Publications
39. Peter Bubenik and Nikola Milicevic. Homotopy, Homology and Persistent Homology Using Closure Spaces and Filtered Closure Spaces, Journal of Applied and Computational Topology, published online, 63pp. doi:10.1007/s41468-024-00183-8 arXiv:2104.10206 [math.AT]
38. Peter Bubenik and Iryna Hartsock. Topological and metric properties of spaces of generalized persistence diagrams, Journal of Applied and Computational Topology, 8, 347–399 (2024). doi:10.1007/s41468-023-00157-2 arXiv:2205.08506 [math.AT]
37. Peter Bubenik and Michael Catanzaro. Multiparameter persistent homology via generalized Morse theory, Fields Institute Communications, 89, 55–59 (2024). doi:10.1007/978-3-031-57204-3 4 arXiv:2107.08856 [math.AT]
36. Michael J. Catanzaro, Sam Rizzo, John Kopchick, Asadur Chowdury, David R Rosenberg, Peter Bubenik, and Vaibhav A. Diwadkar. Topological data analysis captures task-driven fMRI profiles in individual participants: A classification pipeline based on persistence, Neuroinformatics, (2023). doi:10.1007/s12021-023-09645-3
35. Peter Bubenik, Jonathan Scott, and Donald Stanley. Exact weights, path metrics, and algebraic Wasserstein distances, Journal of Applied and Computational Topology, 7, 185—219 (2023). doi:10.1007/s41468-022-00091-9 arXiv:1809.09654 [math.RA]
34. Peter Bubenik and Alexander Elchesen. Virtual persistence diagrams, signed measures, Wasserstein distances, and Banach spaces, Journal of Applied and Computational Topology, 6, 429–474 (2022). doi:10.1007/s41468-022-00091-9 arXiv:2012.10514 [math.AT]
33. Peter Bubenik and Alexander Elchesen. Universality of persistence diagrams and the bottleneck and Wasserstein distances, Computational Geometry, 105-106, 101882 (2022) 18pp. doi:10.1016/j.comgeo.2022.101882 arXiv:1912.02563 [math.AT]
32. Leo Betthauser, Peter Bubenik, and Parker Edwards. Graded persistence diagrams and persistence landscapes, Discrete and Computational Geometry, 67, 203–230 (2022). doi:10.1007/s00454-021-00316-1 arXiv:1904.12807 [math.AT]
31. Matthew Wheeler, Jose Bouza, and Peter Bubenik. Activation Landscapes as a Topological Summary of Neural Network Performance, 2021 IEEE International Conference on Big Data (Big Data), (2021), pp. 3865–3870. doi:10.1109/BigData52589.2021.9671368 arXiv:2110.10136 [cs.LG]
30. Parker Edwards, Kristen Skruber, Nikola Milicevic, James B. Heidings, Tracy-Ann Read, Peter Bubenik, and Eric A. Vitriol. TDAExplore: quantitative analysis of fluorescence microscopy images through topology-based machine learning, Patterns, 2 (2021), no.11, 100367. 11pp + 17pp Suppl. doi:10.1016/j.patter.2021.100367 bioRxiv:2021.06.13.448249
29. Ashleigh Thomas, Kathleen Bates, Alex Elchesen, Iryna Hartsock, Hang Lu, and Peter Bubenik. Topological data analysis of C. elegans locomotion and behavior, Frontiers in Artificial Intelligence, 4:668395 (2021) 16pp. doi:10.3389/frai.2021.668395 arXiv:2102.09380 [math.AT]
28. Peter Bubenik. Discussion of ‘Event History and Topological Data Analysis’, Biometrika, 188 (2021), no.4, 785–788. doi:10.1093/biomet/asab022 arXiv:2205.03310 [math.ST]
27. Peter Bubenik and Nikola Milicevic. Homological Algebra for Persistence Modules, Foundations of Computational Mathematics, 21, 1233–1278 (2021). doi:10.1007/s10208-020-09482-9 arXiv:1905.05744 [math.AT]
26. Peter Bubenik and Alexander Wagner. Embeddings of Persistence Diagrams into Hilbert Spaces, Journal of Applied and Computational Topology, 4, 339–351 (2020). doi:10.1007/s41468-020-00056-w arXiv:1905.05604 [cs.LG]
25. Peter Bubenik. The persistence landscape and some of its properties, In: Baas N., Carlsson G., Quick G., Szymik M., Thaule M. (eds) Topological Data Analysis. Abel Symposia, vol 15. Springer, 2020. pp 97–117. doi:10.1007/978-3-030-43408-3 4 arXiv:1810.04963 [math.AT]
24. Peter Bubenik, Michael Hull, Dhruv Patel, and Benjamin Whittle. Persistent homology detects curvature, Inverse Problems, 36 (2020) 025008 (23pp). doi:10.1088/1361-6420/ab4ac0 arXiv:1905.13196 [cs.CG]
23. Paul Bendich, Peter Bubenik, and Alexander Wagner. Stabilizing the unstable output of persistent homology computations, Journal of Applied and Computational Topology, 4, 309–338 (2020). doi:10.1007/s41468-019-00044-9 arXiv:1512.01700 [cs.CG]
22. Vic Patrangenaru, Peter Bubenik, Robert L. Paige, and Daniel Osborne. Challenges in Topological Object Data Analysis, Sankhya A, 81 (2019), 244–271. doi:10.1007/s13171-018-0137-7 arXiv:1804.10255 [stat.ME]
21. Peter Bubenik and Tane Vergili. Topological spaces of persistence modules and their properties, Journal of Applied and Computational Topology, 2 (2018), 233–269. doi:10.1007/s41468-018-0022-4 arXiv:1802.08117 [math.AT]
