We consider the linear third order (in time) PDE known as the SMGTJequation, defined on a bounded domain, under the action of either Dirichlet or Neumann boundary control
One approach to understanding complex data is to study its shape through the lens of algebraic topology. While the early development of topological data analysis focused primarily on static data, in recent years, theoretical and applied studies have turned to data that varies in time. A timevarying collection of metric spaces as formed, for example, by a moving school of fish or flock of birds, can contain a vast amount of information. There is often a need to simplify or summarize the dynamic behavior. We provide an introduction to topological summaries of timevarying metric spaces including vineyards [
 Award ID(s):
 1934725
 NSFPAR ID:
 10388958
 Date Published:
 Journal Name:
 Foundations of Data Science
 Volume:
 4
 Issue:
 1
 ISSN:
 26398001
 Page Range / eLocation ID:
 1
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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