[{"author":[{"full_name":"Graff, Grzegorz","first_name":"Grzegorz","last_name":"Graff"},{"last_name":"Graff","first_name":"Beata","full_name":"Graff, Beata"},{"id":"3768D56A-F248-11E8-B48F-1D18A9856A87","first_name":"Pawel","last_name":"Pilarczyk","full_name":"Pilarczyk, Pawel"},{"last_name":"Jablonski","first_name":"Grzegorz","orcid":"0000-0002-3536-9866","id":"4483EF78-F248-11E8-B48F-1D18A9856A87","full_name":"Jablonski, Grzegorz"},{"last_name":"Gąsecki","first_name":"Dariusz","full_name":"Gąsecki, Dariusz"},{"full_name":"Narkiewicz, Krzysztof","first_name":"Krzysztof","last_name":"Narkiewicz"}],"volume":16,"date_updated":"2023-08-10T14:21:42Z","date_created":"2021-08-08T22:01:28Z","pmid":1,"acknowledgement":"We express our gratitude to the anonymous referees who provided constructive comments that helped us improve the quality of the paper.","year":"2021","publisher":"Public Library of Science","department":[{"_id":"HeEd"}],"publication_status":"published","file_date_updated":"2021-08-09T09:25:41Z","license":"https://creativecommons.org/licenses/by/4.0/","article_number":"e0253851","doi":"10.1371/journal.pone.0253851","language":[{"iso":"eng"}],"external_id":{"isi":["000678124900050"],"pmid":["34292957"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"quality_controlled":"1","isi":1,"publication_identifier":{"eissn":["19326203"]},"month":"07","file":[{"file_name":"2021_PLoSONE_Graff.pdf","access_level":"open_access","creator":"asandaue","content_type":"application/pdf","file_size":2706919,"file_id":"9832","relation":"main_file","date_updated":"2021-08-09T09:25:41Z","date_created":"2021-08-09T09:25:41Z","success":1,"checksum":"0277aa155d5db1febd2cb384768bba5f"}],"oa_version":"Published Version","_id":"9821","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":" 16","status":"public","ddc":["006"],"title":"Persistent homology as a new method of the assessment of heart rate variability","issue":"7","abstract":[{"lang":"eng","text":"Heart rate variability (hrv) is a physiological phenomenon of the variation in the length of the time interval between consecutive heartbeats. In many cases it could be an indicator of the development of pathological states. The classical approach to the analysis of hrv includes time domain methods and frequency domain methods. However, attempts are still being made to define new and more effective hrv assessment tools. Persistent homology is a novel data analysis tool developed in the recent decades that is rooted at algebraic topology. The Topological Data Analysis (TDA) approach focuses on examining the shape of the data in terms of connectedness and holes, and has recently proved to be very effective in various fields of research. In this paper we propose the use of persistent homology to the hrv analysis. We recall selected topological descriptors used in the literature and we introduce some new topological descriptors that reflect the specificity of hrv, and we discuss their relation to the standard hrv measures. In particular, we show that this novel approach provides a collection of indices that might be at least as useful as the classical parameters in differentiating between series of beat-to-beat intervals (RR-intervals) in healthy subjects and patients suffering from a stroke episode."}],"type":"journal_article","date_published":"2021-07-01T00:00:00Z","citation":{"ista":"Graff G, Graff B, Pilarczyk P, Jablonski G, Gąsecki D, Narkiewicz K. 2021. Persistent homology as a new method of the assessment of heart rate variability. PLoS ONE. 16(7), e0253851.","apa":"Graff, G., Graff, B., Pilarczyk, P., Jablonski, G., Gąsecki, D., & Narkiewicz, K. (2021). Persistent homology as a new method of the assessment of heart rate variability. PLoS ONE. Public Library of Science. https://doi.org/10.1371/journal.pone.0253851","ieee":"G. Graff, B. Graff, P. Pilarczyk, G. Jablonski, D. Gąsecki, and K. Narkiewicz, “Persistent homology as a new method of the assessment of heart rate variability,” PLoS ONE, vol. 16, no. 