Inverse Problems on Networks with Self-Loops and Related Problems in Electrical Impedance Tomography
Date of Award
5-2026
Document Type
Thesis
Degree Name
Bachelor of Arts (BA)
Department
Natural Sciences
First Advisor
McDonald, Patrick
Area of Concentration
Mathematics and Physics
Abstract
The central topic of this thesis is the inverse problem for random walks on graphs, i.e. finding the transition probabilities of some Markov chain restricted to a rooted tree graph with known topology and a set of joint distributions of first hitting time and hitting place. It has already been shown by de la Peña et al. in the case where self-transitions are prohibited that the transition probabilities of such a Markov chain can be determined given these joint distributions on two ’boundary layers.’ This thesis proves that the problem can be solved for Markov chains allowing self-transitions, via an extension of de la Peña and via probability generating functions. The two methods are compared. Previous work on similar problems for more general graph structures and related topics in Electrical Impedance Tomography are also discussed.
Recommended Citation
Steen, Hope, "Inverse Problems on Networks with Self-Loops and Related Problems in Electrical Impedance Tomography" (2026). Theses & ETDs. 6948.
https://digitalcommons.ncf.edu/theses_etds/6948
Rights
The author has granted New College of Florida the nonexclusive right to archive, make accessible, and distribute for educational purposes this work in whole or in part in all forms of media, now or hereafter known. The copyright of this work remains with the author.