[{"project":[{"_id":"26AD5D90-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Algebraic Footprints of Geometric Features in Homology","grant_number":"I04245"}],"title":"Discrete yamabe problem for polyhedral surfaces","author":[{"full_name":"Kourimska, Hana","orcid":"0000-0001-7841-0091","last_name":"Kourimska","first_name":"Hana","id":"D9B8E14C-3C26-11EA-98F5-1F833DDC885E"}],"external_id":{"isi":["000948148000001"]},"article_processing_charge":"Yes (via OA deal)","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Kourimska, Hana. “Discrete Yamabe Problem for Polyhedral Surfaces.” Discrete and Computational Geometry, vol. 70, Springer Nature, 2023, pp. 123–53, doi:10.1007/s00454-023-00484-2.","short":"H. Kourimska, Discrete and Computational Geometry 70 (2023) 123–153.","ieee":"H. Kourimska, “Discrete yamabe problem for polyhedral surfaces,” Discrete and Computational Geometry, vol. 70. Springer Nature, pp. 123–153, 2023.","apa":"Kourimska, H. (2023). Discrete yamabe problem for polyhedral surfaces. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-023-00484-2","ama":"Kourimska H. Discrete yamabe problem for polyhedral surfaces. Discrete and Computational Geometry. 2023;70:123-153. doi:10.1007/s00454-023-00484-2","chicago":"Kourimska, Hana. “Discrete Yamabe Problem for Polyhedral Surfaces.” Discrete and Computational Geometry. Springer Nature, 2023. https://doi.org/10.1007/s00454-023-00484-2.","ista":"Kourimska H. 2023. Discrete yamabe problem for polyhedral surfaces. Discrete and Computational Geometry. 70, 123–153."},"publisher":"Springer Nature","quality_controlled":"1","oa":1,"acknowledgement":"Open access funding provided by the Austrian Science Fund (FWF). This research was supported by the FWF grant, Project number I4245-N35, and by the Deutsche Forschungsgemeinschaft (DFG - German Research Foundation) - Project-ID 195170736 - TRR109.","doi":"10.1007/s00454-023-00484-2","date_published":"2023-07-01T00:00:00Z","date_created":"2023-03-26T22:01:09Z","page":"123-153","day":"01","publication":"Discrete and Computational Geometry","isi":1,"has_accepted_license":"1","year":"2023","status":"public","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"12764","file_date_updated":"2023-10-04T11:46:24Z","department":[{"_id":"HeEd"}],"ddc":["510"],"date_updated":"2023-10-04T11:46:48Z","month":"07","intvolume":" 70","scopus_import":"1","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We study a new discretization of the Gaussian curvature for polyhedral surfaces. This discrete Gaussian curvature is defined on each conical singularity of a polyhedral surface as the quotient of the angle defect and the area of the Voronoi cell corresponding to the singularity. We divide polyhedral surfaces into discrete conformal classes using a generalization of discrete conformal equivalence pioneered by Feng Luo. We subsequently show that, in every discrete conformal class, there exists a polyhedral surface with constant discrete Gaussian curvature. We also provide explicit examples to demonstrate that this surface is in general not unique."}],"volume":70,"file":[{"file_id":"14396","checksum":"cdbf90ba4a7ddcb190d37b9e9d4cb9d3","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2023-10-04T11:46:24Z","file_name":"2023_DiscreteGeometry_Kourimska.pdf","creator":"dernst","date_updated":"2023-10-04T11:46:24Z","file_size":1026683}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"publication_status":"published"},{"volume":70,"related_material":{"record":[{"relation":"earlier_version","id":"9605","status":"public"}]},"language":[{"iso":"eng"}],"file":[{"date_created":"2023-03-07T14:40:14Z","file_name":"2023_DisCompGeo_Corbet.pdf","date_updated":"2023-03-07T14:40:14Z","file_size":1359323,"creator":"cchlebak","checksum":"71ce7e59f7ee4620acc704fecca620c2","file_id":"12715","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"publication_status":"published","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"intvolume":" 70","month":"09","scopus_import":"1","oa_version":"Published