ArticlePloS one2015
Topological data analysis of biological aggregation models.
Article in PloS one, 2015. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 42 papers.
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Who cites it
42 citing papers in PubMed.
- Topologically-based parameter inference for agent-based model selection from spatiotemporal cellular data.PLoS computational biology · 2026Article
- Node persistence from topological data analysis reveals changes in brain functional connectivity.Patterns (New York, N.Y.) · 2026Article
- Topological model selection: a case-study in tumour-induced angiogenesis.Bioinformatics (Oxford, England) · 2026Article
- Article
- Persistent Homology Classifies Parameter Dependence of Patterns in Turing Systems.Bulletin of mathematical biology · 2025Article
- Topology across scales on heterogeneous cell data.PLoS computational biology · 2025Article
- Migrating mesoderm cells self-organize into a dynamic meshwork structure during chick gastrulation.eLife · 2025Article
- Topological classification of tumour-immune interactions and dynamics.Journal of mathematical biology · 2025Article
- Spatial and Sequential Topological Analysis of Molecular Dynamics Simulations of IgG1 Fc Domains.Journal of chemical theory and computation · 2025Article
- Neurospectrum: A Geometric and Topological Deep Learning Framework for Uncovering Spatiotemporal Signatures in Neural Activity.bioRxiv : the preprint server for biology · 2025Article
- Position: Topological Deep Learning is the New Frontier for Relational Learning.Proceedings of machine learning research · 2024Article
- Topological Embedding of Human Brain Networks with Applications to Dynamics of Temporal Lobe Epilepsy.ArXiv · 2024Article
- Quantifying collective motion patterns in mesenchymal cell populations using topological data analysis and agent-based modeling.Mathematical biosciences · 2024Article
- Vision-based collective motion: A locust-inspired reductionist model.PLoS computational biology · 2024Article
- Unified topological inference for brain networks in temporal lobe epilepsy using the Wasserstein distance.NeuroImage · 2023Article
- Topological Data Analysis for Multivariate Time Series Data.Entropy (Basel, Switzerland) · 2023Article
- Topological data analysis of spatial patterning in heterogeneous cell populations: clustering and sorting with varying cell-cell adhesion.NPJ systems biology and applications · 2023Article
- Zigzag persistence for coral reef resilience using a stochastic spatial model.Journal of the Royal Society, Interface · 2023Article
- Article
- Temporal Mapper: Transition networks in simulated and real neural dynamics.Network neuroscience (Cambridge, Mass.) · 2023Article
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Authors and funding
3 authors.
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No grant is acknowledged in the PubMed record.
Abstract
We apply tools from topological data analysis to two mathematical models inspired by biological aggregations such as bird flocks, fish schools, and insect swarms. Our data consists of numerical simulation output from the models of Vicsek and D'Orsogna. These models are dynamical systems describing the movement of agents who interact via alignment, attraction, and/or repulsion. Each simulation time frame is a point cloud in position-velocity space. We analyze the topological structure of these point clouds, interpreting the persistent homology by calculating the first few Betti numbers. These Betti numbers count connected components, topological circles, and trapped volumes present in the data. To interpret our results, we introduce a visualization that displays Betti numbers over simulation time and topological persistence scale. We compare our topological results to order parameters typically used to quantify the global behavior of aggregations, such as polarization and angular momentum. The topological calculations reveal events and structure not captured by the order parameters.
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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.