Lipschitz Functions Have L p -Stable Persistence

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Computing Persistent Homology

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A High-Resolution Root Spatiotemporal Map Reveals Dominant Expression Patterns

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On the Translocation of Masses

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The Segmentation Clock: Converting Embryonic Time into Spatial Pattern

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A Complex Oscillating Network of Signaling Genes Underlies the Mouse Segmentation Clock

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Joint Geometric and Topological Analysis of Hierarchical Datasets

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Application of Persistent Homology in Signal and Image Denoising

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Topology data analysis of critical transitions in financial networksPreprint

Gidea, M. (2017) · RePEc: Research Papers in Economics · doi:10.48550/arxiv.1701.06081 · Cited by 2

Estimation and Quantization of Expected Persistence DiagramsPreprint

Divol, V., & Lacombe, T. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2105.04852 · Cited by 2

Harmonic Persistent Homology (extended abstract)

Basu, S., & Cox, N. (2022) · Annual Symposium on Foundations of Computer Science · doi:10.1109/focs52979.2021.00110 · Cited by 1

Topological Elastic Graph Convolutional Networks for Spatial-Temporal Sequence Forecasting

Wang, Y., Xu, M., & Tang, L. (2024) · IEEE Transactions on Emerging Topics in Computational Intelligence · doi:10.1109/tetci.2024.3449900 · Cited by 1

Topology-based analysis and optimization for agent fleet behavior

Perera-Lago, J., Toscano-Durán, V., Torras-Casas, Á., & González-Dı́az, R. (2025) · Open Research Europe · doi:10.12688/openreseurope.20760.1 · Cited by 1

Explorative Analysis of Dynamic Force Networks in 2D Photoelastic Disks Ensembles

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A persistent homology design space for 3D point cloud deep learning

Kudeshia, P., Peethambaran, J., Ghoneim, A., & Chen, D. (2026) · Computers & Graphics · doi:10.1016/j.cag.2026.104718 · Cited by 1

On the distribution of local extrema in Quantum Chaos

Pausinger, F., & Steinerberger, S. (2014) · Physics Letters A · doi:10.1016/j.physleta.2014.12.010 · Cited by 1

Discovering Metrics and Scale Space

Fasy, B. T. (2010) · Cited by 1

Sinkhorn Divergence of Topological Signature Estimates for Time Series Classification

Stephen, C. (2018) · International Conference on Machine Learning and Applications · doi:10.1109/icmla.2018.00113 · Cited by 1

Topological Correction of Subject-Level Intrinsic Connectivity Networks

Lewis, N., Iraji, A., Miller, R. L., & Calhoun, V. D. (2023) · IEEE International Symposium on Biomedical Imaging (ISBI) · doi:10.1109/isbi53787.2023.10230598 · Cited by 1

Topological data analysis of human vowels: Persistent homologies across representation spaces

Bonafos, G., Pudlo, P., Freyermuth, J., Tronçon, S., & Rey, A. (2026) · Speech Communication · doi:10.1016/j.specom.2026.103363 · Cited by 1

Ladder decomposition for morphisms of persistence modules

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Empowering High-Throughput High-Content Analysis of Microphysiological Models: Open-Source Software for Automated Image Analysis of Microvessel Formation and Cell Invasion

Wiggin, N., Cook, C., Black, M., Cadena, I., Rahal-Arabi, S., Asnes, C. L., Ivanova, Y. I., Hettiaratchi, M. H., Hind, L. E., & Fogg, K. C. (2024) · Cellular and Molecular Bioengineering · doi:10.1007/s12195-024-00821-2 · Cited by 1

Multi-Field Visualization: Trait Design and Trait-Induced Merge Trees

Lei, D., Jankowai, J., Hristov, P., Carr, H. A., Denby, L., Masood, T. B., & Hotz, I. (2025) · IEEE Transactions on Visualization and Computer Graphics · doi:10.1109/tvcg.2025.3525974 · Cited by 1

Suspension models for testing shape similarity methods

Ethier, M., & Kaczyński, T. (2014) · Computer Vision and Image Understanding · doi:10.1016/j.cviu.2013.12.007 · Cited by 1

Asymptotic Improvements on the Exact Matching Distance for 2-parameter Persistence

Bjerkevik, H. B., & Kerber, M. (2021) · Journal of computational geometry · doi:10.20382/jocg.v14i1a12 · Cited by 1

