Useful Links

Please also find our publications at zotero.org/groups/dioscuri-tda.

Journal publications and other published papers:

[1]
A. Mahdi et al., ‘OxCOVID19 Database, a multimodal data repository for better understanding the global impact of COVID-19’, Scientific Reports, vol. 11, p. 9237, 2021, doi: 10.1038/s41598-021-88481-4.
[2]
A. D. Smith, P. Dłotko, and V. M. Zavala, ‘Topological data analysis: Concepts, computation, and applications in chemical engineering’, Computers & Chemical Engineering, vol. 146, p. 107202, 2021, doi: 10.1016/j.compchemeng.2020.107202.
[3]
B. Zieliński, M. Lipiński, M. Juda, M. Zeppelzauer, and P. Dłotko, ‘Persistence codebooks for topological data analysis’, Artificial Intelligence Review, vol. 54, no. 3, pp. 1969–2009, 2021, doi: 10.1007/s10462-020-09897-4.
[4]
R. Khalil, A. Farhat, and P. Dłotko, ‘Developmental changes in pyramidal cell morphology in multiple visual cortical areas using cluster analysis’, Frontiers in Computational Neuroscience, vol. 15, p. 667696, 2021, doi: 10.3389/fncom.2021.667696.
[5]
P. Dłotko, W. Qiu, and S. Rudkin, ‘Financial ratios and stock returns reappraised through a topological data analysis lens’, The European Journal of Finance, 2021, doi: 10.1080/1351847X.2021.2009892.
[6]
R. Khalil, S. Kallel, A. Farhat, and P. Dłotko, ‘Topological Sholl descriptors for neuronal clustering and classification’, PLOS Computational Biology, vol. 18, no. 6, p. e1010229, 2022, doi: 10.1371/journal.pcbi.1010229.
[7]
J. F. Senge, A. Heydari Astaraee, P. Dłotko, S. Bagherifard, and W. A. Bosbach, ‘Extending conventional surface roughness ISO parameters using topological data analysis for shot peened surfaces’, Scientific Reports, vol. 12, p. 5538, 2022, doi: 10.1038/s41598-022-09551-9.
[8]
P. Dłotko, Obrazy funkcji w praktyce, Wydawnictwo Akademia, 2022, available at: link.
[9]
P. Dłotko and N. Hellmer, ‘Bottleneck profiles and discrete Prokhorov metrics for persistence diagrams’, Discrete & Computational Geometry, 2023, doi: 10.1007/s00454-023-00498-w.
[10]
S. Rudkin, D. Webber, and P. Dłotko, ‘Spatial disparities in infection rates at the dawn of a pandemic: wealthy young workers mattered’, Regional Studies, 2023, available at: link.
[11]
D. Woukeng, D. Sadowski, J. Leśkiewicz, M. Lipiński, and T. Kapela, ‘Rigorous computation in dynamics based on topological methods for multivector fields’, Journal of Applied and Computational Topology, vol. 8, pp. 875–908, 2023, doi: 10.1007/s41468-023-00149-2.
[12]
S. Rudkin, W. Qiu, and P. Dłotko, ‘Uncertainty, volatility and the persistence norms of financial time series’, Expert Systems with Applications, vol. 223, p. 119894, 2023, doi: 10.1016/j.eswa.2023.119894.
[13]
S. Rudkin, W. Rudkin, and P. Dłotko, ‘On the topology of cryptocurrency markets’, International Review of Financial Analysis, vol. 89, p. 102759, 2023, doi: 10.1016/j.irfa.2023.102759.
[14]
R. Beckmann, R. Topolnicki, and D. Marx, ‘Deciphering the impact of helium tagging on flexible molecules: Probing microsolvation effects of protonated acetylene by quantum configurational entropy’, The Journal of Physical Chemistry A, vol. 127, no. 11, pp. 2460–2471, 2023, doi: 10.1021/acs.jpca.2c08967.