7. Public Library of Science, 2021.","ama":"Graff G, Graff B, Pilarczyk P, Jablonski G, Gąsecki D, Narkiewicz K. Persistent homology as a new method of the assessment of heart rate variability. PLoS ONE. 2021;16(7). doi:10.1371/journal.pone.0253851","chicago":"Graff, Grzegorz, Beata Graff, Pawel Pilarczyk, Grzegorz Jablonski, Dariusz Gąsecki, and Krzysztof Narkiewicz. “Persistent Homology as a New Method of the Assessment of Heart Rate Variability.” PLoS ONE. Public Library of Science, 2021. https://doi.org/10.1371/journal.pone.0253851.","mla":"Graff, Grzegorz, et al. “Persistent Homology as a New Method of the Assessment of Heart Rate Variability.” PLoS ONE, vol. 16, no. 7, e0253851, Public Library of Science, 2021, doi:10.1371/journal.pone.0253851.","short":"G. Graff, B. Graff, P. Pilarczyk, G. Jablonski, D. Gąsecki, K. Narkiewicz, PLoS ONE 16 (2021)."},"publication":"PLoS ONE","article_type":"original","article_processing_charge":"Yes","has_accepted_license":"1","day":"01","scopus_import":"1"},{"scopus_import":"1","month":"08","day":"01","publication_identifier":{"isbn":["9781728157511"]},"article_processing_charge":"No","quality_controlled":"1","isi":1,"publication":"11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, ","citation":{"chicago":"Graff, Grzegorz, Beata Graff, Grzegorz Jablonski, and Krzysztof Narkiewicz. “The Application of Persistent Homology in the Analysis of Heart Rate Variability.” In 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, . IEEE, 2020. https://doi.org/10.1109/ESGCO49734.2020.9158054.","short":"G. Graff, B. Graff, G. Jablonski, K. Narkiewicz, in:, 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, , IEEE, 2020.","mla":"Graff, Grzegorz, et al. “The Application of Persistent Homology in the Analysis of Heart Rate Variability.” 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, , 9158054, IEEE, 2020, doi:10.1109/ESGCO49734.2020.9158054.","apa":"Graff, G., Graff, B., Jablonski, G., & Narkiewicz, K. (2020). The application of persistent homology in the analysis of heart rate variability. In 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, . Pisa, Italy: IEEE. https://doi.org/10.1109/ESGCO49734.2020.9158054","ieee":"G. Graff, B. Graff, G. Jablonski, and K. Narkiewicz, “The application of persistent homology in the analysis of heart rate variability,” in 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, , Pisa, Italy, 2020.","ista":"Graff G, Graff B, Jablonski G, Narkiewicz K. 2020. The application of persistent homology in the analysis of heart rate variability. 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, . ESGCO: European Study Group on Cardiovascular Oscillations, 9158054.","ama":"Graff G, Graff B, Jablonski G, Narkiewicz K. The application of persistent homology in the analysis of heart rate variability. In: 11th Conference of the European Study Group on Cardiovascular Oscillations: Computation and Modelling in Physiology: New Challenges and Opportunities, . IEEE; 2020. doi:10.1109/ESGCO49734.2020.9158054"},"external_id":{"isi":["000621172600045"]},"language":[{"iso":"eng"}],"conference":{"location":"Pisa, Italy","start_date":"2020-07-15","end_date":"2020-07-15","name":"ESGCO: European Study Group on Cardiovascular Oscillations"},"doi":"10.1109/ESGCO49734.2020.9158054","date_published":"2020-08-01T00:00:00Z","article_number":"9158054","type":"conference","abstract":[{"text":"We evaluate the usefulness of persistent homology in the analysis of heart rate variability. In our approach we extract several topological descriptors characterising datasets of RR-intervals, which are later used in classical machine learning algorithms. By this method we are able to differentiate the group of patients with the history of transient ischemic attack and the group of hypertensive patients.","lang":"eng"}],"status":"public","title":"The application of persistent homology in the analysis of heart rate