--- _id: '9253' abstract: - lang: eng text: In March 2020, the Austrian government introduced a widespread lock-down in response to the COVID-19 pandemic. Based on subjective impressions and anecdotal evidence, Austrian public and private life came to a sudden halt. Here we assess the effect of the lock-down quantitatively for all regions in Austria and present an analysis of daily changes of human mobility throughout Austria using near-real-time anonymized mobile phone data. We describe an efficient data aggregation pipeline and analyze the mobility by quantifying mobile-phone traffic at specific point of interests (POIs), analyzing individual trajectories and investigating the cluster structure of the origin-destination graph. We found a reduction of commuters at Viennese metro stations of over 80% and the number of devices with a radius of gyration of less than 500 m almost doubled. The results of studying crowd-movement behavior highlight considerable changes in the structure of mobility networks, revealed by a higher modularity and an increase from 12 to 20 detected communities. We demonstrate the relevance of mobility data for epidemiological studies by showing a significant correlation of the outflow from the town of Ischgl (an early COVID-19 hotspot) and the reported COVID-19 cases with an 8-day time lag. This research indicates that mobile phone usage data permits the moment-by-moment quantification of mobility behavior for a whole country. We emphasize the need to improve the availability of such data in anonymized form to empower rapid response to combat COVID-19 and future pandemics. article_processing_charge: No author: - first_name: Georg full_name: Heiler, Georg last_name: Heiler - first_name: Tobias full_name: Reisch, Tobias last_name: Reisch - first_name: Jan full_name: Hurt, Jan last_name: Hurt - first_name: Mohammad full_name: Forghani, Mohammad last_name: Forghani - first_name: Aida full_name: Omani, Aida last_name: Omani - first_name: Allan full_name: Hanbury, Allan last_name: Hanbury - first_name: Farid full_name: Karimipour, Farid id: 2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425 last_name: Karimipour orcid: 0000-0001-6746-4174 citation: ama: 'Heiler G, Reisch T, Hurt J, et al. Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic. In: 2020 IEEE International Conference on Big Data. IEEE; 2021:3123-3132. doi:10.1109/bigdata50022.2020.9378374' apa: 'Heiler, G., Reisch, T., Hurt, J., Forghani, M., Omani, A., Hanbury, A., & Karimipour, F. (2021). Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic. In 2020 IEEE International Conference on Big Data (pp. 3123–3132). Atlanta, GA, United States: IEEE. https://doi.org/10.1109/bigdata50022.2020.9378374' chicago: Heiler, Georg, Tobias Reisch, Jan Hurt, Mohammad Forghani, Aida Omani, Allan Hanbury, and Farid Karimipour. “Country-Wide Mobility Changes Observed Using Mobile Phone Data during COVID-19 Pandemic.” In 2020 IEEE International Conference on Big Data, 3123–32. IEEE, 2021. https://doi.org/10.1109/bigdata50022.2020.9378374. ieee: G. Heiler et al., “Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic,” in 2020 IEEE International Conference on Big Data, Atlanta, GA, United States, 2021, pp. 3123–3132. ista: 'Heiler G, Reisch T, Hurt J, Forghani M, Omani A, Hanbury A, Karimipour F. 2021. Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic. 2020 IEEE International Conference on Big Data. Big Data: International Conference on Big Data, 3123–3132.' mla: Heiler, Georg, et al. “Country-Wide Mobility Changes Observed Using Mobile Phone Data during COVID-19 Pandemic.” 2020 IEEE International Conference on Big Data, IEEE, 2021, pp. 3123–32, doi:10.1109/bigdata50022.2020.9378374. short: G. Heiler, T. Reisch, J. Hurt, M. Forghani, A. Omani, A. Hanbury, F. Karimipour, in:, 2020 IEEE International Conference on Big Data, IEEE, 2021, pp. 3123–3132. conference: end_date: 2020-12-13 location: Atlanta, GA, United States name: 'Big Data: International Conference on Big Data' start_date: 2020-12-10 date_created: 2021-03-21T11:34:07Z date_published: 2021-03-19T00:00:00Z date_updated: 2023-08-07T14:00:13Z day: '19' department: - _id: HeEd doi: 10.1109/bigdata50022.2020.9378374 external_id: arxiv: - '2008.10064' isi: - '000662554703032' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2008.10064 month: '03' oa: 1 oa_version: Preprint page: 3123-3132 publication: 2020 IEEE International Conference on Big Data publication_identifier: isbn: - '9781728162515' publication_status: published publisher: IEEE quality_controlled: '1' scopus_import: '1' status: public title: Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic type: conference user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 year: '2021' ... --- _id: '9317' abstract: - lang: eng text: Given a locally finite X⊆Rd and a radius r≥0, the k-fold cover of X and r consists of all points in Rd that have k or more points of X within distance r. We consider two filtrations—one in