--- _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: '12763' abstract: - lang: eng text: 'Kleinjohann (Archiv der Mathematik 35(1):574–582, 1980; Mathematische Zeitschrift 176(3), 327–344, 1981) and Bangert (Archiv der Mathematik 38(1):54–57, 1982) extended the reach rch(S) from subsets S of Euclidean space to the reach rchM(S) of subsets S of Riemannian manifolds M, where M is smooth (we’ll assume at least C3). Bangert showed that sets of positive reach in Euclidean space and Riemannian manifolds are very similar. In this paper we introduce a slight variant of Kleinjohann’s and Bangert’s extension and quantify the similarity between sets of positive reach in Euclidean space and Riemannian manifolds in a new way: Given p∈M and q∈S, we bound the local feature size (a local version of the reach) of its lifting to the tangent space via the inverse exponential map (exp−1p(S)) at q, assuming that rchM(S) and the geodesic distance dM(p,q) are bounded. These bounds are motivated by the importance of the reach and local feature size to manifold learning, topological inference, and triangulating manifolds and the fact that intrinsic approaches circumvent the curse of dimensionality.' acknowledgement: "We thank Eddie Aamari, David Cohen-Steiner, Isa Costantini, Fred Chazal, Ramsay Dyer, André Lieutier, and Alef Sterk for discussion and Pierre Pansu for encouragement. We further acknowledge the anonymous reviewers whose comments helped improve the exposition.\r\nThe research leading to these results has received funding from the European Research Council (ERC) under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement No. 339025 GUDHI (Algorithmic Foundations of Geometry Understanding in Higher Dimensions). The first author is further supported by the French government, through the 3IA Côte d’Azur Investments in the Future project managed by the National Research Agency (ANR) with the reference number ANR-19-P3IA-0002. The second author is supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411 and the Austrian science fund (FWF) M-3073." article_processing_charge: No article_type: original author: - first_name: Jean Daniel full_name: Boissonnat, Jean Daniel last_name: Boissonnat - first_name: Mathijs full_name: Wintraecken, Mathijs id: 307CFBC8-F248-11E8-B48F-1D18A9856A87 last_name: Wintraecken orcid: 0000-0002-7472-2220 citation: ama: Boissonnat JD, Wintraecken M. The reach of subsets of manifolds. Journal of Applied and Computational Topology. 2023;7:619-641. doi:10.1007/s41468-023-00116-x apa: Boissonnat, J. D., & Wintraecken, M. (2023). The reach of subsets of manifolds. Journal of Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-023-00116-x chicago: Boissonnat, Jean Daniel, and Mathijs Wintraecken. “The Reach of Subsets of Manifolds.” Journal of Applied and Computational Topology. Springer Nature, 2023. https://doi.org/10.1007/s41468-023-00116-x. ieee: J. D. Boissonnat and M. Wintraecken, “The reach of subsets of manifolds,” Journal of Applied and Computational Topology, vol. 7. Springer Nature, pp. 619–641, 2023. ista: Boissonnat JD, Wintraecken M. 2023. The reach of subsets of manifolds. Journal of Applied and Computational Topology. 7, 619–641. mla: Boissonnat, Jean Daniel, and Mathijs Wintraecken. “The Reach of Subsets of Manifolds.” Journal of Applied and Computational Topology, vol. 7, Springer Nature, 2023, pp. 619–41, doi:10.1007/s41468-023-00116-x. short: J.D. Boissonnat, M. Wintraecken, Journal of Applied and Computational Topology 7 (2023) 619–641. date_created: 2023-03-26T22:01:08Z date_published: 2023-09-01T00:00:00Z date_updated: 2023-10-04T12:07:18Z day: '01' department: - _id: HeEd doi: 10.1007/s41468-023-00116-x ec_funded: 1 intvolume: ' 7' language: - iso: eng main_file_link: - open_access: '1' url: https://inserm.hal.science/INRIA-SACLAY/hal-04083524v1 month: '09' oa: 1 oa_version: Submitted Version page: 619-641 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships - _id: fc390959-9c52-11eb-aca3-afa58bd282b2 grant_number: M03073 name: Learning and triangulating manifolds via collapses 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: The reach of subsets of manifolds type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 7 year: '2023' ... --- _id: '13221' abstract: - lang: eng text: The safety-liveness dichotomy is a fundamental concept in formal languages which plays a key role in