Investigation of Computational Topology for Data Analysis and Visualization Applications

Robin, K. (2021) · Mathematical Statistician and Engineering Applications · doi:10.17762/msea.v70i1.2517 · Cited by 1

Persistence Diagrams and the Heat Equation HomotopyPreprint

Fasy, B. T. (2010) · arXiv (Cornell University) · doi:10.48550/arxiv.1002.1937 · Cited by 1

Modes of gaussian mixtures and an inequality for the distance between curves in space

Edelsbrunner, H., & Fasy, B. T. (2012) · Cited by 1

Stabilizing the output of persistent homology computations.Preprint

Bendich, P. L., & Bubenik, P. (2015) · arXiv (Cornell University) · Cited by 1

Methods detecting rhythmic gene expression are biologically relevant only for strong signalPreprint

Laloum, D., & Robinson‐Rechavi, M. (2019) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/730937 · Cited by 1

Towards Interaction Detection Using Topological Analysis on Neural NetworksPreprint

Liu, Z., Song, Q., Zhou, K., Wang, T.-H., Shan, Y., & Hu, X. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2010.13015 · Cited by 7

$\ell^p$-Distances on Multiparameter Persistence ModulesPreprint

Bjerkevik, H. B., & Lesnick, M. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2106.13589 · Cited by 9

Noise robustness of persistent homology on greyscale images, across filtrations and signaturesPreprint

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A Metric for Tree-Like Topological SummariesPreprint

Pegoraro, M. (2021) · arXiv (Cornell University) · Cited by 1

Topological Node2vec: Enhanced Graph Embedding via Persistent HomologyPreprint

Hiraoka, Y., Imoto, Y., Meehan, K., Lacombe, T., & Yachimura, T. (2023) · arXiv (Cornell University) · doi:10.48550/arxiv.2309.08241 · Cited by 1

Empowering high-throughput high-content analysis of 3D tumor models: Open-source software for automated non-confocal image analysisPreprint

Wiggin, N., Cook, C., Black, M., Cadena, I., Rahal-Arabi, S., & Fogg, K. C. (2024) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2024.02.20.581231 · Cited by 1

Topological Data Analysis of Protein Structure Manifolds from Molecular Dynamics Computer SimulationPreprint

Sino, M., & Kamberaj, H. (2025) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2025.07.12.664527 · Cited by 1

Capturing Shape Information with Multi-scale Topological Loss Terms for 3D Reconstruction

Waibel, D., Atwell, S. X., Meier, M., Marr, C., & Rieck, B. (2022) · Lecture notes in computer science · doi:10.1007/978-3-031-16440-8_15

Shape Reconstruction with Topological Priors

Zheng, Y. (2012) · DukeSpace (Duke University)

Separating features from noise with persistence and statistics

Wang, B. (2010)

Local Extrema in Quantum ChaosPreprint

Pausinger, F., & Steinerberger, S. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1406.4673

Coordinate-Free Quantification of Coverage in Dynamic Sensor NetworksPreprint

Gamble, J., Chintakunta, H., & Krim, H. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1411.7337

On $C^0$-persistent homology and treesPreprint

Perez, D. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2012.02634

A Domain-Oblivious Approach for Learning Concise Representations of Filtered Topological Spaces.Preprint

Qin, Y. C., Fasy, B. T., Wenk, C., & Summa, B. (2021) · arXiv (Cornell University)

A Domain-Oblivious Approach for Learning Concise Representations of Filtered Topological Spaces for ClusteringPreprint

Qin, Y. C., Fasy, B. T., Wenk, C., & Summa, B. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2105.12208

Report on scipost_202102_00007v2

Spitz, D., Berges, J., Oberthaler, M. K., et al. (2021) · SciPost Physics · doi:10.21468/scipost.report.3454

Multi-Field Visualisation Via Trait-Induced Merge TreesPreprint

Jankowai, J., Masood, T. B., & Hotz, I. (2022) · SSRN Electronic Journal · doi:10.2139/ssrn.4088389

Multi-Field Visualisation Via Trait-Induced Merge TreesPreprint

Jankowai, J., Masood, T. B., & Hotz, I. (2022) · SSRN Electronic Journal · doi:10.2139/ssrn.4088390

