Useful Links

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

Journal publications:

[1]
W. Qiu, S. Rudkin, and P. Dłotko, ‘Refining understanding of corporate failure through a topological data analysis mapping of Altman’s Z-score model’, Expert Systems with Applications, vol. 156, p. 113475, Oct. 2020, doi: 10.1016/j.eswa.2020.113475.
[2]
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, 2021, doi: https://doi.org/10.3389/fncom.2021.667696.
[3]
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, Mar. 2021, doi: 10.1016/j.compchemeng.2020.107202.
[4]
B. Zieliński, M. Lipiński, M. Juda, M. Zeppelzauer, and P. Dłotko, ‘Persistence codebooks for topological data analysis’, Artif Intell Rev, vol. 54, no. 3, pp. 1969–2009, Mar. 2021, doi: 10.1007/s10462-020-09897-4.
[5]
A. Mahdi et al., ‘OxCOVID19 Database, a multimodal data repository for better understanding the global impact of COVID-19’, Scientific Reports, vol. 11, no. 1, Art. no. 1, Apr. 2021, doi: 10.1038/s41598-021-88481-4.
[6]
F. Llovera Trujillo, J. Signerska-Rynkowska, and P. Bartłomiejczyk, ‘Periodic and chaotic dynamics in a map-based neuron model’, Mathematical Methods in the Applied Sciences, vol. 46, no. 11, pp. 11906–11931, 2023, doi: 10.1002/mma.9118.
[7]
P. Dłotko and D. Gurnari, ‘Euler characteristic curves and profiles: a stable shape invariant for big data problems’, GigaScience, vol. 12, p. giad094, Jan. 2023, doi: 10.1093/gigascience/giad094.
[8]
P. Pilarczyk, J. Signerska-Rynkowska, and G. Graff, ‘Topological-numerical analysis of a two-dimensional discrete neuron model’, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 33, no. 4, p. 043110, Apr. 2023, doi: 10.1063/5.0129859.
[9]
P. Dłotko and N. Hellmer, ‘Bottleneck Profiles and Discrete Prokhorov Metrics for Persistence Diagrams’, Discrete Comput Geom, May 2023, doi: 10.1007/s00454-023-00498-w.
[10]
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, Sep. 2023.
[11]
D. Wouken, D. Sadowski, J. Leśkiewicz, M. Lipiński, and T. Kapela, ‘Rigorous computation in dynamics based on topological methods for multivector fields’, J Appl. and Comput. Topology, Oct. 2023, doi: https://doi.org/10.1007/s41468-023-00149-2.
[12]
P. Dłotko, N. Hellmer, Ł. Stettner, and R. Topolnicki, ‘Topology-driven goodness-of-fit tests in arbitrary dimensions’, Stat Comput, vol. 34, no. 1, p. 34, Nov. 2023, doi: 10.1007/s11222-023-10333-0.
[13]
P. Dłotko, D. Gurnari, and R. Sazdanovic, ‘Mapper-type algorithms for complex data and relations’, Journal of Computational and Graphical Statistics June 2024. doi: 10.1080/10618600.2024.2343321.

Conference papers:

[1]
C. Loughrey, N. Orr, A. Jurek-Loughrey, and P. Dlotko, ‘Hotspot identification for Mapper graphs’, presented at the Topological Data Analysis and Beyond Workshop at the 34th Conference on Neural Information Processing Systems, 2020. doi: https://doi.org/10.48550/arXiv.2012.01868.

Preprints:

[1]
S. Rudkin, W. Qiu, and P. Dlotko, ‘Uncertainty, volatility and the persistence norms of financial time series’. arXiv, Sep. 30, 2021. doi: 10.48550/arXiv.2110.00098.
[2]
P. Dłotko and D. Gurnari, ‘Euler Characteristic Curves and Profiles: a stable shape invariant for big data problems’. arXiv, Dec. 03, 2022. doi: 10.48550/arXiv.2212.01666.
[3]
P. Dłotko, N. Hellmer, Ł. Stettner, and R. Topolnicki, ‘Topology-Driven Goodness-of-Fit Tests in Arbitrary Dimensions’. arXiv, Oct. 25, 2022. doi: 10.48550/arXiv.2210.14965.
[4]
P. Dlotko, W. Qiu, and S. Rudkin, ‘Topological Data Analysis Ball Mapper for Finance’. arXiv, Jun. 07, 2022. doi: 10.48550/arXiv.2206.03622.
[5]
B. Naskręcki and M. Verzobio, ‘Common valuations of division polynomials’. arXiv, Nov. 22, 2022. doi: 10.48550/arXiv.2203.02015.
[6]
S. Barańczuk, B. Naskręcki, and M. Verzobio, ‘Divisibility sequences related to abelian varieties isogenous to a power of an elliptic curve’. arXiv, Sep. 18, 2023. doi: 10.48550/arXiv.2309.09699.
[7]
J. Desjardins and B. Naskręcki, ‘Geometry of the del Pezzo surface y^2=x^3+Am^6+Bn^6’. arXiv, May 18, 2023. doi: 10.48550/arXiv.1911.02684.
[9]
P. Dłotko, M. Lipiński, and J. Signerska-Rynkowska, ‘Testing topological conjugacy of time series from finite sample’. arXiv, Jan. 17, 2023. doi: 10.48550/arXiv.2301.06753.
[10]
P. Dłotko, J. F. Senge, and A. Stefanou, ‘Combinatorial Topological Models for Phylogenetic Networks and the Mergegram Invariant’. arXiv, Jul. 27, 2023. doi: 10.48550/arXiv.2305.04860.
[11]
B. Naskręcki, Z. Dauter, and M. Jaskolski, ‘Growth functions of periodic space tessellations’. submitted to Acta Cryst. A, 2023.
[12]
B. Naskręcki, Z. Dauter, and M. Jaskolski, ‘Symmetry aspects of the close packings of spheres’. submitted to Journal of Applied Cryst., 2023.
[13]
T. Fleckenstein and N. Hellmer, ‘When Do Two Distributions Yield the Same Expected Euler Characteristic Curve in the Thermodynamic Limit?’ arXiv, Jan. 09, 2024. doi: https://doi.org/10.48550/arXiv.2401.04580.
[14]
N. Hellmer and J. Spaliński, ‘Density Sensitive Bifiltered Dowker Complexes via Total Weight’. arXiv, May 24, 2024. doi: https://doi.org/10.48550/arXiv.2405.15592.

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 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. BallMapper KnotsBallMapper based visualizations of datasets from knot theory, as described in [13].
  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.