[15]
P. Bartłomiejczyk, F. L. Trujillo, and J. Signerska-Rynkowska, ‘Spike patterns and chaos in a map–based neuron model’, International Journal of Applied Mathematics and Computer Science, vol. 33, no. 3, pp. 395–408, 2023, doi: 10.34768/amcs-2023-0028.
[16]
P. Dłotko and D. Gurnari, ‘Euler characteristic curves and profiles: A stable shape invariant for big data problems’, GigaScience, vol. 12, p. giad094, 2023, doi: 10.1093/gigascience/giad094.
[17]
J. Harvey, B. Chan, T. Srivastava, A. Zarebski, P. Dłotko, P. Błaszczyk, R. Parkinson, L. White, R. Aguas, and A. Mahdi, ‘Epidemiological waves: Types, drivers, and modulators in the COVID-19 pandemic’, Heliyon, vol. 9, no. 5, 2023, doi: 10.1016/j.heliyon.2023.e17199.
[18]
R. Idczak, W. Nowak, B. Rusin, R. Topolnicki, T. Ossowski, M. Babij, and A. Pikul, ‘Enhanced superconducting critical parameters in a new high-entropy alloy Nb0.34Ti0.33Zr0.14Ta0.11Hf0.08’, Materials, vol. 16, no. 17, p. 5814, 2023, doi: 10.3390/ma16175814.
[19]
P. Sobota, R. Topolnicki, T. Ossowski, T. Pikula, D. Gnida, R. Idczak, and A. Pikul, ‘Superconductivity in high-entropy alloy system containing Th’, Scientific Reports, 2023, doi: 10.1038/s41598-023-43085-y.
[20]
P. Dłotko, M. Lipiński, and J. Signerska-Rynkowska, ‘Testing topological conjugacy of time series from finite sample’, SIAM Journal on Applied Dynamical Systems, vol. 23, no. 4, pp. 1559–1584, 2024, doi: 10.1137/23M1594728.
[21]
T. K. Dey, M. Lipiński, M. Mrozek, and R. Slechta, ‘Computing connection matrices via persistence-like reductions’, SIAM Journal on Applied Dynamical Systems, vol. 23, no. 1, pp. 81–97, 2024, doi: 10.1137/23M1562469.
[22]
P. Pilarczyk, J. Signerska-Rynkowska, and G. Graff, ‘Topological-numerical analysis of a two-dimensional discrete neuron model’, Mathematical Methods in the Applied Sciences, 2024, doi: 10.1002/mma.9118.
[23]
P. Dłotko, N. Hellmer, Ł. Stettner, and R. Topolnicki, ‘Topology-driven goodness-of-fit tests in arbitrary dimensions’, Statistics and Computing, 2024, doi: 10.1007/s11222-023-10333-0.
[24]
S. Rudkin, L. Barros, P. Dłotko, and W. Qiu, ‘An economic topology of Brexit vote’, Regional Studies, vol. 58, no. 3, pp. 601–618, 2024, doi: 10.1080/00343404.2023.2204123.
[25]
J. Desjardins and B. Naskręcki, ‘Geometry of the del Pezzo surface y² = x³ + Am⁶ + Bn⁶’, Annales de l'Institut Fourier, vol. 74, no. 5, pp. 2231–2274, 2024, doi: 10.5802/aif.3635.
[26]
S. Rudkin, W. Qiu, and P. Dłotko, ‘Return trajectory and the forecastability of Bitcoin returns’, The Financial Review, 2024, doi: 10.1111/fire.12420.
[27]
B. Naskręcki and M. Verzobio, ‘Common valuations of division polynomials’, Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 2024, doi: 10.1017/prm.2024.7.
[28]
P. Dłotko, D. Gurnari, and R. Sazdanovic, ‘Mapper-type algorithms for complex data and relations’, Journal of Computational and Graphical Statistics, vol. 33, issue 4, 2024, doi: 10.1080/10618600.2024.2343321.
[29]
P. Dłotko, J. F. Senge, and A. Stefanou, ‘Combinatorial topological models for phylogenetic networks and the mergegram invariant’, Foundations of Data Science, 2024, doi: 10.34/fods.2024045.
