@article{21115,
  abstract     = {Quantifying cell morphology is central to understanding cellular regulation, fate, and heterogeneity, yet conventional image-based analyses often struggle with diverse or irregular shapes. We present a computational framework that uses topological data analysis to characterise and compare single-cell morphologies from fluorescence microscopy. Each cell is represented by its contour together with the position of its nucleus, from which we construct a filtration based on a radial distance function and derive a persistence diagram encoding the shape’s topological evolution. The similarity between two cells is quantified using the 2-Wasserstein distance between their diagrams, yielding a shape distance we call the PH distance. We apply this method to two representative experimental systems—primary human mesenchymal stem cells (hMSCs) and HeLa cells—and show that PH distances enable the detection of outliers in those systems, the identification of sub-populations, and the quantification of shape heterogeneity. We benchmark PH against three established contour-based distances (aspect ratio, Fourier descriptors, and elastic shape analysis) and show that PH offers better separation between cell types and greater robustness when clustering heterogeneous populations. Together, these results demonstrate that persistent-homology-based signatures provide a principled and sensitive approach for analysing cell morphology in settings where traditional geometric or image-based descriptors are insufficient.},
  author       = {Bleile, Yossi and Yadav, Pooja and Koehl, Patrice and Rehfeldt, Florian},
  issn         = {1553-7358},
  journal      = {PLoS Computational Biology},
  publisher    = {Public Library of Science},
  title        = {{Persistence diagrams as morphological signatures of cells: A method to measure and compare cells within a population}},
  doi          = {10.1371/journal.pcbi.1013890},
  volume       = {22},
  year         = {2026},
}

@article{21232,
  abstract     = {<jats:title>Abstract</jats:title>
                  <jats:p>In this paper, we consider a simple class of stratified spaces – 2-complexes. We present an algorithm that learns the abstract structure of an embedded 2-complex from a point cloud sampled from it. We use tools and inspiration from computational geometry, algebraic topology, and topological data analysis and prove the correctness of the identified abstract structure under assumptions on the embedding.</jats:p>},
  author       = {Bleile, Yossi},
  issn         = {2730-9657},
  journal      = {La Matematica},
  publisher    = {Springer Nature},
  title        = {{Towards stratified space learning: 2-complexes}},
  doi          = {10.1007/s44007-025-00183-9},
  volume       = {5},
  year         = {2026},
}

@misc{21971,
  abstract     = {A Rust library for analyzing dendritic structures using quadric matrices. This project provides efficient tools for representing dendritic trees, computing quadric error metrics, and visualizing eigenvalue distributions on hexagonal plots.

This library implements quadric-based geometric analysis of dendritic structures, commonly found in neuroscience applications. Key features include:

Tree data structures: Hierarchical vertex and edge representations for dendritic trees
Quadric matrices: Computation of quadric error metrics for edges and vertices
Visualisation: Hexagonal plot generation using NormPolar transformations
Interactive tools: Desktop application with plotting capabilities},
  author       = {Bleile, Yossi and Cortinovis, Emanuele},
  keywords     = {quadratics, mathematics, dendrites, geometry, topology},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{Quadrix}},
  doi          = {10.15479/AT-ISTA-21971},
  year         = {2026},
}

@unpublished{21016,
  abstract     = {Motivated by applications in chemistry, we give a homlogical definition of tunnels, or more generally cobordisms, connecting disjoint parts of a cell complex. For a filtered complex, this defines a persistence module. We give a method for identifying birth and death times using kernel persistence and a matrix reduction algorithm for pairing birth and death times.},
  author       = {Bleile, Yossi and Fajstrup, Lisbeth and Heiss, Teresa and Svane, Anne Marie and Sørensen, Søren Strandskov},
  booktitle    = {arXiv},
  title        = {{Identifying cobordisms using kernel persistence}},
  doi          = {10.48550/arXiv.2505.17858},
  year         = {2025},
}