20. Peter Bubenik, Vin de Silva, and Vidit Nanda. Higher interpolation and extension of persistence modules, SIAM Journal on Applied Algebra and Geometry 1 (2017), 272–284. doi:10.1137/16M1100472 arXiv:1603.07406 [math.AT]
19. Peter Bubenik and Pawel Dlotko. A persistence landscapes toolbox for topological statistics, Journal of Symbolic Computation 78 (2017), 91–114. doi:10.1016/j.jsc.2016.03.009 arXiv:1501.00179 [cs.CG]
18. Violeta Kovacev-Nikolic, Peter Bubenik, Dragan Nikolic, and Giseon Heo. Using persistent homology and dynamical distances to analyze protein binding, Statistical Applications in Genetics and Molecular Biology 15 (2016) no.1, 19–38. doi:10.1515/sagmb-2015-0057 arXiv:1412.1394 [stat.ME]
17. Peter Bubenik, Vin de Silva and Jonathan Scott. Metrics for generalized persistence modules, Foundations of Computational Mathematics 15 (2015), no. 6, 1501–1531. doi:10.1007/s10208-014-9229-5 arXiv:1312.3829 [math.AT]
16. Peter Bubenik. Statistical topological data analysis using persistence landscapes, Journal of Machine Learning Research 16 (2015), 77–102. jmlr.org/papers/volume16/bubenik15a arXiv:1207.6437 [math.AT]
15. Peter Bubenik and Jonathan A. Scott. Categorification of persistent homology, Discrete and Computational Geometry 51 (2014), no. 3, 600–627. doi:10.1007/s00454-014-9573-x arXiv:1205.3669 [math.AT]
14. Yuliy Baryshnikov, Peter Bubenik, and Matthew Kahle. Min-Type Morse Theory for Configuration Spaces of Hard Spheres, International Mathematical Research Notices 2014 (2014), no. 9, 2577–2592. doi:10.1093/imrn/rnt012 arXiv:1108.3061 [math.AT]
13. Peter Bubenik. A comment to “A microbiology primer for pyrosequencing”, Quantitative Bio-Science 31 (2012), no. 2, 85–86. https://qbs.kmu.ac.kr:442/!Board/down.php?wd=4&bf_ code=105
12. Peter Bubenik. Simplicial models for concurrency, Electronic Notes in Theoretical Computer Science 283 (2012), 3–12. doi:10.1016/j.entcs.2012.05.002 arXiv:1011.6599 [cs.DC]
11. Peter Bubenik and Leah H. Gold. Graph products of spheres, associative graded algebras and Hilbert series, Mathematische Zeitschrift 268 (2011), no. 3–4, 821–836. doi:10.1007/s00209-010-0697-2 arXiv:0901.4493 [math.AT]
10. Peter Bubenik, Gunnar Carlsson, Peter T. Kim, and Zhiming Luo. Statistical topology via Morse theory, persistence, and nonparametric estimation, Algebraic Methods in Statistics and Probability II, Contemporary Mathematics 516 (2010), 75–92. doi:10.1090/conm/516/10167 arXiv:0908.3668 [math.ST]
9. Moo K. Chung, Peter Bubenik, and Peter T. Kim. Persistence diagrams of cortical surface data, in Information Processing in Medical Imaging 2009, Lecture Notes in Computer Science 5636 (2009), 386–397. doi:10.1007/978-3-642-02498-6 32
8. Peter Bubenik. Models and van Kampen theorems for directed homotopy theory, Homology, Homotopy and Applications 11 (2009), no. 1, 185–202. euclid.hha/1251832565 arXiv:0810.4164 [math.AT]
7. Peter Bubenik. Context for models of concurrency, Electronic Notes in Theoretical Computer Science 230 (2009), 3–21. doi:10.1016/j.entcs.2009.02.014 arXiv:math/0608733 [math.AT]
6. George A. Bubenik and Peter Bubenik. Palmated antlers of moose may serve as a parabolic reflector of sounds, European Journal of Wildlife Research 54 (2008), 533–535. doi:10.1007/s10344-007-0165-4
5. Peter Bubenik. Separated Lie models and the homotopy Lie algebra, Journal of Pure and Applied Algebra 212 (2008), no.2, 350–369. doi:10.1016/j.jpaa.2007.05.018 arXiv:math/0406405 [math.AT]
4. Peter Bubenik and Peter T. Kim. A statistical approach to persistent homology, Homology, Homotopy and Applications 9 (2007), no. 2, 337–362. euclid.hha/1201127341 arXiv:math/0607634 [math.AT]
3. Peter Bubenik and John A.R.Holbrook. Densities for random balanced sampling, Journal of Multivariate Analysis 98 (2007), no. 2, 350–369. doi:10.1016/j.jmva.2006.01.007 arXiv:math/0608737 [math.ST]
2. Peter Bubenik and Krzysztof Worytkiewicz. A model category for local po-spaces, Homology, Homotopy and Applications 8 (2006), no.1, 263–292. doi:10.4310/HHA.2006.v8.n1.a10 arXiv:math/0506352 [math.AT]
1. Peter Bubenik. Free and semi-inert cell attachments, Transactions of the American Mathematical Society 357 (2005), no. 11, 4533–4553. doi:10.1090/S0002-9947-05-03989-9 arXiv:math/0312387 [math.AT]
PhD Dissertation
Peter Bubenik. Cell attachments and the homology of loop spaces and differential graded algebras, Ph.D. thesis, University of Toronto (2003), v+108pp. arXiv:math/0601421 [math.AT]