[30]
P. Bartłomiejczyk, F. L. Trujillo, and J. Signerska-Rynkowska, ‘Analysis of dynamics of a map-based neuron model via Lorenz maps’, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 34, no. 4, p. 043110, 2024, doi: 10.1063/5.0188464.
[31]
W. Nowak, B. Rusin, M. Babij, R. Topolnicki, T. Ossowski, A. Pikul, and R. Idczak, ‘Superconductivity in a new high-entropy alloy (NbTi)0.67(MoHfV)0.33’, Metallurgical and Materials Transactions A, vol. 55, no. 10, pp. 3789–3798, 2024, doi: 10.1007/s11661-024-07488-4.
[32]
A. Jurek-Loughrey, P. Fitzpatrick, and P. Dłotko, ‘New automated approach to selection of Mapper clustering parameters’, ACM Transactions on Knowledge Discovery from Data, 2025.
[33]
A. Jurek-Loughrey, C. Loughrey, S. Maguire, P. Dłotko, L. Bai, and N. Orr, ‘A novel method for subgroup discovery in precision medicine based on topological data analysis’, BMC Medical Informatics and Decision Making, 2025.
[34]
M. Jaskólski, B. Naskręcki, and Z. Dauter, ‘Periodic arrangements of closely packed spheres’, ChemTexts, vol. 11, p. 2, 2025, doi: 10.1007/s40828-024-00199-8.
[35]
J. W. Malinowski, M. R. Kostrzewa, M. Balcerek, W. Tomczuk, and J. Szwabiński, ‘CINNAMON: A hybrid approach to change point detection and parameter estimation in single-particle tracking data’, Journal of Physics: Photonics, vol. 7, no. 3, p. 035008, 2025.
[36]
B. Naskręcki, J. W. Malinowski, Z. Dauter, and M. Jaskólski, ‘Growth functions of periodic space tessellations’, Acta Crystallographica Section A: Foundations and Advances, vol. 81, no. 1, pp. 64–81, 2025, doi: 10.1107/S2053273324012799.
[37]
P. Dłotko, ‘On the shape that matters – topology and geometry in data science’, European Mathematical Society Magazine, no. 132, pp. 5–13, 2025, available at: link.
[38]
B. Dehingia et al., ‘RNA-binding proteins drive the maturation of CTCF-anchored chromatin topology in cell differentiation’, Nature Cell Biology, 2025, doi: 10.1038/s41556-025-01735-5.
[39]
N. Koljancic, S. A. Park, D. Gurnari, P. Dłotko, J. Hahn, and I. Špánik, ‘Untargeted Chemical Profiling of Two-Dimensional Gas Chromatography Coupled with High-Resolution Mass Spectrometry Data for Botrytized Wines via Topological Data Analysis’, Analytical Chemistry, vol. 97, issue 46, 2025, doi: 10.1021/acs.analchem.5c05342.
[40]
P. Sobota, B. Rusin, D. Gnida, R. Topolnicki, T. Ossowski, W. Nowak, A. Pikul, and R. Idczak, ‘New type of Ti-rich HEA superconductors with high upper critical field’, Acta Materialia, 2025, doi: 10.1016/j.actamat.2024.120666.
[41]
R. Idczak, W. Nowak, M. Babij, D. Gnida, R. Konieczny, M. K. Krawczyk, D. Podsiadła, T. Ossowski, R. Topolnicki, and A. Pikul, ‘Violation of Matthias rule: Elemental composition as the key determinant of critical temperature in bcc high-entropy superconductors’, Physical Review B, 2025, doi: 10.1103/fnz7-bzmw.
[42]
J. Navrátil, R. Topolnicki, M. Otyepka, and P. Błoński, ‘Interpretable machine learning for atomic scale magnetic anisotropy in quantum materials’, npj Computational Materials, 2025, doi: 10.1038/s41524-025-01637-y.