variability","publication_status":"published","publisher":"IEEE","department":[{"_id":"HeEd"}],"_id":"8580","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","year":"2020","date_created":"2020-09-28T08:59:27Z","date_updated":"2023-08-22T09:33:34Z","oa_version":"None","author":[{"full_name":"Graff, Grzegorz","last_name":"Graff","first_name":"Grzegorz"},{"first_name":"Beata","last_name":"Graff","full_name":"Graff, Beata"},{"full_name":"Jablonski, Grzegorz","id":"4483EF78-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-3536-9866","first_name":"Grzegorz","last_name":"Jablonski"},{"full_name":"Narkiewicz, Krzysztof","last_name":"Narkiewicz","first_name":"Krzysztof"}]},{"date_published":"2020-12-01T00:00:00Z","page":"455-480","article_type":"original","citation":{"ama":"Bauer U, Edelsbrunner H, Jablonski G, Mrozek M. Čech-Delaunay gradient flow and homology inference for self-maps. Journal of Applied and Computational Topology. 2020;4(4):455-480. doi:10.1007/s41468-020-00058-8","ista":"Bauer U, Edelsbrunner H, Jablonski G, Mrozek M. 2020. Čech-Delaunay gradient flow and homology inference for self-maps. Journal of Applied and Computational Topology. 4(4), 455–480.","ieee":"U. Bauer, H. Edelsbrunner, G. Jablonski, and M. Mrozek, “Čech-Delaunay gradient flow and homology inference for self-maps,” Journal of Applied and Computational Topology, vol. 4, no. 4. Springer Nature, pp. 455–480, 2020.","apa":"Bauer, U., Edelsbrunner, H., Jablonski, G., & Mrozek, M. (2020). Čech-Delaunay gradient flow and homology inference for self-maps. Journal of Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-020-00058-8","mla":"Bauer, U., et al. “Čech-Delaunay Gradient Flow and Homology Inference for Self-Maps.” Journal of Applied and Computational Topology, vol. 4, no. 4, Springer Nature, 2020, pp. 455–80, doi:10.1007/s41468-020-00058-8.","short":"U. Bauer, H. Edelsbrunner, G. Jablonski, M. Mrozek, Journal of Applied and Computational Topology 4 (2020) 455–480.","chicago":"Bauer, U., Herbert Edelsbrunner, Grzegorz Jablonski, and M. Mrozek. “Čech-Delaunay Gradient Flow and Homology Inference for Self-Maps.” Journal of Applied and Computational Topology. Springer Nature, 2020. https://doi.org/10.1007/s41468-020-00058-8."},"publication":"Journal of Applied and Computational Topology","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"01","scopus_import":"1","oa_version":"Published Version","file":[{"access_level":"open_access","file_name":"2020_JourApplCompTopology_Bauer.pdf","creator":"dernst","content_type":"application/pdf","file_size":851190,"file_id":"15065","relation":"main_file","success":1,"checksum":"eed1168b6e66cd55272c19bb7fca8a1c","date_created":"2024-03-04T10:52:42Z","date_updated":"2024-03-04T10:52:42Z"}],"intvolume":" 4","title":"Čech-Delaunay gradient flow and homology inference for self-maps","status":"public","ddc":["500"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"15064","issue":"4","abstract":[{"text":"We call a continuous self-map that reveals itself through a discrete set of point-value pairs a sampled dynamical system. Capturing the available information with chain maps on Delaunay complexes, we use persistent homology to quantify the evidence of recurrent behavior. We establish a sampling theorem to recover the eigenspaces of the endomorphism on homology induced by the self-map. Using a combinatorial gradient flow arising from the discrete Morse theory for Čech and Delaunay complexes, we construct a chain map to transform the problem from the natural but expensive Čech complexes to the computationally efficient Delaunay triangulations. The fast chain map algorithm has applications beyond dynamical systems.","lang":"eng"}],"type":"journal_article","language":[{"iso":"eng"}],"doi":"10.1007/s41468-020-00058-8","quality_controlled":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"publication_identifier":{"eissn":["2367-1734"],"issn":["2367-1726"]},"month":"12","volume":4,"date_created":"2024-03-04T10:47:49Z","date_updated":"2024-03-04T10:54:04Z","author":[{"last_name":"Bauer","first_name":"U.","full_name":"Bauer, U."