Useful Links

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

Journal publications:

  1. Paweł Dłotko, Niklas Hellmer, ‘Bottleneck Profiles and Discrete Prokhorov Metrics for Persistence Diagrams’, Discrete Comput Geom, May 2023, doi: 10.1007/s00454-023-00498-w.
  2. P. Pilarczyk, J. Signerska-Rynkowska, G. Graff, Topological-numerical analysis of a two-dimensional discrete neuron model. Chaos 33 (2023), no. 4 https://doi.org/10.1063/5.0129859
  3. F. Llovera Trujillo, J. Signerska-Rynkowska, P. Bartłomiejczyk, Periodic and chaotic dynamics in a map-based neuron model. Math Meth Appl Sci. (2023); 1- 26. https://doi.org/10.1002/mma.9118
  4. P. Bartłomiejczyk, F. Llovera Trujillo, J. Signerska-Rynkowska, Spike patterns and chaos in a map-based neuron model, AMCS - International Journal of Applied Mathematics and Computer Science (2023) (accepted)
  5. R. Khalil, A. Farhat, P. Dlotko, Developmental changes in pyramidal cell morphology in multiple visual cortical areas using cluster analysis., Frontiers in Computational Neuroscience, 2021 , https://doi.org/10.3389/fncom.2021.667696
  6. A. Mahdi, P. Blaszczyk, P. Dlotko, D. Salvi, T-S. Chan, J. Harvey, D. Gurnari, Y. Wu, A. Farhat, N. Hellmer, A. Zarebski, B. Hogan, L. Tarassenko, OxCOVID19 Database, a multimodal data repository for better understanding the global impact of COVID-19, Nature Scientific Reports, 2021 , https://doi.org/10.1038/s41598-021-88481-4accepted
  7. A.D. Smith, P. Dlotko, V.M. Zavala, Topological data analysis: Concepts, computation, and applications in chemical engineering, Computers and Chemical Engineering, 2021, 146, 107202.
  8. Q.W., Rudkin, S. Rudkinm P. Dłotko, Refining understanding of corporate failure through a topological data analysis mapping of Altman's Z-score model, Expert Systems with Applications, 2020, 156, 113475.
  9. B. Zielinski, M. Lipinski, M. Juda, M. Zeppelzauer, P. Dlotko, Persistence Codebooks for Topological Data Analysis, Artificial Intelligence Review, Accepted.
  10. P. Dłotko, N. Hellmer, Ł. Stettner, and R. Topolnicki, Topology-driven goodness-of-fit tests in arbitrary dimensions, Statistics and Computing, 34(1), p. 34, Nov. 2023. doi: https://doi.org/10.1007/s11222-023-10333-0.
  11. P. Dłotko and D. Gurnari, Euler characteristic curves and profiles: a stable shape invariant for big data problems, GigaScience, Volume 12, 2023, giad094, https://doi.org/10.1093/gigascience/giad094

Conference papers:

  1. Ciara Frances Loughrey, Nick Orr, Anna Jurek-Loughrey, Paweł Dłotko, Hotspot identification for Mapper graphs

Preprints:

  1. P. Dłotko, M. Lipiński, J. Signerska-Rynkowska, Testing topological conjugacy of time series from finite sample, (2023) preprint: https://doi.org/10.48550/arXiv.2301.06753
  2. Paweł Dłotko, Davide Gurnari, Radmila Sazdanovic Knot invariants and their relations: a topological perspective. Supplemental material can be found here.

Software libraries:

  1. R BallMapper: R implementation of the Ball Mapper algorithm described in "Ball mapper: a shape summary for topological data analysis" by Pawel Dlotko, (2019) arXiv:1901.07410. Please consult the following youtube video the idea of functionality. Ball Mapper provides a topologically accurate summary of a data in a form of an abstract graph.
  2. PyBallMapper: Python implementation of the Ball Mapper algorithm that can be run in a Jupyter notebook. Allows to plot the resulting graphs using Matplotlib or Bokeh.
  3. Mapper GUI: Python code to interactively compare two Ball Mapper graphs as described here. A short video example can be found on youtube.
  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. Pease 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, J. Signerska-Rynkowska.