--- _id: '12086' abstract: - lang: eng text: We present a simple algorithm for computing higher-order Delaunay mosaics that works in Euclidean spaces of any finite dimensions. The algorithm selects the vertices of the order-k mosaic from incrementally constructed lower-order mosaics and uses an algorithm for weighted first-order Delaunay mosaics as a black-box to construct the order-k mosaic from its vertices. Beyond this black-box, the algorithm uses only combinatorial operations, thus facilitating easy implementation. We extend this algorithm to compute higher-order α-shapes and provide open-source implementations. We present experimental results for properties of higher-order Delaunay mosaics of random point sets. acknowledgement: Open access funding provided by Austrian Science Fund (FWF). 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. 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. A simple algorithm for higher-order Delaunay mosaics and alpha shapes. Algorithmica. 2023;85:277-295. doi:10.1007/s00453-022-01027-6 apa: Edelsbrunner, H., & Osang, G. F. (2023). A simple algorithm for higher-order Delaunay mosaics and alpha shapes. Algorithmica. Springer Nature. https://doi.org/10.1007/s00453-022-01027-6 chicago: Edelsbrunner, Herbert, and Georg F Osang. “A Simple Algorithm for Higher-Order Delaunay Mosaics and Alpha Shapes.” Algorithmica. Springer Nature, 2023. https://doi.org/10.1007/s00453-022-01027-6. ieee: H. Edelsbrunner and G. F. Osang, “A simple algorithm for higher-order Delaunay mosaics and alpha shapes,” Algorithmica, vol. 85. Springer Nature, pp. 277–295, 2023. ista: Edelsbrunner H, Osang GF. 2023. A simple algorithm for higher-order Delaunay mosaics and alpha shapes. Algorithmica. 85, 277–295. mla: Edelsbrunner, Herbert, and Georg F. Osang. “A Simple Algorithm for Higher-Order Delaunay Mosaics and Alpha Shapes.” Algorithmica, vol. 85, Springer Nature, 2023, pp. 277–95, doi:10.1007/s00453-022-01027-6. short: H. Edelsbrunner, G.F. Osang, Algorithmica 85 (2023) 277–295. date_created: 2022-09-11T22:01:57Z date_published: 2023-01-01T00:00:00Z date_updated: 2023-06-27T12:53:43Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.1007/s00453-022-01027-6 ec_funded: 1 external_id: isi: - '000846967100001' file: - access_level: open_access checksum: 71685ca5121f4c837f40c3f8eb50c915 content_type: application/pdf creator: dernst date_created: 2023-01-20T10:02:48Z date_updated: 2023-01-20T10:02:48Z file_id: '12322' file_name: 2023_Algorithmica_Edelsbrunner.pdf file_size: 911017 relation: main_file success: 1 file_date_updated: 2023-01-20T10:02:48Z has_accepted_license: '1' intvolume: ' 85' isi: 1 language: - iso: eng month: '01' oa: 1 oa_version: Published Version page: 277-295 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: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication: Algorithmica publication_identifier: eissn: - 1432-0541 issn: - 0178-4617 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: A simple algorithm for higher-order Delaunay mosaics and alpha shapes 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: 2EBD1598-F248-11E8-B48F-1D18A9856A87 volume: 85 year: '2023' ... --- _id: '12709' 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: We thank the anonymous reviewers for many helpful comments and suggestions, which led to substantial improvements of the paper. The first two authors were supported by the Austrian Science Fund (FWF) grant number P 29984-N35 and W1230. The first author was partly supported by an Austrian Marshall Plan Scholarship, and by the Brummer & Partners MathDataLab. A conference version of this paper was presented at the 37th International Symposium on Computational Geometry (SoCG 2021). Open access funding provided by the Royal Institute of Technology. article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: René full_name: Corbet, René last_name: Corbet - first_name: Michael full_name: Kerber, Michael id: 36E4574A-F248-11E8-B48F-1D18A9856A87 last_name: Kerber orcid: 0000-0002-8030-9299 - 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. Discrete and Computational Geometry. 2023;70:376-405. doi:10.1007/s00454-022-00476-8 apa: Corbet, R., Kerber, M., Lesnick, M., & Osang, G. F. (2023). Computing the multicover bifiltration. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-022-00476-8 chicago: Corbet, René, Michael Kerber, Michael Lesnick, and Georg F Osang. “Computing the Multicover Bifiltration.” Discrete and Computational Geometry. Springer Nature, 2023. https://doi.org/10.1007/s00454-022-00476-8. ieee: R. Corbet, M. Kerber, M. Lesnick, and G. F. Osang, “Computing the multicover bifiltration,” Discrete and Computational Geometry, vol. 70. Springer Nature, pp. 376–405, 2023. ista: Corbet R, Kerber M, Lesnick M, Osang GF. 2023. Computing the multicover bifiltration. Discrete and Computational Geometry. 70, 376–405. mla: Corbet, René, et al. “Computing the Multicover Bifiltration.” Discrete and Computational Geometry, vol. 70, Springer Nature, 2023, pp. 376–405, doi:10.1007/s00454-022-00476-8. short: R. Corbet, M. Kerber, M. Lesnick, G.F. Osang, Discrete and Computational Geometry 70 (2023) 376–405. date_created: 2023-03-05T23:01:06Z date_published: 2023-09-01T00:00:00Z date_updated: 2023-10-04T12:03:40Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1007/s00454-022-00476-8 external_id: arxiv: - '2103.07823' isi: - '000936496800001' file: - access_level: open_access checksum: 71ce7e59f7ee4620acc704fecca620c2 content_type: application/pdf creator: cchlebak date_created: 2023-03-07T14:40:14Z date_updated: 2023-03-07T14:40:14Z file_id: '12715' file_name: 2023_DisCompGeo_Corbet.pdf file_size: 1359323 relation: main_file success: 1 file_date_updated: 2023-03-07T14:40:14Z has_accepted_license: '1' intvolume: ' 70' isi: 1 language: - iso: eng month: '09' oa: 1 oa_version: Published Version page: 376-405 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: '9605' relation: earlier_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: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 70 year: '2023' ... --- _id: '10367' abstract: - lang: eng text: How information is created, shared and consumed has changed rapidly in recent decades, in part thanks to new social platforms and technologies on the web. With ever-larger amounts of unstructured and limited labels, organizing and reconciling information from different sources and modalities is a central challenge in machine learning. This cutting-edge tutorial aims to introduce the multimodal entailment task, which can be useful for detecting semantic alignments when a single modality alone does not suffice for a whole content understanding. Starting with a brief overview of natural language processing, computer vision, structured data and neural graph learning, we lay the foundations for the multimodal sections to follow. We then discuss recent multimodal learning literature covering visual, audio and language streams, and explore case studies focusing on tasks which require fine-grained understanding of visual and linguistic semantics question answering, veracity and hatred classification. Finally, we introduce a new dataset for recognizing multimodal entailment, exploring it in a hands-on collaborative section. Overall, this tutorial gives an overview of multimodal learning, introduces a multimodal entailment dataset, and encourages future research in the topic. acknowledgement: "We would like to thank Abby Schantz, Abe Ittycheriah, Aliaksei Severyn, Allan Heydon, Aly\r\nGrealish, Andrey Vlasov, Arkaitz Zubiaga, Ashwin Kakarla, Chen Sun, Clayton Williams, Cong\r\nYu, Cordelia Schmid, Da-Cheng Juan, Dan Finnie, Dani Valevski, Daniel Rocha, David Price, David Sklar, Devi Krishna, Elena Kochkina, Enrique Alfonseca, Franc¸oise Beaufays, Isabelle Augenstein, Jialu Liu, John Cantwell, John Palowitch, Jordan Boyd-Graber, Lei Shi, Luis Valente, Maria Voitovich, Mehmet Aktuna, Mogan Brown, Mor Naaman, Natalia P, Nidhi Hebbar, Pete Aykroyd, Rahul Sukthankar, Richa Dixit, Steve Pucci, Tania Bedrax-Weiss, Tobias Kaufmann, Tom Boulos, Tu Tsao, Vladimir Chtchetkine, Yair Kurzion, Yifan Xu and Zach Hynes." article_processing_charge: No author: - first_name: Cesar full_name: Ilharco, Cesar last_name: Ilharco - first_name: Afsaneh full_name: Shirazi, Afsaneh last_name: Shirazi - first_name: Arjun full_name: Gopalan, Arjun last_name: Gopalan - first_name: Arsha full_name: Nagrani, Arsha last_name: Nagrani - first_name: Blaž full_name: Bratanič, Blaž last_name: Bratanič - first_name: Chris full_name: Bregler, Chris last_name: Bregler - first_name: Christina full_name: Liu, Christina last_name: Liu - first_name: Felipe full_name: Ferreira, Felipe last_name: Ferreira - first_name: Gabriek full_name: Barcik, Gabriek last_name: Barcik - first_name: Gabriel full_name: Ilharco, Gabriel last_name: Ilharco - first_name: Georg F full_name: Osang, Georg F id: 464B40D6-F248-11E8-B48F-1D18A9856A87 