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.
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. Dlotko, W. Qiu, and S. Rudkin, ‘Topological Data Analysis Ball Mapper for Finance’. arXiv, Jun. 07, 2022. doi: 10.48550/arXiv.2206.03622.
[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]
B. Naskręcki and M. Verzobio, ‘Common valuations of division polynomials’. arXiv, Nov. 22, 2022. doi: 10.48550/arXiv.2203.02015.
[5]
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.
[6]
B. Naskręcki, Z. Dauter, and M. Jaskolski, ‘Growth functions of periodic space tessellations’. submitted to Acta Cryst. A, 2023.
[7]
B. Naskręcki, Z. Dauter, and M. Jaskolski, ‘Symmetry aspects of the close packings of spheres’. submitted to Journal of Applied Cryst., 2023.
[8]
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.
[9]
P. Dłotko, D. Gurnari, and R. Sazdanovic, ‘Mapper-type algorithms for complex data and relations’. arXiv, Mar. 28, 2023. doi: 10.48550/arXiv.2109.00831.
[10]
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.
[11]
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.
[12]
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.
[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.
Software libraries:
Please also have a look at our GitHub.- 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.
- 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.
- Mapper GUI: Python code to interactively compare two Ball Mapper graphs as described here. A short video example can be found on youtube.
- 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.
- 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.
- TopoTests: Code accompanying the paper "Topology-Driven Goodness-of-Fit Tests in Arbitrary Dimensions" by Paweł Dłotko, Niklas Hellmer, Łukasz Stettner and Rafał Topolnicki.
- ConjTest Code accompanying the paper "Testing topological conjugacy of time series from finite sample" by P. Dłotko, M. Lipiński, J. Signerska-Rynkowska.