Conference papers:

[1]
M. Contessoto, F. Mémoli, A. Stefanou, and L. Zhou, ‘Persistent Cup-Length’, in Proceedings of the Symposium on Computational Geometry (SoCG), 2022, available at: link.
[2]
C. Loughrey, P. Dłotko, and A. Jurek-Loughrey, ‘A mapper-based classifier for patient subgroup prediction’, in Proceedings of the 11th International Conference on e-Health and Bioengineering, 2023, available at: link.
[3]
P. Fitzpatrick, A. Jurek-Loughrey, P. Dłotko, and J. M. Del Rincon, ‘Ensemble learning for mapper parameter optimization’, in Proceedings of the 2023 IEEE 35th International Conference on Tools with Artificial Intelligence, 2023, available at: link.
[4]
P. Dłotko, D. Gurnari, and R. Sazdanovic, ‘The Art of Knot Data’, in Proceedings of Bridges 2024: Mathematics, Music, Art, Architecture, Culture, pp. 443–446, 2024, available at: link.

Preprints, submitted, and accepted papers:

[1]
S. Jokiel-Rokita, S. Piątek, and R. Topolnicki, ‘Estimation of conditional inequality measures’, arXiv, 2024, doi: 10.48550/arXiv.2412.20228.
[2]
P. Dłotko, D. Gurnari, M. Hallier, and A. Jurek-Loughrey, ‘ClusterGraph: a new tool for visualization and compression of multidimensional data’, arXiv preprint, 2024, doi: 10.48550/arXiv.2411.05443.
[3]
N. Hellmer and J. Spaliński, ‘Density Sensitive Bifiltered Dowker Complexes via Total Weight’, arXiv preprint, 2024, doi: 10.48550/arXiv.2405.15592.
[4]
T. Fleckenstein and N. Hellmer, ‘When Do Two Distributions Yield the Same Expected Euler Characteristic Curve in the Thermodynamic Limit?’, arXiv preprint, 2024, doi: 10.48550/arXiv.2401.04580.
[5]
J. A. D. Binnie, P. Dłotko, J. Harvey, J. Malinowski, and K. M. Yim, ‘A Survey of Dimension Estimation Methods’, arXiv preprint, 2025, doi: 10.48550/arXiv.2507.13887.
[6]
W. A. Bosbach, L. Schoeni, J. F. Senge, M. Mitrakovic, M.-A. Weber, P. Dłotko, and K. Daneshvar, ‘Novel artificial intelligence chest x-ray diagnostics: a quality assessment on the agreement to human doctors during clinical routine’, RöFo, accepted, 2025.
[7]
S. Zorkaltsev, R. Topolnicki, T.-E. Carmon, S. Mathesan, P. Dłotko, D. Mordehai, and M. Harańczyk, ‘Transferable 3D Convolutional Neural Networks for Elastic Constants Prediction in Nanoporous Metals’, Materials & Design, accepted, 2025.
[8]
J. R. Manzanares, ‘Leveraging topological data analysis to estimate bone strength from micro-CT as a surrogate for advanced imaging’, submitted to IEEE Transactions on Medical Imaging, preprint available at: arXiv.

Software libraries:

Please also have a look at our GitHub.
  1. R BallMapper: R implementation of the Ball Mapper algorithm described in "Ball mapper: a shape summary for topological data analysis" by Paweł Dłotko, (2019) arXiv:1901.07410. Please consult the following youtube video for the idea of functionality. Ball Mapper provides a topologically accurate summary of data in the form of an abstract graph.
  2. PyBallMapper: Python implementation of the Ball Mapper algorithm that can be run in a Jupyter notebook. Allows plotting of the resulting graphs using Matplotlib or Bokeh.
  3. BallMapper Knots: BallMapper-based visualizations of datasets from knot theory.
  4. ECC: Python code to compute the Euler Characteristic Curve of a filtered Vietoris-Rips complex. A pipeline for parallel computations using GNU Parallel is also provided. For a theoretical introduction and a description of the algorithm please watch Davide's talk at the Second Symposium on Machine Learning and Dynamical Systems.
  5. Prokhorov metric: A fork of Gudhi implementing the Prokhorov metric for persistence diagrams. Please watch Niklas's talks at the Second Symposium on Machine Learning and Dynamical Systems for the theoretical background.
  6. TopoTests: Code accompanying the paper "Topology-Driven Goodness-of-Fit Tests in Arbitrary Dimensions" by Paweł Dłotko, Niklas Hellmer, Łukasz Stettner and Rafał Topolnicki.
  7. ConjTest: Code accompanying the paper "Testing topological conjugacy of time series from finite sample" by P. Dłotko, M. Lipiński, and J. Signerska-Rynkowska.
  8. pyEulerCurves: C++/Python package for computing Euler characteristic curves, designed for scalable analysis of large and high-dimensional datasets.
  9. ClusterGraph: A tool for visualizing the geometric organization of clusters by combining clustering output with topological data analysis.
  10. Game of Trees: A mathematics-inspired educational puzzle game illustrating graph-theoretic and combinatorial ideas.
  11. ECP experiments: Experimental code reproducing workflows and examples related to Euler characteristic curves and profiles.
  12. Phylogenetic models and invariants of graphs: Implementations of combinatorial-topological descriptors for phylogenetic networks, including Treegram, Cliquegram, and Facegram.
  13. TopoExplainer: Jupyter notebooks and supporting code for interpreting and explaining outputs of topological data analysis pipelines.
  14. pydowker: Python package for constructing and analyzing bifiltered Dowker complexes, including density-sensitive filtrations.
  15. crystgrowthpoly_julia: Julia package implementing growth functions of periodic tessellations, linked to crystallography and space-tessellation analysis.
  16. tfbm: Software for simulation and detection of tempered fractional Brownian motion variants.
  17. modifiedOtsu: Modified Otsu segmentation tools for image analysis.
  18. otsu2D: Local two-dimensional Otsu segmentation tools.
  19. torchPersLay: PyTorch implementation of PersLay for learning from persistence diagrams.
  20. ballMapper: An optimized Ball Mapper implementation with range search accelerated using BallTree/FAISS.