last_name: Osang - first_name: Jannis full_name: Bulian, Jannis last_name: Bulian - first_name: Jared full_name: Frank, Jared last_name: Frank - first_name: Lucas full_name: Smaira, Lucas last_name: Smaira - first_name: Qin full_name: Cao, Qin last_name: Cao - first_name: Ricardo full_name: Marino, Ricardo last_name: Marino - first_name: Roma full_name: Patel, Roma last_name: Patel - first_name: Thomas full_name: Leung, Thomas last_name: Leung - first_name: Vaiva full_name: Imbrasaite, Vaiva last_name: Imbrasaite citation: ama: 'Ilharco C, Shirazi A, Gopalan A, et al. Recognizing multimodal entailment. In: 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts. Association for Computational Linguistics; 2021:29-30. doi:10.18653/v1/2021.acl-tutorials.6' apa: 'Ilharco, C., Shirazi, A., Gopalan, A., Nagrani, A., Bratanič, B., Bregler, C., … Imbrasaite, V. (2021). Recognizing multimodal entailment. In 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts (pp. 29–30). Bangkok, Thailand: Association for Computational Linguistics. https://doi.org/10.18653/v1/2021.acl-tutorials.6' chicago: Ilharco, Cesar, Afsaneh Shirazi, Arjun Gopalan, Arsha Nagrani, Blaž Bratanič, Chris Bregler, Christina Liu, et al. “Recognizing Multimodal Entailment.” In 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts, 29–30. Association for Computational Linguistics, 2021. https://doi.org/10.18653/v1/2021.acl-tutorials.6. ieee: C. Ilharco et al., “Recognizing multimodal entailment,” in 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts, Bangkok, Thailand, 2021, pp. 29–30. ista: 'Ilharco C, Shirazi A, Gopalan A, Nagrani A, Bratanič B, Bregler C, Liu C, Ferreira F, Barcik G, Ilharco G, Osang GF, Bulian J, Frank J, Smaira L, Cao Q, Marino R, Patel R, Leung T, Imbrasaite V. 2021. Recognizing multimodal entailment. 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts. ACL: Association for Computational Linguistics ; IJCNLP: International Joint Conference on Natural Language Processing, 29–30.' mla: Ilharco, Cesar, et al. “Recognizing Multimodal Entailment.” 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts, Association for Computational Linguistics, 2021, pp. 29–30, doi:10.18653/v1/2021.acl-tutorials.6. short: C. Ilharco, A. Shirazi, A. Gopalan, A. Nagrani, B. Bratanič, C. Bregler, C. Liu, F. Ferreira, G. Barcik, G. Ilharco, G.F. Osang, J. Bulian, J. Frank, L. Smaira, Q. Cao, R. Marino, R. Patel, T. Leung, V. Imbrasaite, in:, 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts, Association for Computational Linguistics, 2021, pp. 29–30. conference: end_date: 2021-08-06 location: Bangkok, Thailand name: 'ACL: Association for Computational Linguistics ; IJCNLP: International Joint Conference on Natural Language Processing' start_date: 2021-08-01 date_created: 2021-11-28T23:01:30Z date_published: 2021-08-01T00:00:00Z date_updated: 2022-01-26T14:26:36Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.18653/v1/2021.acl-tutorials.6 file: - access_level: open_access checksum: b14052a025a6ecf675bdfe51db98c0d7 content_type: application/pdf creator: cchlebak date_created: 2021-11-29T08:41:00Z date_updated: 2021-11-29T08:41:00Z file_id: '10368' file_name: 2021_ACL_Ilharco.pdf file_size: 1227703 relation: main_file success: 1 file_date_updated: 2021-11-29T08:41:00Z has_accepted_license: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://aclanthology.org/2021.acl-tutorials.6/ month: '08' oa: 1 oa_version: Published Version page: 29-30 publication: 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts publication_identifier: isbn: - 9-781-9540-8557-2 publication_status: published publisher: Association for Computational Linguistics quality_controlled: '1' scopus_import: '1' status: public title: Recognizing multimodal entailment 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: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2021' ... --- _id: '9465' abstract: - lang: eng text: "Given a locally finite set \U0001D44B⊆ℝ\U0001D451 and an integer \U0001D458≥0, we consider the function \U0001D430\U0001D458:Del\U0001D458(\U0001D44B)→ℝ on the dual of the order-k Voronoi tessellation, whose sublevel sets generalize the notion of alpha shapes from order-1 to order-k (Edelsbrunner et al. in IEEE Trans Inf Theory IT-29:551–559, 1983; Krasnoshchekov and Polishchuk in Inf Process Lett 114:76–83, 2014). While this function is not necessarily generalized discrete Morse, in the sense of Forman (Adv Math 