on philosophy, particularly focusing on post-Kantian continental works, and likes to think about how these ideas apply to the paradigm of modern science.
Project: Inverse Problem and Learning in Random Probabilistic Automata
In probabilistic cellular automata, the rule that specifies the probabilities for each color of the cell to be generated in a state is determined by the colors of its neighboring cells from the previous state. This implies that each time the cellular automaton (CA) is run, a new distinct pattern will emerge. However, each probabilistic CA will have an overall pattern that can be determined after enough cells have been generated. The goal of this project is to investigate the directed percolation of probabilistic cellular automata from an initial state that results in a particular output pattern. A new rule will then be applied that will allow for replication of this output directly through a deterministic CA. This is known as the inverse problem, and could be related to machine learning in cellular automata, much like artificial neural networks.