Martin Hermann | Searcharxiv

arXiv2026

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↗

arXiv2025

Qualitative and Quantitative Analysis of Riemannian Optimization Methods for Ground States of Rotating Multicomponent Bose-Einstein Condensates

We develop and analyze Riemannian optimization methods for computing ground states of rotating multicomponent Bose-Einstein condensates, defined as minimizers of the Gross-Pitaevskii energy functional. To resolve the non-uniqueness of ground states induced by phase invariance, we work on a quotient manifold endowed with a general Riemannian metric. By introducing an auxiliary phase-aligned iteration and employing fixed-point convergence theory, we establish a unified local convergence framework for Riemannian gradient descent methods and derive explicit convergence rates. Specializing this framework to two metrics tailored to the energy landscape, we study the energy-adaptive and Lagrangian-based Riemannian gradient descent methods. While monotone energy decay and global convergence are established only for the former, a quantified local convergence analysis is provided for both methods. Numerical experiments confirm the theoretical results and demonstrate that the Lagrangian-based method, which incorporates second-order information on the energy functional and mass constraints, achieves faster local convergence than the energy-adaptive scheme.

math.NA↗