Version","abstract":[{"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.","lang":"eng"}],"file_date_updated":"2023-03-07T14:40:14Z","department":[{"_id":"HeEd"}],"ddc":["000"],"date_updated":"2023-10-04T12:03:40Z","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","_id":"12709","date_created":"2023-03-05T23:01:06Z","doi":"10.1007/s00454-022-00476-8","date_published":"2023-09-01T00:00:00Z","page":"376-405","publication":"Discrete and Computational Geometry","day":"01","year":"2023","isi":1,"has_accepted_license":"1","oa":1,"publisher":"Springer Nature","quality_controlled":"1","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.","title":"Computing the multicover bifiltration","external_id":{"isi":["000936496800001"],"arxiv":["2103.07823"]},"article_processing_charge":"Yes (via OA deal)","author":[{"first_name":"René","last_name":"Corbet","full_name":"Corbet, René"},{"full_name":"Kerber, Michael","orcid":"0000-0002-8030-9299","last_name":"Kerber","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","first_name":"Michael"},{"first_name":"Michael","full_name":"Lesnick, Michael","last_name":"Lesnick"},{"id":"464B40D6-F248-11E8-B48F-1D18A9856A87","first_name":"Georg F","full_name":"Osang, Georg F","orcid":"0000-0002-8882-5116","last_name":"Osang"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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.","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.","ista":"Corbet R, Kerber M, Lesnick M, Osang GF. 2023. Computing the multicover bifiltration. Discrete and Computational Geometry. 70, 376–405."}},{"day":"01","publication":"Journal of Applied and Computational Topology","year":"2023","doi":"10.1007/s41468-023-00116-x","date_published":"2023-09-01T00:00:00Z","date_created":"2023-03-26T22:01:08Z","page":"619-641","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.","publisher":"Springer Nature","quality_controlled":"1","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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","short":"J.D. Boissonnat, M. Wintraecken, Journal of Applied and Computational Topology 7 (2023) 619–641.","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.","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.","ista":"Boissonnat JD, Wintraecken M. 2023. The reach of subsets of manifolds. Journal of Applied and Computational Topology. 7, 619–641."},"title":"The reach of subsets of manifolds","author":[{"first_name":"Jean Daniel","last_name":"Boissonnat","full_name":"Boissonnat, Jean Daniel"},{"last_name":"Wintraecken","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs"}],"article_processing_charge":"No","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"},{"grant_number":"M03073","name":"Learning and triangulating manifolds via collapses","_id":"fc390959-9c52-11eb-aca3-afa58bd282b2"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["2367-1734"],"issn":["2367-1726"]},"publication_status":"published","volume":7,"ec_funded":1,"oa_version":"Submitted Version","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."}],"month":"09","intvolume":" 7","scopus_import":"1","main_file_link":[{"url":"https://inserm.hal.science/INRIA-SACLAY/hal-04083524v1","open_access":"1"}],"date_updated":"2023-10-04T12:07:18Z","department":[{"_id":"HeEd"}],"_id":"12763","status":"public","article_type":"original","type":"journal_article"},{"author":[{"first_name":"Jean Daniel","last_name":"Boissonnat","full_name":"Boissonnat, Jean Daniel"},{"first_name":"Siargey","full_name":"Kachanovich, Siargey","last_name":"Kachanovich"},{"orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","last_name":"Wintraecken","first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"external_id":{"isi":["001013183000012"]},"article_processing_charge":"No","title":"Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations","citation":{"chicago":"Boissonnat, Jean Daniel, Siargey Kachanovich, and Mathijs Wintraecken. “Tracing Isomanifolds in Rd in Time Polynomial in d Using Coxeter–Freudenthal–Kuhn Triangulations.” SIAM Journal on Computing. Society for Industrial and Applied Mathematics, 2023. https://doi.org/10.1137/21M1412918.","ista":"Boissonnat JD, Kachanovich S, Wintraecken M. 2023. Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations. SIAM Journal on Computing. 