134:90–145, 1998) and Freij (Discrete Math 309:3821–3829, 2009), we prove that it satisfies similar properties so that its increments can be meaningfully classified into critical and non-critical steps. This result extends to the case of weighted points and sheds light on k-fold covers with balls in Euclidean space." article_number: '15' 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: Anton full_name: Nikitenko, Anton id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87 last_name: Nikitenko - first_name: Georg F full_name: Osang, Georg F id: 464B40D6-F248-11E8-B48F-1D18A9856A87 last_name: Osang citation: ama: Edelsbrunner H, Nikitenko A, Osang GF. A step in the Delaunay mosaic of order k. Journal of Geometry. 2021;112(1). doi:10.1007/s00022-021-00577-4 apa: Edelsbrunner, H., Nikitenko, A., & Osang, G. F. (2021). A step in the Delaunay mosaic of order k. Journal of Geometry. Springer Nature. https://doi.org/10.1007/s00022-021-00577-4 chicago: Edelsbrunner, Herbert, Anton Nikitenko, and Georg F Osang. “A Step in the Delaunay Mosaic of Order K.” Journal of Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00022-021-00577-4. ieee: H. Edelsbrunner, A. Nikitenko, and G. F. Osang, “A step in the Delaunay mosaic of order k,” Journal of Geometry, vol. 112, no. 1. Springer Nature, 2021. ista: Edelsbrunner H, Nikitenko A, Osang GF. 2021. A step in the Delaunay mosaic of order k. Journal of Geometry. 112(1), 15. mla: Edelsbrunner, Herbert, et al. “A Step in the Delaunay Mosaic of Order K.” Journal of Geometry, vol. 112, no. 1, 15, Springer Nature, 2021, doi:10.1007/s00022-021-00577-4. short: H. Edelsbrunner, A. Nikitenko, G.F. Osang, Journal of Geometry 112 (2021). date_created: 2021-06-06T22:01:29Z date_published: 2021-04-01T00:00:00Z date_updated: 2022-05-12T11:41:45Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.1007/s00022-021-00577-4 file: - access_level: open_access checksum: e52a832f1def52a2b23d21bcc09e646f content_type: application/pdf creator: kschuh date_created: 2021-06-11T13:16:26Z date_updated: 2021-06-11T13:16:26Z file_id: '9544' file_name: 2021_Geometry_Edelsbrunner.pdf file_size: 694706 relation: main_file success: 1 file_date_updated: 2021-06-11T13:16:26Z has_accepted_license: '1' intvolume: ' 112' issue: '1' language: - iso: eng month: '04' oa: 1 oa_version: Published Version publication: Journal of Geometry publication_identifier: eissn: - '14208997' issn: - '00472468' publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: A step in the Delaunay mosaic of order k 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 volume: 112 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: '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' ... --- _id: '8703' abstract: - lang: eng text: 'Even though Delaunay originally introduced his famous triangulations in the case of infinite point sets with translational periodicity, a software that computes such triangulations in the general case is not yet available, to the best of our knowledge. Combining and generalizing previous work, we present a practical algorithm for computing such triangulations. The algorithm has been implemented and experiments show that its performance is as good as the one of the CGAL package, which is restricted to cubic periodicity. ' alternative_title: - LIPIcs article_number: '75' 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 - first_name: Mael full_name: Rouxel-Labbé, Mael last_name: Rouxel-Labbé - first_name: Monique full_name: Teillaud, Monique last_name: Teillaud citation: ama: 'Osang GF, Rouxel-Labbé M, Teillaud M. Generalizing CGAL periodic Delaunay triangulations. In: 28th Annual European Symposium on Algorithms. Vol 173. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.ESA.2020.75' apa: 'Osang, G. F., Rouxel-Labbé, M., & Teillaud, M. (2020). Generalizing CGAL periodic Delaunay triangulations. In 28th Annual European Symposium on Algorithms (Vol. 173). Virtual, Online; Pisa, Italy: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.ESA.2020.75' chicago: Osang, Georg F, Mael Rouxel-Labbé, and Monique Teillaud. “Generalizing CGAL Periodic Delaunay Triangulations.” In 28th Annual European Symposium on Algorithms, Vol. 173. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. https://doi.org/10.4230/LIPIcs.ESA.2020.75. ieee: G. F. Osang, M. Rouxel-Labbé, and M. Teillaud, “Generalizing CGAL periodic Delaunay triangulations,” in 28th Annual European Symposium on Algorithms, Virtual, Online; Pisa, Italy, 2020, vol. 173. ista: 'Osang GF, Rouxel-Labbé M, Teillaud M. 2020. Generalizing CGAL periodic Delaunay triangulations. 