verification. Recently, this dichotomy has been lifted to quantitative properties, which are arbitrary functions from infinite words to partially-ordered domains. We look into harnessing the dichotomy for the specific classes of quantitative properties expressed by quantitative automata. These automata contain finitely many states and rational-valued transition weights, and their common value functions Inf, Sup, LimInf, LimSup, LimInfAvg, LimSupAvg, and DSum map infinite words into the totallyordered domain of real numbers. In this automata-theoretic setting, we establish a connection between quantitative safety and topological continuity and provide an alternative characterization of quantitative safety and liveness in terms of their boolean counterparts. For all common value functions, we show how the safety closure of a quantitative automaton can be constructed in PTime, and we provide PSpace-complete checks of whether a given quantitative automaton is safe or live, with the exception of LimInfAvg and LimSupAvg automata, for which the safety check is in ExpSpace. Moreover, for deterministic Sup, LimInf, and LimSup automata, we give PTime decompositions into safe and live automata. These decompositions enable the separation of techniques for safety and liveness verification for quantitative specifications. acknowledgement: We thank Christof Löding for pointing us to some results on PSpace-hardess of universality problems and the anonymous reviewers for their helpful comments. This work was supported in part by the ERC-2020-AdG 101020093 and the Israel Science Foundation grant 2410/22. alternative_title: - LIPIcs article_number: '17' article_processing_charge: No author: - first_name: Udi full_name: Boker, Udi id: 31E297B6-F248-11E8-B48F-1D18A9856A87 last_name: Boker - first_name: Thomas A full_name: Henzinger, Thomas A id: 40876CD8-F248-11E8-B48F-1D18A9856A87 last_name: Henzinger orcid: 0000-0002-2985-7724 - first_name: Nicolas Adrien full_name: Mazzocchi, Nicolas Adrien id: b26baa86-3308-11ec-87b0-8990f34baa85 last_name: Mazzocchi - first_name: Naci E full_name: Sarac, Naci E id: 8C6B42F8-C8E6-11E9-A03A-F2DCE5697425 last_name: Sarac citation: ama: 'Boker U, Henzinger TA, Mazzocchi NA, Sarac NE. Safety and liveness of quantitative automata. In: 34th International Conference on Concurrency Theory. Vol 279. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2023. doi:10.4230/LIPIcs.CONCUR.2023.17' apa: 'Boker, U., Henzinger, T. A., Mazzocchi, N. A., & Sarac, N. E. (2023). Safety and liveness of quantitative automata. In 34th International Conference on Concurrency Theory (Vol. 279). Antwerp, Belgium: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.CONCUR.2023.17' chicago: Boker, Udi, Thomas A Henzinger, Nicolas Adrien Mazzocchi, and Naci E Sarac. “Safety and Liveness of Quantitative Automata.” In 34th International Conference on Concurrency Theory, Vol. 279. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. https://doi.org/10.4230/LIPIcs.CONCUR.2023.17. ieee: U. Boker, T. A. Henzinger, N. A. Mazzocchi, and N. E. Sarac, “Safety and liveness of quantitative automata,” in 34th International Conference on Concurrency Theory, Antwerp, Belgium, 2023, vol. 279. ista: 'Boker U, Henzinger TA, Mazzocchi NA, Sarac NE. 2023. Safety and liveness of quantitative automata. 34th International Conference on Concurrency Theory. CONCUR: Conference on Concurrency Theory, LIPIcs, vol. 279, 17.' mla: Boker, Udi, et al. “Safety and Liveness of Quantitative Automata.” 34th International Conference on Concurrency Theory, vol. 279, 17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023, doi:10.4230/LIPIcs.CONCUR.2023.17. short: U. Boker, T.A. Henzinger, N.A. Mazzocchi, N.E. Sarac, in:, 34th International Conference on Concurrency Theory, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. conference: end_date: 2023-09-23 location: Antwerp, Belgium name: 'CONCUR: Conference on Concurrency Theory' start_date: 2023-09-18 date_created: 2023-07-14T10:00:15Z date_published: 2023-09-01T00:00:00Z date_updated: 2023-10-09T07:14:03Z day: '01' ddc: - '000' department: - _id: GradSch - _id: ToHe doi: 10.4230/LIPIcs.CONCUR.2023.17 ec_funded: 1 external_id: arxiv: - '2307.06016' file: - access_level: open_access checksum: d40e57a04448ea5c77d7e1cfb9590a81 content_type: application/pdf creator: esarac date_created: 2023-07-14T12:03:48Z date_updated: 2023-07-14T12:03:48Z