Topological Representations of Temporal Data with Applications to Biological Spheroid Dynamics
Author
Knudsen, Theresa Reinhold
Term
4. term
Education
Publication year
2026
Submitted on
2026-05-27
Pages
49
Abstract
This thesis explores how to describe the shape and connectivity (topology) of data that change over time. We introduce a new topological representation and formulate a theorem about the method's stability, meaning the results are robust to small changes in the input data. Using both established and new techniques, we analyze time-lapse imaging data that track how endothelial cell structures (the cells lining blood vessels) evolve under different external stimuli. In our analyses, the methods did not detect any topology-based differences in the cells' dynamics that could be attributed to changes in stimulus.
Dette speciale undersøger, hvordan man kan beskrive form og sammenhæng (topologi) i data, der ændrer sig over tid. Vi introducerer en ny topologisk repræsentation og formulerer en sætning om metodens stabilitet, dvs. at resultaterne er robuste over for små ændringer i inputdata. Med både etablerede og nye metoder analyserer vi billeddata over tid, der viser, hvordan endotelcellestrukturer (celler, der beklæder blodkar) udvikler sig under forskellige ydre påvirkninger. I vores analyser kunne metoderne ikke påvise nogen topologiske forskelle i cellernes dynamik, som kunne forklares med ændringer i påvirkningen.
[This apstract has been rewritten with the help of AI based on the project's original abstract]