28th Annual European Symposium on Algorithms. ESA: Annual European Symposium on Algorithms, LIPIcs, vol. 173, 75.' mla: Osang, Georg F., et al. “Generalizing CGAL Periodic Delaunay Triangulations.” 28th Annual European Symposium on Algorithms, vol. 173, 75, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:10.4230/LIPIcs.ESA.2020.75. short: G.F. Osang, M. Rouxel-Labbé, M. Teillaud, in:, 28th Annual European Symposium on Algorithms, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. conference: end_date: 2020-09-09 location: Virtual, Online; Pisa, Italy name: 'ESA: Annual European Symposium on Algorithms' start_date: 2020-09-07 date_created: 2020-10-25T23:01:18Z date_published: 2020-08-26T00:00:00Z date_updated: 2023-09-07T13:29:00Z day: '26' ddc: - '000' department: - _id: HeEd doi: 10.4230/LIPIcs.ESA.2020.75 ec_funded: 1 file: - access_level: open_access checksum: fe0f7c49a99ed870c671b911e10d5496 content_type: application/pdf creator: cziletti date_created: 2020-10-27T14:31:52Z date_updated: 2020-10-27T14:31:52Z file_id: '8712' file_name: 2020_LIPIcs_Osang.pdf file_size: 733291 relation: main_file success: 1 file_date_updated: 2020-10-27T14:31:52Z has_accepted_license: '1' intvolume: ' 173' language: - iso: eng month: '08' oa: 1 oa_version: Published Version project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended publication: 28th Annual European Symposium on Algorithms publication_identifier: isbn: - '9783959771627' issn: - '18688969' publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' related_material: record: - id: '9056' relation: dissertation_contains status: public scopus_import: '1' status: public title: Generalizing CGAL periodic Delaunay triangulations tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/3.0/legalcode name: Creative Commons Attribution 3.0 Unported (CC BY 3.0) short: CC BY (3.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 173 year: '2020' ... --- _id: '7216' abstract: - lang: eng text: 'We present LiveTraVeL (Live Transit Vehicle Labeling), a real-time system to label a stream of noisy observations of transit vehicle trajectories with the transit routes they are serving (e.g., northbound bus #5). In order to scale efficiently to large transit networks, our system first retrieves a small set of candidate routes from a geometrically indexed data structure, then applies a fine-grained scoring step to choose the best match. Given that real-time data remains unavailable for the majority of the world’s transit agencies, these inferences can help feed a real-time map of a transit system’s trips, infer transit trip delays in real time, or measure and correct noisy transit tracking data. This system can run on vehicle observations from a variety of sources that don’t attach route information to vehicle observations, such as public imagery streams or user-contributed transit vehicle sightings.We abstract away the specifics of the sensing system and demonstrate the effectiveness of our system on a "semisynthetic" dataset of all New York City buses, where we simulate sensed trajectories by starting with fully labeled vehicle trajectories reported via the GTFS-Realtime protocol, removing the transit route IDs, and perturbing locations with synthetic noise. Using just the geometric shapes of the trajectories, we demonstrate that our system converges on the correct route ID within a few minutes, even after a vehicle switches from serving one trip to the next.' article_number: '8917514' 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 - first_name: James full_name: Cook, James last_name: Cook - first_name: Alex full_name: Fabrikant, Alex last_name: Fabrikant - first_name: Marco full_name: Gruteser, Marco last_name: Gruteser citation: ama: 'Osang GF, Cook J, Fabrikant A, Gruteser M. LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale. In: 2019 IEEE Intelligent Transportation Systems Conference. IEEE; 2019. doi:10.1109/ITSC.2019.8917514' apa: 'Osang, G. F., Cook, J., Fabrikant, A., & Gruteser, M. (2019). LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale. In 2019 IEEE Intelligent Transportation Systems Conference. Auckland, New Zealand: IEEE. https://doi.org/10.1109/ITSC.2019.8917514' chicago: 'Osang, Georg F, James Cook, Alex Fabrikant, and Marco Gruteser. “LiveTraVeL: Real-Time Matching of Transit