Report on scipost_202102_00007v1

Spitz, D., Berges, J., Oberthaler, M. K., et al. (2021) · SciPost Physics · doi:10.21468/scipost.report.2838

Report on scipost_202102_00007v1

Spitz, D., Berges, J., Oberthaler, M. K., et al. (2021) · SciPost Physics · doi:10.21468/scipost.report.2534

Local Versus Global Distances for Zigzag and Multi-Parameter Persistence Modules

Gasparovic, E., Gommel, M., Purvine, E., Sazdanović, R., Wang, B., Wang, Y., & Ziegelmeier, L. (2022) · Association for Women in Mathematics series · doi:10.1007/978-3-030-95519-9_3

Autoencoder-Aided Visualization of Collections of Morse Complexes

Li, J., Boxel, D. V., & Levine, J. A. (2022) · Topological Data Analysis and Visualization (TopoInVis) · doi:10.1109/topoinvis57755.2022.00009

Topological Analysis of Simple Segmentation Maps

Jiménez, M.-J., & Medrano, B. (2022) · Lecture notes in computer science · doi:10.1007/978-3-031-19897-7_11

On the estimation of persistence intensity functions and linear representations of persistence diagrams

Wu, W., Kim, J., & Rinaldo, A. (2023) · PubMed · doi:10.48550/arxiv.2310.11982

Head Direction Cells and Grid Cells as the Core Components of the Core-periphery StructurePreprint

Qian, R., Chen, Y., Wang, T., Wang, W., & Liu, F. (2023) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2023.11.21.568067

State Dependent Delay Maps: Numerical Algorithms and Dynamics of Projections

James, J. D. M., Motta, F. C., & Naudot, V. (2024) · Experimental Mathematics · doi:10.1080/10586458.2024.2337910

The Internal Topology of Rocks

Korvin, G. (2024) · Earth and environmental sciences library · doi:10.1007/978-3-031-46700-4_3

Topology-based segmentation of 3D confocal images of emerging hematopoietic stem cells in the zebrafish embryo

Nardi, G., Torcq, L., Schmidt, A., & Olivo‐Marín, J. (2024) · Biological Imaging · doi:10.1017/s2633903x24000102

Algebraic Wasserstein distances and stable homological invariants of data

Agerberg, J., Guidolin, A., Ren, I., & Scolamiero, M. (2025) · Journal of Applied and Computational Topology · doi:10.1007/s41468-024-00200-w

Convergence of persistence diagrams for discrete time stationary processes

Thomas, A. M. (2025) · Journal of Applied and Computational Topology · doi:10.1007/s41468-025-00211-1

Computing p-Presentation Distances is Hard

Bjerkevik, H. B., & Botnan, M. B. (2025) · Discrete & Computational Geometry · doi:10.1007/s00454-025-00744-3

Computational topology of Drosophila melanogaster embryos: Emergent anatomy from the spatiotemporal distributions of hemocytes

Hu, X., Nickolay Korabel, A., Millard, T. H., & Waigh, T. A. (2025) · Physical review. E · doi:10.1103/mc9z-kw1q

Topologically Optimized Intrinsic Brain Networks

Lewis, N., Iraji, A., Miller, R. L., Agcaoglu, O., & Calhoun, V. D. (2025) · Human Brain Mapping · doi:10.1002/hbm.70380

Toward a topological data analysis for heavy-ion collisions

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Additional file 5 of Conservation of dynamic characteristics of transcriptional regulatory elements in periodic biological processes

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Topological Structure of the Cyclonic-Anticyclonic InteractionsPreprint

Yadav, H., Charó, G. D., & Faranda, D. (2025) · SSRN Electronic Journal · doi:10.2139/ssrn.5986084

Stability and Inference of the Euler Characteristic Transform

Marsh, L., & Beers, D. (2026) · Discrete & Computational Geometry · doi:10.1007/s00454-025-00763-0

Cusp solitons mediated by a topological nonlinearity

Cao, H., & Leykam, D. (2026) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0303577

Statistics for Topological Descriptors using optimal transport

Lacombe, T. (2020) · doi:10.70675/2a0c608fz69d5z439ez91c3z1556ded8d944

Contributions to geometric inference for manifolds and to the statistical study of persistence diagrams

Divol, V. (2021) · doi:10.70675/7061c574z4e43z40a8zb069za102a26cd652

Two complementary approaches in multi-parameter persistence : interval-decompositions and constructible functions