scale obtained by fixing k and increasing r, and the other in depth obtained by fixing r and decreasing k—and we compute the persistence diagrams of both. While standard methods suffice for the filtration in scale, we need novel geometric and topological concepts for the filtration in depth. In particular, we introduce a rhomboid tiling in Rd+1 whose horizontal integer slices are the order-k Delaunay mosaics of X, and construct a zigzag module of Delaunay mosaics that is isomorphic to the persistence module of the multi-covers. acknowledgement: "This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 78818 Alpha), and by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through Grant No. I02979-N35 of the Austrian Science Fund (FWF)\r\nOpen Access funding provided by the Institute of Science and Technology (IST Austria)." article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Georg F full_name: Osang, Georg F id: 464B40D6-F248-11E8-B48F-1D18A9856A87 last_name: Osang citation: ama: Edelsbrunner H, Osang GF. The multi-cover persistence of Euclidean balls. Discrete and Computational Geometry. 2021;65:1296–1313. doi:10.1007/s00454-021-00281-9 apa: Edelsbrunner, H., & Osang, G. F. (2021). The multi-cover persistence of Euclidean balls. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-021-00281-9 chicago: Edelsbrunner, Herbert, and Georg F Osang. “The Multi-Cover Persistence of Euclidean Balls.” Discrete and Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-021-00281-9. ieee: H. Edelsbrunner and G. F. Osang, “The multi-cover persistence of Euclidean balls,” Discrete and Computational Geometry, vol. 65. Springer Nature, pp. 1296–1313, 2021. ista: Edelsbrunner H, Osang GF. 2021. The multi-cover persistence of Euclidean balls. Discrete and Computational Geometry. 65, 1296–1313. mla: Edelsbrunner, Herbert, and Georg F. Osang. “The Multi-Cover Persistence of Euclidean Balls.” Discrete and Computational Geometry, vol. 65, Springer Nature, 2021, pp. 1296–1313, doi:10.1007/s00454-021-00281-9. short: H. Edelsbrunner, G.F. Osang, Discrete and Computational Geometry 65 (2021) 1296–1313. date_created: 2021-04-11T22:01:15Z date_published: 2021-03-31T00:00:00Z date_updated: 2023-08-07T14:35:44Z day: '31' ddc: - '516' department: - _id: HeEd doi: 10.1007/s00454-021-00281-9 ec_funded: 1 external_id: isi: - '000635460400001' file: - access_level: open_access checksum: 59b4e1e827e494209bcb4aae22e1d347 content_type: application/pdf creator: cchlebak date_created: 2021-12-01T10:56:53Z date_updated: 2021-12-01T10:56:53Z file_id: '10394' file_name: 2021_DisCompGeo_Edelsbrunner_Osang.pdf file_size: 677704 relation: main_file success: 1 file_date_updated: 2021-12-01T10:56:53Z has_accepted_license: '1' intvolume: ' 65' isi: 1 language: - iso: eng month: '03' oa: 1 oa_version: Published Version page: 1296–1313 project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication: Discrete and Computational Geometry publication_identifier: eissn: - 1432-0444 issn: - 0179-5376 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '187' relation: earlier_version status: public scopus_import: '1' status: public title: The multi-cover persistence of Euclidean balls tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 65 year: '2021' ... --- _id: '9602' abstract: - lang: eng text: "An ordered graph is a graph with a linear ordering on its vertex set. We prove that for every positive integer k, there exists a constant ck > 0 such that any ordered graph G on n vertices with the property that neither G nor its complement contains an induced monotone path of size k, has either a clique or an independent set of size at least n^ck . This strengthens a result of Bousquet, Lagoutte, and Thomassé, who proved the analogous result for unordered graphs.\r\nA key idea of the above paper was to show that any unordered graph on n vertices that does not contain an induced path of size k, and whose maximum degree is at most c(k)n for some small c(k) > 0, contains two disjoint linear size subsets with no edge between them. This approach fails for ordered graphs, because the analogous statement is false for k ≥ 3, by a construction of Fox. We provide some further examples showing that this statement also fails for ordered graphs avoiding other ordered trees." acknowledgement: We would like to thank the anonymous referees for their useful comments and suggestions. János Pach is partially supported by Austrian Science Fund (FWF) grant Z 342-N31 and by ERC Advanced grant “GeoScape.” István Tomon is partially supported by Swiss National Science Foundation grant no. 200021_196965, and thanks the support of MIPT Moscow. Both authors are partially supported by The Russian Government in the framework of MegaGrant no. 075-15-2019-1926. article_processing_charge: No article_type: original author: - first_name: János full_name: Pach, János id: E62E3130-B088-11EA-B919-BF823C25FEA4 last_name: Pach - first_name: István full_name: Tomon, István last_name: Tomon