},{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Jablonski, Grzegorz","last_name":"Jablonski","first_name":"Grzegorz","orcid":"0000-0002-3536-9866","id":"4483EF78-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Mrozek","first_name":"M.","full_name":"Mrozek, M."}],"publisher":"Springer Nature","department":[{"_id":"HeEd"}],"publication_status":"published","acknowledgement":"This research has been supported by the DFG Collaborative Research Center SFB/TRR 109 “Discretization in Geometry and Dynamics”, by Polish MNiSzW Grant No. 2621/7.PR/12/2013/2, by the Polish National Science Center under Maestro Grant No. 2014/14/A/ST1/00453 and Grant No. DEC-2013/09/N/ST6/02995. Open Access funding provided by Projekt DEAL.","year":"2020","file_date_updated":"2024-03-04T10:52:42Z"},{"publisher":"Springer","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2017","volume":198,"date_updated":"2023-09-26T15:50:52Z","date_created":"2018-12-11T11:48:46Z","author":[{"full_name":"Ethier, Marc","first_name":"Marc","last_name":"Ethier"},{"first_name":"Grzegorz","last_name":"Jablonski","id":"4483EF78-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-3536-9866","full_name":"Jablonski, Grzegorz"},{"full_name":"Mrozek, Marian","last_name":"Mrozek","first_name":"Marian"}],"ec_funded":1,"publist_id":"6812","project":[{"call_identifier":"FP7","name":"Topological Complex Systems","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"isi":1,"quality_controlled":"1","external_id":{"isi":["000434088200008"]},"language":[{"iso":"eng"}],"doi":"10.1007/978-3-319-56932-1_8","conference":{"name":"ACA: Applications of Computer Algebra","end_date":"2015-07-23","start_date":"2015-07-20","location":"Kalamata, Greece"},"publication_identifier":{"isbn":["978-331956930-7"]},"month":"07","intvolume":" 198","status":"public","title":"Finding eigenvalues of self-maps with the Kronecker canonical form","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"836","oa_version":"None","alternative_title":["PROMS"],"type":"conference","abstract":[{"text":"Recent research has examined how to study the topological features of a continuous self-map by means of the persistence of the eigenspaces, for given eigenvalues, of the endomorphism induced in homology over a field. This raised the question of how to select dynamically significant eigenvalues. The present paper aims to answer this question, giving an algorithm that computes the persistence of eigenspaces for every eigenvalue simultaneously, also expressing said eigenspaces as direct sums of “finite” and “singular” subspaces.","lang":"eng"}],"page":"119 - 136","citation":{"ama":"Ethier M, Jablonski G, Mrozek M. Finding eigenvalues of self-maps with the Kronecker canonical form. In: Special Sessions in Applications of Computer Algebra. Vol 198. Springer; 2017:119-136. doi:10.1007/978-3-319-56932-1_8","ieee":"M. Ethier, G. Jablonski, and M. Mrozek, “Finding eigenvalues of self-maps with the Kronecker canonical form,” in Special Sessions in Applications of Computer Algebra, Kalamata, Greece, 2017, vol. 198, pp. 119–136.","apa":"Ethier, M., Jablonski, G., & Mrozek, M. (2017). Finding eigenvalues of self-maps with the Kronecker canonical form. In Special Sessions in Applications of Computer Algebra (Vol. 198, pp. 119–136). Kalamata, Greece: Springer. https://doi.org/10.1007/978-3-319-56932-1_8","ista":"Ethier M, Jablonski G, Mrozek M. 2017. Finding eigenvalues of self-maps with the Kronecker canonical form. Special Sessions in Applications of Computer Algebra. ACA: Applications of Computer Algebra, PROMS, vol. 198, 119–136.","short":"M. Ethier, G. Jablonski, M. Mrozek, in:, Special Sessions in Applications of Computer Algebra, Springer, 2017, pp. 119–136.","mla":"Ethier, Marc, et al. “Finding Eigenvalues of Self-Maps with the Kronecker Canonical Form.” Special Sessions in Applications of Computer Algebra, vol. 198, Springer, 2017, pp. 119–36, doi:10.1007/978-3-319-56932-1_8.","chicago":"Ethier, Marc, Grzegorz Jablonski, and Marian Mrozek. “Finding Eigenvalues of Self-Maps with the Kronecker Canonical Form.” In Special Sessions in Applications of Computer Algebra, 198:119–36. Springer, 2017. https://doi.org/10.1007/978-3-319-56932-1_8."