52(2), 452–486.","mla":"Boissonnat, Jean Daniel, et al. “Tracing Isomanifolds in Rd in Time Polynomial in d Using Coxeter–Freudenthal–Kuhn Triangulations.” SIAM Journal on Computing, vol. 52, no. 2, Society for Industrial and Applied Mathematics, 2023, pp. 452–86, doi:10.1137/21M1412918.","apa":"Boissonnat, J. D., Kachanovich, S., & Wintraecken, M. (2023). Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations. SIAM Journal on Computing. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/21M1412918","ama":"Boissonnat JD, Kachanovich S, Wintraecken M. Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations. SIAM Journal on Computing. 2023;52(2):452-486. doi:10.1137/21M1412918","short":"J.D. Boissonnat, S. Kachanovich, M. Wintraecken, SIAM Journal on Computing 52 (2023) 452–486.","ieee":"J. D. Boissonnat, S. Kachanovich, and M. Wintraecken, “Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations,” SIAM Journal on Computing, vol. 52, no. 2. Society for Industrial and Applied Mathematics, pp. 452–486, 2023."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"_id":"fc390959-9c52-11eb-aca3-afa58bd282b2","name":"Learning and triangulating manifolds via collapses","grant_number":"M03073"}],"page":"452-486","date_published":"2023-04-30T00:00:00Z","doi":"10.1137/21M1412918","date_created":"2023-05-14T22:01:00Z","isi":1,"year":"2023","day":"30","publication":"SIAM Journal on Computing","quality_controlled":"1","publisher":"Society for Industrial and Applied Mathematics","oa":1,"acknowledgement":"The authors have received funding from the European Research Council under the European Union's ERC grant greement 339025 GUDHI (Algorithmic Foundations of Geometric Un-derstanding in Higher Dimensions). The first author was supported by the French government,through the 3IA C\\^ote d'Azur Investments in the Future project managed by the National ResearchAgency (ANR) with the reference ANR-19-P3IA-0002. The third author was supported by the Eu-ropean Union's Horizon 2020 research and innovation programme under the Marie Sk\\lodowska-Curiegrant agreement 754411 and the FWF (Austrian Science Fund) grant M 3073.","department":[{"_id":"HeEd"}],"date_updated":"2023-10-10T07:34:35Z","type":"journal_article","article_type":"original","status":"public","_id":"12960","related_material":{"record":[{"relation":"earlier_version","status":"public","id":"9441"}]},"issue":"2","volume":52,"ec_funded":1,"publication_identifier":{"issn":["0097-5397"],"eissn":["1095-7111"]},"publication_status":"published","language":[{"iso":"eng"}],"scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://hal-emse.ccsd.cnrs.fr/3IA-COTEDAZUR/hal-04083489v1"}],"month":"04","intvolume":" 52","abstract":[{"lang":"eng","text":"Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e., submanifolds of Rd defined as the zero set of some multivariate multivalued smooth function f:Rd→Rd−n, where n is the intrinsic dimension of the manifold. A natural way to approximate a smooth isomanifold M=f−1(0) is to consider its piecewise linear (PL) approximation M^\r\n based on a triangulation T of the ambient space Rd. In this paper, we describe a simple algorithm to trace isomanifolds from a given starting point. The algorithm works for arbitrary dimensions n and d, and any precision D. Our main result is that, when f (or M) has bounded complexity, the complexity of the algorithm is polynomial in d and δ=1/D (and unavoidably exponential in n). Since it is known that for δ=Ω(d2.5), M^ is O(D2)-close and isotopic to M\r\n, our algorithm produces a faithful PL-approximation of isomanifolds of bounded complexity in time polynomial in d. Combining this algorithm with dimensionality reduction techniques, the dependency on d in the size of M^ can be completely removed with high probability. We also show that the algorithm can handle isomanifolds with boundary and, more generally, isostratifolds. The algorithm for isomanifolds with boundary has been implemented and experimental results are reported, showing that it is practical and can handle cases that are far ahead of the state-of-the-art. "}],"oa_version":"Submitted Version"},{"month":"10","intvolume":" 