Bernadette J. Stolz

May 09, 2025

Title: Topological learning for spatial data

Abstract: Topological data analysis (TDA) has been successfully applied to study many biological phenomena. In this talk I will highlight two recent applications to spatial data from oncology, including synthetic and real-world data. The first application is a case study of topological model selection in tumour-induced angiogenesis, the process in which blood vessel networks are formed during tumour growth. While many mathematical models of tumour-induced angiogenesis exist, significant challenges persist in objectively evaluating and comparing their outputs. We showcase a combination of TDA and approximate Bayesian Computation for parameter inference and model selection. In the second application I will present two techniques in relational TDA that we develop to encode spatial heterogeneity of multispecies data. Our approaches are based on Dowker complexes and Witness complexes. We demonstrate that relational TDA features can extract biological insight, including dominant immune cell phenotype (an important predictor of patient prognosis) and parameter regimes in a data-generating model of tumour-immune cell interactions. Our pipelines can be combined with graph neural networks (GNN), a popular machine learning approach for spatial data. I will present how we can incorporate local relational TDA into a GNN and significantly enhance its performance on real-world data.

Keywords: Topological learning, Bayesian Computation, Oncology, Spatial heterogeneity, Multispecies data.

Dante Chialvo

May 23, 2025

Title: TBA

Abstract: TBA

Keywords: TBA.

María del Rocío González Díaz

June 6, 2025

Title: Topology-based Optimization for Robot Fleet Behavior

Abstract: In this talk, I introduce novel topological methods for the analysis of robot fleet behaviors simulated using Navground software [1]. Our aim is to understand and improve the evolution of robot fleet behaviors to, for example, reduce unintended behaviors such as collisions and deadlocks. Understanding the robot fleet's dynamics will allow us to predict safer and more efficient routes for robot displacement. To achieve this, we propose employing TDA techniques such as persistent homology, block functions induced by persistence morphisms, and persistent entropy. These methods leverage the geometric and topological structure of the data, allowing us to capture high-level spatial and relational patterns in agent behaviors and configurations. Unlike classical approaches, which often rely on predefined features or statistical assumptions, TDA provides an interpretable framework that can highlight qualitative differences in the robot fleet's dynamics. While we do not claim definitive performance improvements over traditional methods, the added interpretability and the ability to capture intrinsic spatial structures make these techniques particularly suitable for characterizing different agent behaviors and ensuring safe and efficient simulations. This work is part of the European Project 'REliable & eXplainable Swarm Intelligence for People with Reduced mObility - REXASIPRO [2].
[1] https://idsia-robotics.github.io/navground/_build/html/index.html
[2] https://cordis.europa.eu/project/id/101070028

Keywords: Topological data analysis, persistent homology, persistent divergence, reliability and explainability, robot fleet behaviour..