},"publication":"Special Sessions in Applications of Computer Algebra","date_published":"2017-07-27T00:00:00Z","scopus_import":"1","article_processing_charge":"No","day":"27"},{"issue":"5","abstract":[{"lang":"eng","text":"Considering a continuous self-map and the induced endomorphism on homology, we study the eigenvalues and eigenspaces of the latter. Taking a filtration of representations, we define the persistence of the eigenspaces, effectively introducing a hierarchical organization of the map. The algorithm that computes this information for a finite sample is proved to be stable, and to give the correct answer for a sufficiently dense sample. Results computed with an implementation of the algorithm provide evidence of its practical utility.\r\n"}],"type":"journal_article","file":[{"creator":"system","file_size":1317546,"content_type":"application/pdf","access_level":"open_access","file_name":"IST-2016-486-v1+1_s10208-014-9223-y.pdf","checksum":"3566f3a8b0c1bc550e62914a88c584ff","date_created":"2018-12-12T10:08:10Z","date_updated":"2020-07-14T12:45:26Z","file_id":"4670","relation":"main_file"}],"oa_version":"Published Version","pubrep_id":"486","intvolume":" 15","title":"The persistent homology of a self-map","ddc":["000"],"status":"public","_id":"2035","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","has_accepted_license":"1","day":"01","scopus_import":1,"date_published":"2015-10-01T00:00:00Z","page":"1213 - 1244","citation":{"apa":"Edelsbrunner, H., Jablonski, G., & Mrozek, M. (2015). The persistent homology of a self-map. Foundations of Computational Mathematics. Springer. https://doi.org/10.1007/s10208-014-9223-y","ieee":"H. Edelsbrunner, G. Jablonski, and M. Mrozek, “The persistent homology of a self-map,” Foundations of Computational Mathematics, vol. 15, no. 5. Springer, pp. 1213–1244, 2015.","ista":"Edelsbrunner H, Jablonski G, Mrozek M. 2015. The persistent homology of a self-map. Foundations of Computational Mathematics. 15(5), 1213–1244.","ama":"Edelsbrunner H, Jablonski G, Mrozek M. The persistent homology of a self-map. Foundations of Computational Mathematics. 2015;15(5):1213-1244. doi:10.1007/s10208-014-9223-y","chicago":"Edelsbrunner, Herbert, Grzegorz Jablonski, and Marian Mrozek. “The Persistent Homology of a Self-Map.” Foundations of Computational Mathematics. Springer, 2015. https://doi.org/10.1007/s10208-014-9223-y.","short":"H. Edelsbrunner, G. Jablonski, M. Mrozek, Foundations of Computational Mathematics 15 (2015) 1213–1244.","mla":"Edelsbrunner, Herbert, et al. “The Persistent Homology of a Self-Map.” Foundations of Computational Mathematics, vol. 15, no. 5, Springer, 2015, pp. 1213–44, doi:10.1007/s10208-014-9223-y."},"publication":"Foundations of Computational Mathematics","ec_funded":1,"publist_id":"5022","file_date_updated":"2020-07-14T12:45:26Z","volume":15,"date_updated":"2021-01-12T06:54:53Z","date_created":"2018-12-11T11:55:20Z","author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"},{"full_name":"Jablonski, Grzegorz","id":"4483EF78-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-3536-9866","first_name":"Grzegorz","last_name":"Jablonski"},{"full_name":"Mrozek, Marian","first_name":"Marian","last_name":"Mrozek"}],"publisher":"Springer","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2015","acknowledgement":"This research is partially supported by the Toposys project FP7-ICT-318493-STREP, by ESF under the ACAT Research Network Programme, by the Russian Government under mega project 11.G34.31.0053, and by the Polish National Science Center under Grant No. N201 419639.","month":"10","language":[{"iso":"eng"}],"doi":"10.1007/s10208-014-9223-y","project":[{"name":"Topological Complex Systems","call_identifier":"FP7","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1}]