citation: ama: Pach J, Tomon I. Erdős-Hajnal-type results for monotone paths. Journal of Combinatorial Theory Series B. 2021;151:21-37. doi:10.1016/j.jctb.2021.05.004 apa: Pach, J., & Tomon, I. (2021). Erdős-Hajnal-type results for monotone paths. Journal of Combinatorial Theory. Series B. Elsevier. https://doi.org/10.1016/j.jctb.2021.05.004 chicago: Pach, János, and István Tomon. “Erdős-Hajnal-Type Results for Monotone Paths.” Journal of Combinatorial Theory. Series B. Elsevier, 2021. https://doi.org/10.1016/j.jctb.2021.05.004. ieee: J. Pach and I. Tomon, “Erdős-Hajnal-type results for monotone paths,” Journal of Combinatorial Theory. Series B, vol. 151. Elsevier, pp. 21–37, 2021. ista: Pach J, Tomon I. 2021. Erdős-Hajnal-type results for monotone paths. Journal of Combinatorial Theory. Series B. 151, 21–37. mla: Pach, János, and István Tomon. “Erdős-Hajnal-Type Results for Monotone Paths.” Journal of Combinatorial Theory. Series B, vol. 151, Elsevier, 2021, pp. 21–37, doi:10.1016/j.jctb.2021.05.004. short: J. Pach, I. Tomon, Journal of Combinatorial Theory. Series B 151 (2021) 21–37. date_created: 2021-06-27T22:01:47Z date_published: 2021-06-09T00:00:00Z date_updated: 2023-08-10T13:38:00Z day: '09' ddc: - '510' department: - _id: HeEd doi: 10.1016/j.jctb.2021.05.004 external_id: isi: - '000702280800002' file: - access_level: open_access checksum: 15fbc9064cd9d1c777ac0043b78c8f12 content_type: application/pdf creator: asandaue date_created: 2021-06-28T13:33:23Z date_updated: 2021-06-28T13:33:23Z file_id: '9612' file_name: 2021_JournalOfCombinatorialTheory_Pach.pdf file_size: 418168 relation: main_file success: 1 file_date_updated: 2021-06-28T13:33:23Z has_accepted_license: '1' intvolume: ' 151' isi: 1 language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: 21-37 project: - _id: 268116B8-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00342 name: The Wittgenstein Prize publication: Journal of Combinatorial Theory. Series B publication_identifier: issn: - 0095-8956 publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: Erdős-Hajnal-type results for monotone paths tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 151 year: '2021' ... --- _id: '9821' 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. acknowledgement: We express our gratitude to the anonymous referees who provided constructive comments that helped us improve the quality of the paper. article_number: e0253851 article_processing_charge: Yes article_type: original author: - first_name: Grzegorz full_name: Graff, Grzegorz last_name: Graff - first_name: Beata full_name: Graff, Beata last_name: Graff - first_name: Pawel full_name: Pilarczyk, Pawel id: 3768D56A-F248-11E8-B48F-1D18A9856A87 last_name: Pilarczyk - first_name: Grzegorz full_name: Jablonski, Grzegorz id: 4483EF78-F248-11E8-B48F-1D18A9856A87 last_name: Jablonski orcid: 0000-0002-3536-9866 - first_name: Dariusz full_name: Gąsecki, Dariusz last_name: Gąsecki - first_name: Krzysztof full_name: Narkiewicz, Krzysztof last_name: Narkiewicz citation: 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 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 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. 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. 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. 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). date_created: 2021-08-08T22:01:28Z date_published: 2021-07-01T00:00:00Z date_updated: 2023-08-10T14:21:42Z day: '01' ddc: - '006' department: - _id: HeEd doi: 10.1371/journal.pone.0253851 external_id: isi: - '000678124900050' pmid: - '34292957' file: - access_level: open_access checksum: 0277aa155d5db1febd2cb384768bba5f content_type: application/pdf creator: asandaue date_created: 2021-08-09T09:25:41Z date_updated: 2021-08-09T09:25:41Z file_id: '9832' file_name: 2021_PLoSONE_Graff.pdf file_size: 2706919 relation: main_file success: 1 file_date_updated: 2021-08-09T09:25:41Z has_accepted_license: '1' intvolume: ' 16' isi: 1 issue: '7' language: - iso: eng month: '07' oa: 1 oa_version: Published Version pmid: 1 publication: PLoS ONE publication_identifier: eissn: - '19326203' publication_status: published publisher: Public Library of Science quality_controlled: '1' scopus_import: '1' status: public title: Persistent homology as a new method of the assessment of heart rate variability tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 16 year: '2021' ... --- _id: '10222' abstract: - lang: eng text: Consider a random set of points on the unit sphere in ℝd, which can be either uniformly sampled or a Poisson point process. Its convex hull is a random inscribed polytope, whose boundary approximates the sphere. We focus on the case d = 3, for which there are elementary proofs and fascinating formulas for metric properties. In particular, we study the fraction of acute facets, the expected intrinsic volumes, the total edge length, and the distance to a fixed point. Finally we generalize the results to the ellipsoid with homeoid density. acknowledgement: "This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35.