arXiv subjects

Simon J. Leedham

Publications and source records attributed to Simon J. Leedham.

2 recordsLinked to original sources

arXiv2026

Topology of Multi-species Localization

Spatial relationships in multi-species data can indicate and affect system outcomes and behaviors, ranging from disease progression in cancer to coral reef resilience in ecology; therefore, quantifying these relationships is an important problem across scientific disciplines. Persistent homology (PH), a key mathematical and computational tool in topological data analysis (TDA), provides a multiscale description of the shape of data. While it effectively describes spatial organization of species, such as cellular patterns in pathology, it cannot detect the shape relations between different types of species. Traditionally, PH analyzes single-species data, which limits the spatial analysis of interactions between different species. Leveraging recent developments in TDA and computational geometry, we introduce a scalable approach to quantify higher-order interactions in multi-species data. The framework can distinguish the presence of shape features or patterns in the data that are (i) common to multiple species of points, (ii) present in some species but disappear in the presence of other species, (iii) only visible when multiple species are considered together, and (iv) formed by some species and remain visible in the presence of others. We demonstrate our approach on two example applications. We identify (1) different behavioral regimes in a synthetic tumor micro-environment model, and (2) interspecies spatial interactions that are most significantly altered in colorectal cancer tissue samples during disease progression.

math.AT↗

arXiv2025

TopROI: A topology-informed network approach for tissue partitioning

Mammalian tissue architecture is central to biological function, and its disruption is a hallmark of disease. Medical imaging techniques can generate large point cloud datasets that capture changes in the cellular composition of such tissues with disease progression. However, regions of interest (ROIs) are usually defined by quadrat-based methods that ignore intrinsic structure and risk fragmenting meaningful features. Here, we introduce TopROI, a topology-informed, network-based method for partitioning point clouds into ROIs that preserves both local geometry and higher-order architecture. TopROI integrates geometry-informed networks with persistent homology, combining cell neighbourhoods and multiscale cycles to guide community detection. Applied to synthetic point clouds that mimic glandular structure, TopROI outperforms quadrat-based and purely geometric partitions by maintaining biologically plausible ROI geometry and better preserving ground-truth structures. Applied to cellular point clouds obtained from human colorectal cancer biopsies, TopROI generates ROIs that preserve crypt-like structures and enable persistent homology analysis of individual regions. This study reveals a continuum of architectural changes from healthy mucosa to carcinoma, reflecting progressive disorganisation in tissue structure. TopROI thus provides a principled and flexible framework for defining biologically meaningful ROIs in large point clouds, enabling more accurate quantification of tissue organization and new insights into structural changes associated with disease progression.

q-bio.QM↗