file_id: '13224' file_name: CONCUR23.pdf file_size: 755529 relation: main_file success: 1 file_date_updated: 2023-07-14T12:03:48Z has_accepted_license: '1' intvolume: ' 279' language: - iso: eng month: '09' oa: 1 oa_version: Published Version project: - _id: 62781420-2b32-11ec-9570-8d9b63373d4d call_identifier: H2020 grant_number: '101020093' name: Vigilant Algorithmic Monitoring of Software publication: 34th International Conference on Concurrency Theory publication_identifier: eissn: - 1868-8969 isbn: - '9783959772990' publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' status: public title: Safety and liveness of quantitative automata 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: 279 year: '2023' ... --- _id: '14406' abstract: - lang: eng text: "Recently, a concept of generalized multifractality, which characterizes fluctuations and correlations of critical eigenstates, was introduced and explored for all 10 symmetry classes of disordered systems. Here, by using the nonlinear sigma-model (\r\nNL\r\nσ\r\nM\r\n) field theory, we extend the theory of generalized multifractality to boundaries of systems at criticality. Our numerical simulations on two-dimensional systems of symmetry classes A, C, and AII fully confirm the analytical predictions of pure-scaling observables and Weyl symmetry relations between critical exponents of surface generalized multifractality. This demonstrates the validity of the \r\nNL\r\nσ\r\nM\r\n for the description of Anderson-localization critical phenomena, not only in the bulk but also on the boundary. The critical exponents strongly violate generalized parabolicity, in analogy with earlier results for the bulk, corroborating the conclusion that the considered Anderson-localization critical points are not described by conformal field theories. We further derive relations between generalized surface multifractal spectra and linear combinations of Lyapunov exponents of a strip in quasi-one-dimensional geometry, which hold under the assumption of invariance with respect to a logarithmic conformal map. Our numerics demonstrate that these relations hold with an excellent accuracy. Taken together, our results indicate an intriguing situation: the conformal invariance is broken but holds partially at critical points of Anderson localization." acknowledgement: "We thank Ilya Gruzberg for many illuminating discussions. S.S.B., J.F.K., and A.D.M. acknowledge support by the Deutsche Forschungsgemeinschaft (DFG) via the Grant\r\nNo. MI 658/14-1. I.S.B. acknowledges support from Russian Science Foundation (Grant No. 22-42-04416)." article_number: '104205' article_processing_charge: No article_type: original author: - first_name: Serafim full_name: Babkin, Serafim id: 41e64307-6672-11ee-b9ad-cc7a0075a479 last_name: Babkin orcid: 0009-0003-7382-8036 - first_name: Jonas F. full_name: Karcher, Jonas F. last_name: Karcher - first_name: Igor S. full_name: Burmistrov, Igor S. last_name: Burmistrov - first_name: Alexander D. full_name: Mirlin, Alexander D. last_name: Mirlin citation: ama: Babkin S, Karcher JF, Burmistrov IS, Mirlin AD. Generalized surface multifractality in two-dimensional disordered systems. Physical Review B. 2023;108(10). doi:10.1103/PhysRevB.108.104205 apa: Babkin, S., Karcher, J. F., Burmistrov, I. S., & Mirlin, A. D. (2023). Generalized surface multifractality in two-dimensional disordered systems. Physical Review B. American Physical Society. https://doi.org/10.1103/PhysRevB.108.104205 chicago: Babkin, Serafim, Jonas F. Karcher, Igor S. Burmistrov, and Alexander D. Mirlin. “Generalized Surface Multifractality in Two-Dimensional Disordered Systems.” Physical Review B. American Physical Society, 2023. https://doi.org/10.1103/PhysRevB.108.104205. ieee: S. Babkin, J. F. Karcher, I. S. Burmistrov, and A. D. Mirlin, “Generalized surface multifractality in two-dimensional disordered systems,” Physical Review B, vol. 108, no. 10. American Physical Society, 2023. ista: Babkin S, Karcher JF, Burmistrov IS, Mirlin AD. 2023. Generalized surface multifractality in two-dimensional disordered systems. Physical Review B. 108(10), 104205. mla: Babkin, Serafim, et al. “Generalized Surface Multifractality in Two-Dimensional Disordered Systems.” Physical Review B, vol. 108, no. 10, 104205, American Physical Society, 2023, doi:10.1103/PhysRevB.108.104205. short: S. Babkin, J.F. Karcher, I.S. Burmistrov, A.D. Mirlin, Physical