\r\nWe are grateful to Dmitry Zaporozhets and Christoph Thäle for valuable comments and for directing us to relevant references. We also thank to Anton Mellit for a useful discussion on Bessel functions." article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Anton full_name: Nikitenko, Anton id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87 last_name: Nikitenko orcid: 0000-0002-0659-3201 citation: ama: Akopyan A, Edelsbrunner H, Nikitenko A. The beauty of random polytopes inscribed in the 2-sphere. Experimental Mathematics. 2021:1-15. doi:10.1080/10586458.2021.1980459 apa: Akopyan, A., Edelsbrunner, H., & Nikitenko, A. (2021). The beauty of random polytopes inscribed in the 2-sphere. Experimental Mathematics. Taylor and Francis. https://doi.org/10.1080/10586458.2021.1980459 chicago: Akopyan, Arseniy, Herbert Edelsbrunner, and Anton Nikitenko. “The Beauty of Random Polytopes Inscribed in the 2-Sphere.” Experimental Mathematics. Taylor and Francis, 2021. https://doi.org/10.1080/10586458.2021.1980459. ieee: A. Akopyan, H. Edelsbrunner, and A. Nikitenko, “The beauty of random polytopes inscribed in the 2-sphere,” Experimental Mathematics. Taylor and Francis, pp. 1–15, 2021. ista: Akopyan A, Edelsbrunner H, Nikitenko A. 2021. The beauty of random polytopes inscribed in the 2-sphere. Experimental Mathematics., 1–15. mla: Akopyan, Arseniy, et al. “The Beauty of Random Polytopes Inscribed in the 2-Sphere.” Experimental Mathematics, Taylor and Francis, 2021, pp. 1–15, doi:10.1080/10586458.2021.1980459. short: A. Akopyan, H. Edelsbrunner, A. Nikitenko, Experimental Mathematics (2021) 1–15. date_created: 2021-11-07T23:01:25Z date_published: 2021-10-25T00:00:00Z date_updated: 2023-08-14T11:57:07Z day: '25' ddc: - '510' department: - _id: HeEd doi: 10.1080/10586458.2021.1980459 ec_funded: 1 external_id: arxiv: - '2007.07783' isi: - '000710893500001' file: - access_level: open_access checksum: 3514382e3a1eb87fa6c61ad622874415 content_type: application/pdf creator: dernst date_created: 2023-08-14T11:55:10Z date_updated: 2023-08-14T11:55:10Z file_id: '14053' file_name: 2023_ExperimentalMath_Akopyan.pdf file_size: 1966019 relation: main_file success: 1 file_date_updated: 2023-08-14T11:55:10Z has_accepted_license: '1' isi: 1 language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: 1-15 project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended - _id: 268116B8-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00342 name: The Wittgenstein Prize - _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316 grant_number: I4887 name: Discretization in Geometry and Dynamics - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication: Experimental Mathematics publication_identifier: eissn: - 1944-950X issn: - 1058-6458 publication_status: published publisher: Taylor and Francis quality_controlled: '1' scopus_import: '1' status: public title: The beauty of random polytopes inscribed in the 2-sphere tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2021' ... --- _id: '8940' abstract: - lang: eng text: We quantise Whitney’s construction to prove the existence of a triangulation for any C^2 manifold, so that we get an algorithm with explicit bounds. We also give a new elementary proof, which is completely geometric. acknowledgement: This work has been funded by the European Research Council under the European Union’s ERC Grant Agreement Number 339025 GUDHI (Algorithmic Foundations of Geometric Understanding in Higher Dimensions). The third author also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. Open access funding provided by the Institute of Science and Technology (IST Austria). article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Jean-Daniel full_name: Boissonnat, Jean-Daniel last_name: Boissonnat - first_name: Siargey full_name: Kachanovich, Siargey last_name: Kachanovich - first_name: Mathijs full_name: Wintraecken, Mathijs id: 307CFBC8-F248-11E8-B48F-1D18A9856A87 last_name: Wintraecken orcid: 0000-0002-7472-2220 citation: ama: 'Boissonnat J-D, Kachanovich S, Wintraecken M. Triangulating submanifolds: An elementary and quantified version of Whitney’s method. Discrete & Computational Geometry. 2021;66(1):386-434. doi:10.1007/s00454-020-00250-8' apa: 'Boissonnat, J.-D., Kachanovich, S., & Wintraecken, M. (2021). Triangulating submanifolds: An elementary and quantified version of Whitney’s method. Discrete & Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00250-8' chicago: 'Boissonnat, Jean-Daniel, Siargey Kachanovich, and Mathijs Wintraecken. “Triangulating Submanifolds: An Elementary and Quantified Version of Whitney’s Method.” Discrete & Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-020-00250-8.' ieee: 'J.