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Freya Jensen

Publications and source records attributed to Freya Jensen.

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Persistent Homology as a Morphological Signature of Fibrin Networks

We present an investigation of the applicability of topological data analysis (TDA) to the study of high-resolution confocal microscopy images of fibrin network structures from patients with oesophageal cancer undergoing intended curative surgery. Investigation of clot structure brings new knowledge about blood coagulation, risk of bleeding, and thrombosis in this group of patients. Images of fibrin network formation in the collected blood samples were captured by confocal microscopy and three-dimensional z-stacks were analysed. Each z-stack was cropped to a centre region for analysis, the validity of which is assessed in detail. Overall, we found no significant differences in fibrin network topology across the perioperative period, and no consistent differences in network structure between the standard and intervention groups.

q-bio.OT

Distributed Persistent Homology for 2D Alpha Complexes

We introduce a new algorithm to parallelise the computation of persistent homology of 2D alpha complexes. Our algorithm distributes the input point cloud among the cores which then compute a cover based on a rectilinear grid. We show how to compute the persistence Mayer-Vietoris spectral sequence from these covers and how to obtain persistent homology from it. For this, we introduce second-page collapse conditions and explain how to solve the extension problem. Finally, we give an overview of an implementation in C++ using Open MPI and discuss some experimental results.

math.AT