Vehicle Trajectories to Transit Routes at Scale.” In 2019 IEEE Intelligent Transportation Systems Conference. IEEE, 2019. https://doi.org/10.1109/ITSC.2019.8917514.' ieee: 'G. F. Osang, J. Cook, A. Fabrikant, and M. Gruteser, “LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale,” in 2019 IEEE Intelligent Transportation Systems Conference, Auckland, New Zealand, 2019.' ista: 'Osang GF, Cook J, Fabrikant A, Gruteser M. 2019. LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale. 2019 IEEE Intelligent Transportation Systems Conference. ITSC: Intelligent Transportation Systems Conference, 8917514.' mla: 'Osang, Georg F., et al. “LiveTraVeL: Real-Time Matching of Transit Vehicle Trajectories to Transit Routes at Scale.” 2019 IEEE Intelligent Transportation Systems Conference, 8917514, IEEE, 2019, doi:10.1109/ITSC.2019.8917514.' short: G.F. Osang, J. Cook, A. Fabrikant, M. Gruteser, in:, 2019 IEEE Intelligent Transportation Systems Conference, IEEE, 2019. conference: end_date: 2019-10-30 location: Auckland, New Zealand name: 'ITSC: Intelligent Transportation Systems Conference' start_date: 2019-10-27 date_created: 2019-12-29T23:00:47Z date_published: 2019-11-28T00:00:00Z date_updated: 2023-09-06T14:50:28Z day: '28' department: - _id: HeEd doi: 10.1109/ITSC.2019.8917514 external_id: isi: - '000521238102050' isi: 1 language: - iso: eng month: '11' oa_version: None publication: 2019 IEEE Intelligent Transportation Systems Conference publication_identifier: isbn: - '9781538670248' publication_status: published publisher: IEEE quality_controlled: '1' scopus_import: '1' status: public title: 'LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale' type: conference user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2019' ... --- _id: '187' 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 from Delaunay mosaics that is isomorphic to the persistence module of the multi-covers. ' acknowledgement: This work is partially supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF). alternative_title: - LIPIcs article_number: '34' 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 orcid: 0000-0002-8882-5116 citation: ama: 'Edelsbrunner H, Osang GF. The multi-cover persistence of Euclidean balls. In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018. doi:10.4230/LIPIcs.SoCG.2018.34' apa: 'Edelsbrunner, H., & Osang, G. F. (2018). The multi-cover persistence of Euclidean balls (Vol. 99). Presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2018.34' chicago: Edelsbrunner, Herbert, and Georg F Osang. “The Multi-Cover Persistence of Euclidean Balls,” Vol. 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. https://doi.org/10.4230/LIPIcs.SoCG.2018.34. ieee: 'H. Edelsbrunner and G. F. Osang, “The multi-cover persistence of Euclidean balls,” presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary, 2018, vol. 99.' ista: 'Edelsbrunner H, Osang GF. 2018. The multi-cover persistence of Euclidean balls. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 99, 34.' mla: Edelsbrunner, Herbert, and Georg F. Osang. The Multi-Cover Persistence of Euclidean Balls. Vol. 99, 34, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, doi:10.4230/LIPIcs.SoCG.2018.34. short: H. Edelsbrunner, G.F. Osang, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. conference: end_date: 2018-06-14 location: Budapest, Hungary name: 'SoCG: Symposium on Computational Geometry' start_date: 2018-06-11 date_created: 2018-12-11T11:45:05Z date_published: 2018-06-11T00:00:00Z date_updated: 2023-09-07T13:29:00Z day: '11' ddc: - '516' department: - _id: HeEd doi: 10.4230/LIPIcs.SoCG.2018.34 file: - access_level: open_access checksum: d8c0533ad0018eb4ed1077475eb8fc18 content_type: application/pdf creator: dernst date_created: 2018-12-18T09:27:22Z date_updated: 2020-07-14T12:45:19Z file_id: '5738' file_name: 2018_LIPIcs_Edelsbrunner_Osang.pdf file_size: 528018 relation: main_file file_date_updated: 2020-07-14T12:45:19Z has_accepted_license: '1' intvolume: ' 99' language: - iso: eng month: '06' oa: 1 oa_version: Published Version project: - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik publist_id: '7732' quality_controlled: '1' related_material: record: - id: '9317' relation: later_version status: public - id: '9056' relation: dissertation_contains 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: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 99 year: '2018' ... --- _id: '193' abstract: - lang: eng