-D. Boissonnat, S. Kachanovich, and M. Wintraecken, “Triangulating submanifolds: An elementary and quantified version of Whitney’s method,” Discrete & Computational Geometry, vol. 66, no. 1. Springer Nature, pp. 386–434, 2021.' ista: 'Boissonnat J-D, Kachanovich S, Wintraecken M. 2021. Triangulating submanifolds: An elementary and quantified version of Whitney’s method. Discrete & Computational Geometry. 66(1), 386–434.' mla: 'Boissonnat, Jean-Daniel, et al. “Triangulating Submanifolds: An Elementary and Quantified Version of Whitney’s Method.” Discrete & Computational Geometry, vol. 66, no. 1, Springer Nature, 2021, pp. 386–434, doi:10.1007/s00454-020-00250-8.' short: J.-D. Boissonnat, S. Kachanovich, M. Wintraecken, Discrete & Computational Geometry 66 (2021) 386–434. date_created: 2020-12-12T11:07:02Z date_published: 2021-07-01T00:00:00Z date_updated: 2023-09-05T15:02:40Z day: '01' ddc: - '516' department: - _id: HeEd doi: 10.1007/s00454-020-00250-8 ec_funded: 1 external_id: isi: - '000597770300001' file: - access_level: open_access checksum: c848986091e56699dc12de85adb1e39c content_type: application/pdf creator: kschuh date_created: 2021-08-06T09:52:29Z date_updated: 2021-08-06T09:52:29Z file_id: '9795' file_name: 2021_DescreteCompGeopmetry_Boissonnat.pdf file_size: 983307 relation: main_file success: 1 file_date_updated: 2021-08-06T09:52:29Z has_accepted_license: '1' intvolume: ' 66' isi: 1 issue: '1' keyword: - Theoretical Computer Science - Computational Theory and Mathematics - Geometry and Topology - Discrete Mathematics and Combinatorics language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: 386-434 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Discrete & Computational Geometry publication_identifier: eissn: - 1432-0444 issn: - 0179-5376 publication_status: published publisher: Springer Nature quality_controlled: '1' status: public title: 'Triangulating submanifolds: An elementary and quantified version of Whitney’s method' tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 66 year: '2021' ... --- _id: '9111' abstract: - lang: eng text: 'We study the probabilistic convergence between the mapper graph and the Reeb graph of a topological space X equipped with a continuous function f:X→R. We first give a categorification of the mapper graph and the Reeb graph by interpreting them in terms of cosheaves and stratified covers of the real line R. We then introduce a variant of the classic mapper graph of Singh et al. (in: Eurographics symposium on point-based graphics, 2007), referred to as the enhanced mapper graph, and demonstrate that such a construction approximates the Reeb graph of (X,f) when it is applied to points randomly sampled from a probability density function concentrated on (X,f). Our techniques are based on the interleaving distance of constructible cosheaves and topological estimation via kernel density estimates. Following Munch and Wang (In: 32nd international symposium on computational geometry, volume 51 of Leibniz international proceedings in informatics (LIPIcs), Dagstuhl, Germany, pp 53:1–53:16, 2016), we first show that the mapper graph of (X,f), a constructible R-space (with a fixed open cover), approximates the Reeb graph of the same space. We then construct an isomorphism between the mapper of (X,f) to the mapper of a super-level set of a probability density function concentrated on (X,f). Finally, building on the approach of Bobrowski et al. (Bernoulli 23(1):288–328, 2017b), we show that, with high probability, we can recover the mapper of the super-level set given a sufficiently large sample. Our work is the first to consider the mapper construction using the theory of cosheaves in a probabilistic setting. It is part of an ongoing effort to combine sheaf theory, probability, and statistics, to support topological data analysis with random data.' acknowledgement: "AB was supported in part by the European Union’s Horizon 2020 research and innovation\r\nprogramme under the Marie Sklodowska-Curie GrantAgreement No. 754411 and NSF IIS-1513616. OB was supported in part by the Israel Science Foundation, Grant 1965/19. BW was supported in part by NSF IIS-1513616 and DBI-1661375. EM was supported in part by NSF CMMI-1800466, DMS-1800446, and CCF-1907591.We would like to thank the Institute for Mathematics and its Applications for hosting a workshop titled Bridging Statistics and Sheaves in May 2018, where this work was conceived.\r\nOpen Access funding provided by Institute of Science and Technology (IST Austria)." article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Adam full_name: Brown, Adam id: 70B7FDF6-608D-11E9-9333-8535E6697425 last_name: Brown - first_name: Omer full_name: Bobrowski, Omer last_name: Bobrowski - first_name: Elizabeth full_name: Munch, Elizabeth last_name: Munch - first_name: Bei full_name: Wang, Bei last_name: Wang citation: ama: Brown A, Bobrowski O, Munch E, Wang B. Probabilistic convergence and stability of random mapper graphs. Journal of Applied and Computational Topology. 