arXiv subjects

Yossi Bokor Bleile

Publications and source records attributed to Yossi Bokor Bleile.

5 recordsLinked to original sources

arXiv2026

Quadratic Forms for Measuring Geometric Trees in 3-dimensional Space

Tree-like structures appear in many areas of science, and their shapes can help understand the underlying processes they drive or that give rise to them. By thinking of these structures as geometric graphs in $\mathbb{R}^3$, we gain access to tools from computational geometry and topology to study them. In this paper, we adopt the theory of quadratic forms to measure the directional spread of geometric graphs, and we introduce the hexplot model -- equipped with a metric derived from the Fisher metric on the standard triangle -- to visualize, measure, and collect statistics.

cs.CG↗

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

Persistence diagrams as morphological signatures of cells: A method to measure and compare cells within a population

Cell biologists study in parallel the morphology of cells with the regulation mechanisms that modify this morphology. Such studies are complicated by the inherent heterogeneity present in the cell population. It remains difficult to define the morphology of a cell with parameters that can quantify this heterogeneity, leaving the cell biologist to rely on manual inspection of cell images. We propose an alternative to this manual inspection that is based on topological data analysis. We characterise the shape of a cell by its contour and nucleus. We build a filtering of the edges defining the contour using a radial distance function initiated from the nucleus. This filtering is then used to construct a persistence diagram that serves as a signature of the cell shape. Two cells can then be compared by computing the Wasserstein distance between their persistence diagrams. Given a cell population, we then compute a distance matrix that includes all pairwise distances between its members. We analyse this distance matrix using hierarchical clustering with different linkage schemes and define a purity score that quantifies consistency between those different schemes, which can then be used to assess homogeneity within the cell population. We illustrate and validate our approach to identify sub-populations in human mesenchymal stem cell populations.

q-bio.QM↗

arXiv2025

Identifying cobordisms using kernel persistence

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.

math.AT↗

arXiv2023

Towards Stratified Space Learning: 2-complexes

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.

cs.CG↗