Review B 108 (2023). date_created: 2023-10-08T22:01:17Z date_published: 2023-09-01T00:00:00Z date_updated: 2023-10-09T07:09:30Z day: '01' department: - _id: MaSe doi: 10.1103/PhysRevB.108.104205 external_id: arxiv: - '2306.09455' intvolume: ' 108' issue: '10' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2306.09455 month: '09' oa: 1 oa_version: Preprint publication: Physical Review B publication_identifier: eissn: - 2469-9969 issn: - 2469-9950 publication_status: published publisher: American Physical Society quality_controlled: '1' scopus_import: '1' status: public title: Generalized surface multifractality in two-dimensional disordered systems type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 108 year: '2023' ... --- _id: '14410' abstract: - lang: eng text: This paper focuses on the implementation details of the baseline methods and a recent lightweight conditional model extrapolation algorithm LIMES [5] for streaming data under class-prior shift. LIMES achieves superior performance over the baseline methods, especially concerning the minimum-across-day accuracy, which is important for the users of the system. In this work, the key measures to facilitate reproducibility and enhance the credibility of the results are described. alternative_title: - LNCS article_processing_charge: No author: - first_name: Paulina full_name: Tomaszewska, Paulina last_name: Tomaszewska - first_name: Christoph full_name: Lampert, Christoph id: 40C20FD2-F248-11E8-B48F-1D18A9856A87 last_name: Lampert orcid: 0000-0001-8622-7887 citation: ama: 'Tomaszewska P, Lampert C. On the implementation of baselines and lightweight conditional model extrapolation (LIMES) under class-prior shift. In: International Workshop on Reproducible Research in Pattern Recognition. Vol 14068. Springer Nature; 2023:67-73. doi:10.1007/978-3-031-40773-4_6' apa: 'Tomaszewska, P., & Lampert, C. (2023). On the implementation of baselines and lightweight conditional model extrapolation (LIMES) under class-prior shift. In International Workshop on Reproducible Research in Pattern Recognition (Vol. 14068, pp. 67–73). Montreal, Canada: Springer Nature. https://doi.org/10.1007/978-3-031-40773-4_6' chicago: Tomaszewska, Paulina, and Christoph Lampert. “On the Implementation of Baselines and Lightweight Conditional Model Extrapolation (LIMES) under Class-Prior Shift.” In International Workshop on Reproducible Research in Pattern Recognition, 14068:67–73. Springer Nature, 2023. https://doi.org/10.1007/978-3-031-40773-4_6. ieee: P. Tomaszewska and C. Lampert, “On the implementation of baselines and lightweight conditional model extrapolation (LIMES) under class-prior shift,” in International Workshop on Reproducible Research in Pattern Recognition, Montreal, Canada, 2023, vol. 14068, pp. 67–73. ista: 'Tomaszewska P, Lampert C. 2023. On the implementation of baselines and lightweight conditional model extrapolation (LIMES) under class-prior shift. International Workshop on Reproducible Research in Pattern Recognition. RRPR: Reproducible Research in Pattern Recognition, LNCS, vol. 14068, 67–73.' mla: Tomaszewska, Paulina, and Christoph Lampert. “On the Implementation of Baselines and Lightweight Conditional Model Extrapolation (LIMES) under Class-Prior Shift.” International Workshop on Reproducible Research in Pattern Recognition, vol. 14068, Springer Nature, 2023, pp. 67–73, doi:10.1007/978-3-031-40773-4_6. short: P. Tomaszewska, C. Lampert, in:, International Workshop on Reproducible Research in Pattern Recognition, Springer Nature, 2023, pp. 67–73. conference: end_date: 2022-08-21 location: Montreal, Canada name: 'RRPR: Reproducible Research in Pattern Recognition' start_date: 2022-08-21 date_created: 2023-10-08T22:01:18Z date_published: 2023-08-20T00:00:00Z date_updated: 2023-10-09T06:48:02Z day: '20' department: - _id: ChLa doi: 10.1007/978-3-031-40773-4_6 intvolume: ' 14068' language: - iso: eng month: '08' oa_version: None page: 67-73 publication: International Workshop on Reproducible Research in Pattern Recognition publication_identifier: eissn: - 1611-3349 isbn: - '9783031407727' issn: - 0302-9743 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: On the implementation of baselines and lightweight conditional model extrapolation (LIMES) under class-prior shift type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 14068 year: '2023' ...