2021;5(1):99-140. doi:10.1007/s41468-020-00063-x apa: Brown, A., Bobrowski, O., Munch, E., & Wang, B. (2021). Probabilistic convergence and stability of random mapper graphs. Journal of Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-020-00063-x chicago: Brown, Adam, Omer Bobrowski, Elizabeth Munch, and Bei Wang. “Probabilistic Convergence and Stability of Random Mapper Graphs.” Journal of Applied and Computational Topology. Springer Nature, 2021. https://doi.org/10.1007/s41468-020-00063-x. ieee: A. Brown, O. Bobrowski, E. Munch, and B. Wang, “Probabilistic convergence and stability of random mapper graphs,” Journal of Applied and Computational Topology, vol. 5, no. 1. Springer Nature, pp. 99–140, 2021. ista: Brown A, Bobrowski O, Munch E, Wang B. 2021. Probabilistic convergence and stability of random mapper graphs. Journal of Applied and Computational Topology. 5(1), 99–140. mla: Brown, Adam, et al. “Probabilistic Convergence and Stability of Random Mapper Graphs.” Journal of Applied and Computational Topology, vol. 5, no. 1, Springer Nature, 2021, pp. 99–140, doi:10.1007/s41468-020-00063-x. short: A. Brown, O. Bobrowski, E. Munch, B. Wang, Journal of Applied and Computational Topology 5 (2021) 99–140. date_created: 2021-02-11T14:41:02Z date_published: 2021-03-01T00:00:00Z date_updated: 2023-09-05T15:37:56Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.1007/s41468-020-00063-x ec_funded: 1 external_id: arxiv: - '1909.03488' file: - access_level: open_access checksum: 3f02e9d47c428484733da0f588a3c069 content_type: application/pdf creator: dernst date_created: 2021-02-11T14:43:59Z date_updated: 2021-02-11T14:43:59Z file_id: '9112' file_name: 2020_JourApplCompTopology_Brown.pdf file_size: 2090265 relation: main_file success: 1 file_date_updated: 2021-02-11T14:43:59Z has_accepted_license: '1' intvolume: ' 5' issue: '1' language: - iso: eng month: '03' oa: 1 oa_version: Published Version page: 99-140 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Journal of Applied and Computational Topology publication_identifier: eissn: - 2367-1734 issn: - 2367-1726 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Probabilistic convergence and stability of random mapper graphs tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 5 year: '2021' ... --- _id: '9056' abstract: - lang: eng text: "In this thesis we study persistence of multi-covers of Euclidean balls and the geometric structures underlying their computation, in particular Delaunay mosaics and Voronoi tessellations. The k-fold cover for some discrete input point set consists of the space where at least k balls of radius r around the input points overlap. Persistence is a notion that captures, in some sense, the topology of the shape underlying the input. While persistence is usually computed for the union of balls, the k-fold cover is of interest as it captures local density,\r\nand thus might approximate the shape of the input better if the input data is noisy. To compute persistence of these k-fold covers, we need a discretization that is provided by higher-order Delaunay mosaics. We present and implement a simple and efficient algorithm for the computation of higher-order Delaunay mosaics, and use it to give experimental results for their combinatorial properties. The algorithm makes use of a new geometric structure, the rhomboid tiling. It contains the higher-order Delaunay mosaics as slices, and by introducing a filtration\r\nfunction on the tiling, we also obtain higher-order α-shapes as slices. These allow us to compute persistence of the multi-covers for varying radius r; the computation for varying k is less straight-foward and involves the rhomboid tiling directly. We apply our algorithms to experimental sphere packings to shed light on their structural properties. Finally, inspired by periodic structures in packings and materials, we propose and implement an algorithm for periodic Delaunay triangulations to be integrated into the Computational Geometry Algorithms Library (CGAL), and discuss the implications on persistence for periodic data sets." alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Georg F full_name: Osang, Georg F id: 464B40D6-F248-11E8-B48F-1D18A9856A87 last_name: Osang orcid: 0000-0002-8882-5116 citation: ama: Osang GF. Multi-cover persistence and Delaunay mosaics. 2021. doi:10.15479/AT:ISTA:9056 apa: Osang, G. F. (2021). Multi-cover persistence and Delaunay mosaics. Institute of Science and Technology Austria, Klosterneuburg. https://doi.org/10.15479/AT:ISTA:9056 chicago: Osang, Georg F. “Multi-Cover Persistence and Delaunay Mosaics.” Institute of Science and Technology Austria, 2021. https://doi.org/10.15479/AT:ISTA:9056. ieee: G. F. Osang, “Multi-cover persistence and Delaunay mosaics,” Institute of Science and Technology Austria, Klosterneuburg, 2021. ista: 'Osang GF. 2021. Multi-cover persistence and Delaunay mosaics. Klosterneuburg: Institute of Science and Technology Austria.' mla: Osang, Georg F. Multi-Cover Persistence and Delaunay Mosaics. Institute of Science and Technology Austria, 2021, doi:10.15479/AT:ISTA:9056. short: