Comprehensive Exam of CMSE David E. Muñoz
Department of Computational Mathematics, Science & Engineering
Michigan State University
Comprehensive Exam Notice
March 18, 2024 – 10:00 AM
CMSE Room 1502
Zoom link: https://msu.zoom.us/j/92824900556
Passcode: 220554
Topological Methods for Network Analysis
David E. Muñoz
Abstract:Networks are essential structures in many fields, such as biology, economics, neuroscience, and electrical and mechanical engineering. There are numerous datasets that can be interpreted in the form of networks or graphs, and these graphs may change with time or be augmented with direction or weight information. It is key to understand the practical meaning of the structure within these networks. The main goal of this research is to propose new methods and techniques to apply persistent homology to analyze and highlight structure within networks. We present the completed work in two main components: a study on zigzag persistence applied to temporal network data and a proposed filtration for persistence on directed graphs called walk-length filtration. We also give a general framework for extending the study on walk-length persistence and developing a framework for implementing this method in different applications.
Committee:
Elizabeth Munch (chair)
Firas Khasawneh
Mengsen Zhang
Ekaterina Rapinchuk
