--- _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' ...