G.F. Osang, Multi-Cover Persistence and Delaunay Mosaics, Institute of Science and Technology Austria, 2021. date_created: 2021-02-02T14:11:06Z date_published: 2021-02-01T00:00:00Z date_updated: 2023-09-07T13:29:01Z day: '01' ddc: - '006' - '514' - '516' degree_awarded: PhD department: - _id: HeEd - _id: GradSch doi: 10.15479/AT:ISTA:9056 file: - access_level: closed checksum: bcf27986147cab0533b6abadd74e7629 content_type: application/zip creator: patrickd date_created: 2021-02-02T14:09:25Z date_updated: 2021-02-03T10:37:28Z file_id: '9063' file_name: thesis_source.zip file_size: 13446994 relation: source_file - access_level: open_access checksum: 9cc8af266579a464385bbe2aff6af606 content_type: application/pdf creator: patrickd date_created: 2021-02-02T14:09:18Z date_updated: 2021-02-02T14:09:18Z file_id: '9064' file_name: thesis_pdfA2b.pdf file_size: 5210329 relation: main_file success: 1 file_date_updated: 2021-02-03T10:37:28Z has_accepted_license: '1' language: - iso: eng month: '02' oa: 1 oa_version: Published Version page: '134' place: Klosterneuburg publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '187' relation: part_of_dissertation status: public - id: '8703' relation: part_of_dissertation status: public status: public supervisor: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 title: Multi-cover persistence and Delaunay mosaics tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: dissertation user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2021' ... --- _id: '10204' abstract: - lang: eng text: Two common representations of close packings of identical spheres consisting of hexagonal layers, called Barlow stackings, appear abundantly in minerals and metals. These motifs, however, occupy an identical portion of space and bear identical first-order topological signatures as measured by persistent homology. Here we present a novel method based on k-fold covers that unambiguously distinguishes between these patterns. Moreover, our approach provides topological evidence that the FCC motif is the more stable of the two in the context of evolving experimental sphere packings during the transition from disordered to an ordered state. We conclude that our approach can be generalised to distinguish between various Barlow stackings manifested in minerals and metals. acknowledgement: MS acknowledges the support by Australian Research Council funding through the ARC Training Centre for M3D Innovation (IC180100008). MS thanks M. Hanifpour and N. Francois for their input and valuable discussions. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme, grant no. 788183 and from the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31. article_processing_charge: No article_type: original author: - first_name: Georg F full_name: Osang, Georg F id: 464B40D6-F248-11E8-B48F-1D18A9856A87 last_name: Osang orcid: 0000-0002-8882-5116 - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Mohammad full_name: Saadatfar, Mohammad last_name: Saadatfar citation: ama: Osang GF, Edelsbrunner H, Saadatfar M. Topological signatures and stability of hexagonal close packing and Barlow stackings. Soft Matter. 2021;17(40):9107-9115. doi:10.1039/d1sm00774b apa: Osang, G. F., Edelsbrunner, H., & Saadatfar, M. (2021). Topological signatures and stability of hexagonal close packing and Barlow stackings. Soft Matter. Royal Society of Chemistry . https://doi.org/10.1039/d1sm00774b chicago: Osang, Georg F, Herbert Edelsbrunner, and Mohammad Saadatfar. “Topological Signatures and Stability of Hexagonal Close Packing and Barlow Stackings.” Soft Matter. Royal Society of Chemistry , 2021. https://doi.org/10.1039/d1sm00774b. ieee: G. F. Osang, H. Edelsbrunner, and M. Saadatfar, “Topological signatures and stability of hexagonal close packing and Barlow stackings,” Soft Matter, vol. 17, no. 40. Royal Society of Chemistry , pp. 9107–9115, 2021. ista: Osang GF, Edelsbrunner H, Saadatfar M. 2021. Topological signatures and stability of hexagonal close packing and Barlow stackings. Soft Matter. 17(40), 9107–9115. mla: Osang, Georg F., et al. “Topological Signatures and Stability of Hexagonal Close Packing and Barlow Stackings.” Soft Matter, vol. 17, no. 40, Royal Society of Chemistry , 2021, pp. 9107–15, doi:10.1039/d1sm00774b. short: G.F. Osang, H. Edelsbrunner, M. Saadatfar, Soft Matter 17 (2021) 9107–9115. date_created: 2021-10-31T23:01:30Z date_published: 2021-10-20T00:00:00Z date_updated: 2023-10-03T09:24:27Z day: '20' ddc: - '540' department: - _id: HeEd doi: 10.1039/d1sm00774b ec_funded: 1 external_id: isi: - '000700090000001' pmid: - '34569592' file: - access_level: open_access checksum: b4da0c420530295e61b153960f6cb350 content_type: application/pdf creator: dernst date_created: 2023-10-03T09:21:42Z date_updated: 2023-10-03T09:21:42Z file_id: '14385' file_name: 2021_SoftMatter_acceptedversion_Osang.pdf file_size: 4678788 relation: main_file success: 1 file_date_updated: 2023-10-03T09:21:42Z has_accepted_license: '1' intvolume: ' 