text: 'We show attacks on five data-independent memory-hard functions (iMHF) that were submitted to the password hashing competition (PHC). Informally, an MHF is a function which cannot be evaluated on dedicated hardware, like ASICs, at significantly lower hardware and/or energy cost than evaluating a single instance on a standard single-core architecture. Data-independent means the memory access pattern of the function is independent of the input; this makes iMHFs harder to construct than data-dependent ones, but the latter can be attacked by various side-channel attacks. Following [Alwen-Blocki''16], we capture the evaluation of an iMHF as a directed acyclic graph (DAG). The cumulative parallel pebbling complexity of this DAG is a measure for the hardware cost of evaluating the iMHF on an ASIC. Ideally, one would like the complexity of a DAG underlying an iMHF to be as close to quadratic in the number of nodes of the graph as possible. Instead, we show that (the DAGs underlying) the following iMHFs are far from this bound: Rig.v2, TwoCats and Gambit each having an exponent no more than 1.75. Moreover, we show that the complexity of the iMHF modes of the PHC finalists Pomelo and Lyra2 have exponents at most 1.83 and 1.67 respectively. To show this we investigate a combinatorial property of each underlying DAG (called its depth-robustness. By establishing upper bounds on this property we are then able to apply the general technique of [Alwen-Block''16] for analyzing the hardware costs of an iMHF.' acknowledgement: Leonid Reyzin was supported in part by IST Austria and by US NSF grants 1012910, 1012798, and 1422965; this research was performed while he was visiting IST Austria. article_processing_charge: No author: - first_name: Joel F full_name: Alwen, Joel F id: 2A8DFA8C-F248-11E8-B48F-1D18A9856A87 last_name: Alwen - first_name: Peter full_name: Gazi, Peter last_name: Gazi - first_name: Chethan full_name: Kamath Hosdurg, Chethan id: 4BD3F30E-F248-11E8-B48F-1D18A9856A87 last_name: Kamath Hosdurg - first_name: Karen full_name: Klein, Karen id: 3E83A2F8-F248-11E8-B48F-1D18A9856A87 last_name: Klein - 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: Krzysztof Z full_name: Pietrzak, Krzysztof Z id: 3E04A7AA-F248-11E8-B48F-1D18A9856A87 last_name: Pietrzak orcid: 0000-0002-9139-1654 - first_name: Lenoid full_name: Reyzin, Lenoid last_name: Reyzin - first_name: Michal full_name: Rolinek, Michal id: 3CB3BC06-F248-11E8-B48F-1D18A9856A87 last_name: Rolinek - first_name: Michal full_name: Rybar, Michal id: 2B3E3DE8-F248-11E8-B48F-1D18A9856A87 last_name: Rybar citation: ama: 'Alwen JF, Gazi P, Kamath Hosdurg C, et al. On the memory hardness of data independent password hashing functions. In: Proceedings of the 2018 on Asia Conference on Computer and Communication Security. ACM; 2018:51-65. doi:10.1145/3196494.3196534' apa: 'Alwen, J. F., Gazi, P., Kamath Hosdurg, C., Klein, K., Osang, G. F., Pietrzak, K. Z., … Rybar, M. (2018). On the memory hardness of data independent password hashing functions. In Proceedings of the 2018 on Asia Conference on Computer and Communication Security (pp. 51–65). Incheon, Republic of Korea: ACM. https://doi.org/10.1145/3196494.3196534' chicago: Alwen, Joel F, Peter Gazi, Chethan Kamath Hosdurg, Karen Klein, Georg F Osang, Krzysztof Z Pietrzak, Lenoid Reyzin, Michal Rolinek, and Michal Rybar. “On the Memory Hardness of Data Independent Password Hashing Functions.” In Proceedings of the 2018 on Asia Conference on Computer and Communication Security, 51–65. ACM, 2018. https://doi.org/10.1145/3196494.3196534. ieee: J. F. Alwen et al., “On the memory hardness of data independent password hashing functions,” in Proceedings of the 2018 on Asia Conference on Computer and Communication Security, Incheon, Republic of Korea, 2018, pp. 51–65. ista: 'Alwen JF, Gazi P, Kamath Hosdurg C, Klein K, Osang GF, Pietrzak KZ, Reyzin L, Rolinek M, Rybar M. 2018. On the memory hardness of data independent password hashing functions. Proceedings of the 2018 on Asia Conference on Computer and Communication Security. ASIACCS: Asia Conference on Computer and Communications Security , 51–65.' mla: Alwen, Joel F., et al. “On the Memory Hardness of Data Independent Password Hashing Functions.” Proceedings of the 2018 on Asia Conference on Computer and Communication Security, ACM, 2018, pp. 51–65, doi:10.1145/3196494.3196534. short: J.F. Alwen, P. Gazi, C. Kamath