Lebovici, V. (2023) · theses.fr (ABES) · doi:10.70675/73b3f02fz6061z4912zbceeze596d4068b3d

Topological techniques for inference on periodic functions with phase variation

Reise, W. (2023) · doi:10.70675/346355dcz422fz45a1za211z3db056db0c6d

Analyse biogéométrique de l'évolution des protéines et des traits d'histoire de vie

Dagher, L. B. (2024) · theses.fr (ABES) · doi:10.70675/3a39f4f2zb57dz4fb3z8990zbd5d3fe1a6bf

Hybrid Distance for Classification of Complex Biological Data Based on Elastic Shape Analysis of Curves and Topological Data Analysis of Point Clouds

Choi, Y. J., Bharath, K., & Kurtek, S. (2026) · ICSA book series in statistics · doi:10.1007/978-3-032-06649-7_13

Topological biomarkers for seizure state transitions

Fernández, X., & Mateos, D. (2026) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0326217

A Topology-Preserving Coreset for Kernel Regression in Scientific Visualization

Lyu, W., Gorski, N., Phillips, J. M., & Wang, B. (2026) · IEEE Transactions on Visualization and Computer Graphics · doi:10.1109/tvcg.2026.3694452

Topology enhanced DeepSDF with applications

Dong, W., & Lin, H. (2026) · Computer-Aided Design · doi:10.1016/j.cad.2026.104130

Subpattern matching persistent homology for coupling complexity analysis of multivariate time series

Haruna, T. (2026) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0335719

A COMPARATIVE STUDY OF PERSISTENCE AND MAPPER IN TOPOLOGICAL DATA ANALYSIS

Nizegha, K. M. M., Rathilal, C., & Visaya, M. V. (2026) · Advances in Complex Systems · doi:10.1142/s0219525926500049

Multimodal Diagnostic Overlays for Tabular Deep Learning: Fractal, Spectral, and Reflex-Aware Interpretability

Quinn, H. O., & Sedky, M. (2026) · Electronics · doi:10.3390/electronics15184126

Validating a jointly trained neural Heston calibrator: Persistent homology, no-arbitrage bounds, and a conditioning trap

Garví-Gualda, J. (2026) · Expert Systems with Applications · doi:10.1016/j.eswa.2026.134547

3D CT-GraphEdgeMAE: 3D CT Image Anomaly Detection Using Self-Supervised Graph Edge Mask AutoencodersPreprint

Wu, Q. (2026) · Research Square · doi:10.21203/rs.3.rs-11273413/v1

Predicting Drug-Resistant Tuberculosis Treatment Outcomes: A Leakage-Controlled Evaluation of Topological Data Analysis AugmentationPreprint

Mutakwa, D., Visaya, M. V., & Chirove, F. (2026) · medRxiv · doi:10.64898/2026.10.23.26366286

Nearly-Doubling Spaces of Persistence Diagrams

Sheehy, D. R., & Sheth, S. (2022) · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · doi:10.4230/lipics.socg.2022.60

Topological Difference between Bound and Decoupled States Correlates with Protein–Ligand Binding Affinity

Liu, X., An, N., Tu, Z., & Liu, H. (2026) · The Journal of Physical Chemistry B · doi:10.1021/acs.jpcb.6c03840

Persistent Conformal Geometry and Loewner Evolution

Al-Shbeil, I., Salameh, W. M. M., Emam, W., Saliu, A., & Alderiny, M. (2026) · Journal of Function Spaces · doi:10.1155/jofs/7312931

On bi-Lipschitz stability of families of functions

Valette, G. (2012) · Journal of Singularities · doi:10.5427/jsing.2012.6n · Cited by 2

Wasserstein Stability for Persistence DiagramsPreprint

Škraba, P., & Turner, K. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2006.16824 · Cited by 135

Hausdorff Stability of Persistence Spaces

Cerri, A., & Landi, C. (2015) · Foundations of Computational Mathematics · doi:10.1007/s10208-015-9244-1 · Cited by 12

Stability of persistence spaces of vector-valued continuous functionsPreprint

Cerri, A., & Landi, C. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1305.6425 · Cited by 4

STABILITY OF CLASSES OF LIPSCHITZ MAPPINGS

Korobkov, M. V. (2000)