17' isi: 1 issue: '40' language: - iso: eng month: '10' oa: 1 oa_version: Submitted Version page: 9107-9115 pmid: 1 project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended - _id: 268116B8-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00342 name: The Wittgenstein Prize publication: Soft Matter publication_identifier: eissn: - 1744-6848 issn: - 1744-683X publication_status: published publisher: 'Royal Society of Chemistry ' quality_controlled: '1' scopus_import: '1' status: public title: Topological signatures and stability of hexagonal close packing and Barlow stackings type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 17 year: '2021' ... --- _id: '9605' abstract: - lang: eng text: 'Given a finite set A ⊂ ℝ^d, let Cov_{r,k} denote the set of all points within distance r to at least k points of A. Allowing r and k to vary, we obtain a 2-parameter family of spaces that grow larger when r increases or k decreases, called the multicover bifiltration. Motivated by the problem of computing the homology of this bifiltration, we introduce two closely related combinatorial bifiltrations, one polyhedral and the other simplicial, which are both topologically equivalent to the multicover bifiltration and far smaller than a Čech-based model considered in prior work of Sheehy. Our polyhedral construction is a bifiltration of the rhomboid tiling of Edelsbrunner and Osang, and can be efficiently computed using a variant of an algorithm given by these authors as well. Using an implementation for dimension 2 and 3, we provide experimental results. Our simplicial construction is useful for understanding the polyhedral construction and proving its correctness. ' acknowledgement: The authors want to thank the reviewers for many helpful comments and suggestions. alternative_title: - LIPIcs article_number: '27' article_processing_charge: No author: - first_name: René full_name: Corbet, René last_name: Corbet - first_name: Michael full_name: Kerber, Michael last_name: Kerber - first_name: Michael full_name: Lesnick, Michael last_name: Lesnick - first_name: Georg F full_name: Osang, Georg F id: 464B40D6-F248-11E8-B48F-1D18A9856A87 last_name: Osang orcid: 0000-0002-8882-5116 citation: ama: 'Corbet R, Kerber M, Lesnick M, Osang GF. Computing the multicover bifiltration. In: Leibniz International Proceedings in Informatics. Vol 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021. doi:10.4230/LIPIcs.SoCG.2021.27' apa: 'Corbet, R., Kerber, M., Lesnick, M., & Osang, G. F. (2021). Computing the multicover bifiltration. In Leibniz International Proceedings in Informatics (Vol. 189). Online: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.27' chicago: Corbet, René, Michael Kerber, Michael Lesnick, and Georg F Osang. “Computing the Multicover Bifiltration.” In Leibniz International Proceedings in Informatics, Vol. 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.27. ieee: R. Corbet, M. Kerber, M. Lesnick, and G. F. Osang, “Computing the multicover bifiltration,” in Leibniz International Proceedings in Informatics, Online, 2021, vol. 189. ista: 'Corbet R, Kerber M, Lesnick M, Osang GF. 2021. Computing the multicover bifiltration. Leibniz International Proceedings in Informatics. SoCG: International Symposium on Computational Geometry, LIPIcs, vol. 189, 27.' mla: Corbet, René, et al. “Computing the Multicover Bifiltration.” Leibniz International Proceedings in Informatics, vol. 189, 27, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, doi:10.4230/LIPIcs.SoCG.2021.27. short: R. Corbet, M. Kerber, M. Lesnick, G.F. Osang, in:, Leibniz International Proceedings in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. conference: end_date: 2021-06-11 location: Online name: 'SoCG: International Symposium on Computational Geometry' start_date: 2021-06-07 date_created: 2021-06-27T22:01:49Z date_published: 2021-06-02T00:00:00Z date_updated: 2023-10-04T12:03:39Z day: '02' ddc: - '516' department: - _id: HeEd doi: 10.4230/LIPIcs.SoCG.2021.27 external_id: arxiv: - '2103.07823' file: - access_level: open_access checksum: 0de217501e7ba8b267d58deed0d51761 content_type: application/pdf creator: cziletti date_created: 2021-06-28T12:40:47Z date_updated: 2021-06-28T12:40:47Z file_id: '9610' file_name: 2021_LIPIcs_Corbet.pdf file_size: '1367983' relation: main_file success: 1 file_date_updated: 2021-06-28T12:40:47Z has_accepted_license: '1' intvolume: ' 189' language: - iso: eng month: '06' oa: 1 oa_version: Published Version publication: Leibniz International Proceedings in Informatics publication_identifier: isbn: - '9783959771849' issn: - '18688969' publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' related_material: link: - relation: extended_version url: https://arxiv.org/abs/2103.07823 record: - id: '12709' relation: later_version status: public scopus_import: '1' status: public title: Computing the multicover bifiltration tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425 volume: 189 year: '2021' ...