Hosdurg, K. Klein, G.F. Osang, K.Z. Pietrzak, L. Reyzin, M. Rolinek, M. Rybar, in:, Proceedings of the 2018 on Asia Conference on Computer and Communication Security, ACM, 2018, pp. 51–65. conference: end_date: 2018-06-08 location: Incheon, Republic of Korea name: 'ASIACCS: Asia Conference on Computer and Communications Security ' start_date: 2018-06-04 date_created: 2018-12-11T11:45:07Z date_published: 2018-06-01T00:00:00Z date_updated: 2023-09-13T09:13:12Z day: '01' department: - _id: KrPi - _id: HeEd - _id: VlKo doi: 10.1145/3196494.3196534 ec_funded: 1 external_id: isi: - '000516620100005' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://eprint.iacr.org/2016/783 month: '06' oa: 1 oa_version: Submitted Version page: 51 - 65 project: - _id: 25FBA906-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '616160' name: 'Discrete Optimization in Computer Vision: Theory and Practice' - _id: 258AA5B2-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '682815' name: Teaching Old Crypto New Tricks publication: Proceedings of the 2018 on Asia Conference on Computer and Communication Security publication_status: published publisher: ACM publist_id: '7723' quality_controlled: '1' scopus_import: '1' status: public title: On the memory hardness of data independent password hashing functions type: conference user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2018' ... --- _id: '1065' abstract: - lang: eng text: 'We consider the problem of reachability in pushdown graphs. We study the problem for pushdown graphs with constant treewidth. Even for pushdown graphs with treewidth 1, for the reachability problem we establish the following: (i) the problem is PTIME-complete, and (ii) any subcubic algorithm for the problem would contradict the k-clique conjecture and imply faster combinatorial algorithms for cliques in graphs.' article_processing_charge: No author: - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - 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: Chatterjee K, Osang GF. Pushdown reachability with constant treewidth. Information Processing Letters. 2017;122:25-29. doi:10.1016/j.ipl.2017.02.003 apa: Chatterjee, K., & Osang, G. F. (2017). Pushdown reachability with constant treewidth. Information Processing Letters. Elsevier. https://doi.org/10.1016/j.ipl.2017.02.003 chicago: Chatterjee, Krishnendu, and Georg F Osang. “Pushdown Reachability with Constant Treewidth.” Information Processing Letters. Elsevier, 2017. https://doi.org/10.1016/j.ipl.2017.02.003. ieee: K. Chatterjee and G. F. Osang, “Pushdown reachability with constant treewidth,” Information Processing Letters, vol. 122. Elsevier, pp. 25–29, 2017. ista: Chatterjee K, Osang GF. 2017. Pushdown reachability with constant treewidth. Information Processing Letters. 122, 25–29. mla: Chatterjee, Krishnendu, and Georg F. Osang. “Pushdown Reachability with Constant Treewidth.” Information Processing Letters, vol. 122, Elsevier, 2017, pp. 25–29, doi:10.1016/j.ipl.2017.02.003. short: K. Chatterjee, G.F. Osang, Information Processing Letters 122 (2017) 25–29. date_created: 2018-12-11T11:49:57Z date_published: 2017-06-01T00:00:00Z date_updated: 2023-09-20T12:08:18Z day: '01' ddc: - '000' department: - _id: KrCh - _id: HeEd doi: 10.1016/j.ipl.2017.02.003 ec_funded: 1 external_id: isi: - '000399506600005' file: - access_level: open_access content_type: application/pdf creator: system date_created: 2018-12-12T10:13:17Z date_updated: 2019-10-15T07:44:51Z file_id: '4998' file_name: IST-2018-991-v1+2_2018_Chatterjee_Pushdown_PREPRINT.pdf file_size: 247657 relation: main_file file_date_updated: 2019-10-15T07:44:51Z has_accepted_license: '1' intvolume: ' 122' isi: 1 language: - iso: eng month: '06' oa: 1 oa_version: Submitted Version page: 25 - 29 project: - _id: 2584A770-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P 23499-N23 name: Modern Graph Algorithmic Techniques in Formal Verification - _id: 25863FF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S11407 name: Game Theory - _id: 2581B60A-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '279307' name: 'Quantitative Graph Games: Theory and Applications' publication: Information Processing Letters publication_identifier: issn: - '00200190' publication_status: published publisher: Elsevier publist_id: '6323' pubrep_id: '991' quality_controlled: '1' scopus_import: '1' status: public title: Pushdown reachability with constant treewidth type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 122 year: '2017' ...