142","scopus_import":"1","oa_version":"None","abstract":[{"lang":"eng","text":"We propose a characterization of discrete analytical spheres, planes and lines in the body-centered cubic (BCC) grid, both in the Cartesian and in the recently proposed alternative compact coordinate system, in which each integer triplet addresses some voxel in the grid. We define spheres and planes through double Diophantine inequalities and investigate their relevant topological features, such as functionality or the interrelation between the thickness of the objects and their connectivity and separation properties. We define lines as the intersection of planes. The number of the planes (up to six) is equal to the number of the pairs of faces of a BCC voxel that are parallel to the line."}],"issue":"10","volume":142,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0031-3203"]},"publication_status":"published","status":"public","type":"journal_article","article_type":"original","_id":"13134","department":[{"_id":"HeEd"}],"date_updated":"2023-10-10T07:37:16Z","quality_controlled":"1","publisher":"Elsevier","acknowledgement":"The first author has been partially supported by the Ministry of Science, Technological Development and Innovation of the Republic of Serbia through the project no. 451-03-47/2023-01/200156. The fourth author is funded by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35.","doi":"10.1016/j.patcog.2023.109693","date_published":"2023-10-01T00:00:00Z","date_created":"2023-06-18T22:00:45Z","day":"01","publication":"Pattern Recognition","isi":1,"year":"2023","project":[{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","grant_number":"I4887","name":"Discretization in Geometry and Dynamics"}],"article_number":"109693","title":"Discrete analytical objects in the body-centered cubic grid","author":[{"first_name":"Lidija","last_name":"Čomić","full_name":"Čomić, Lidija"},{"full_name":"Largeteau-Skapin, Gaëlle","last_name":"Largeteau-Skapin","first_name":"Gaëlle"},{"first_name":"Rita","last_name":"Zrour","full_name":"Zrour, Rita"},{"first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5372-7890","full_name":"Biswas, Ranita","last_name":"Biswas"},{"last_name":"Andres","full_name":"Andres, Eric","first_name":"Eric"}],"article_processing_charge":"No","external_id":{"isi":["001013526000001"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Čomić, Lidija, et al. “Discrete Analytical Objects in the Body-Centered Cubic Grid.” Pattern Recognition, vol. 142, no. 10, 109693, Elsevier, 2023, doi:10.1016/j.patcog.2023.109693.","short":"L. Čomić, G. Largeteau-Skapin, R. Zrour, R. Biswas, E. Andres, Pattern Recognition 142 (2023).","ieee":"L. Čomić, G. Largeteau-Skapin, R. Zrour, R. Biswas, and E. Andres, “Discrete analytical objects in the body-centered cubic grid,” Pattern Recognition, vol. 142, no. 10. Elsevier, 2023.","ama":"Čomić L, Largeteau-Skapin G, Zrour R, Biswas R, Andres E. Discrete analytical objects in the body-centered cubic grid. Pattern Recognition. 2023;142(10). doi:10.1016/j.patcog.2023.109693","apa":"Čomić, L., Largeteau-Skapin, G., Zrour, R., Biswas, R., & Andres, E. (2023). Discrete analytical objects in the body-centered cubic grid. Pattern Recognition. Elsevier. https://doi.org/10.1016/j.patcog.2023.109693","chicago":"Čomić, Lidija, Gaëlle Largeteau-Skapin, Rita Zrour, Ranita Biswas, and Eric Andres. “Discrete Analytical Objects in the Body-Centered Cubic Grid.” Pattern Recognition. Elsevier, 2023. https://doi.org/10.1016/j.patcog.2023.109693.","ista":"Čomić L, Largeteau-Skapin G, Zrour R, Biswas R, Andres E. 2023. Discrete analytical objects in the body-centered cubic grid. Pattern Recognition. 142(10), 109693."}},{"project":[{"call_identifier":"FWF","_id":"26AD5D90-B435-11E9-9278-68D0E5697425","grant_number":"I04245","name":"Algebraic Footprints of Geometric Features in Homology"}],"article_processing_charge":"No","author":[{"first_name":"D.","last_name":"Dikranjan","full_name":"Dikranjan, D."},{"full_name":"Giordano Bruno, A.","last_name":"Giordano Bruno","first_name":"A."},{"orcid":"0000-0001-8686-1888","full_name":"Zava, Nicolò","last_name":"Zava","first_name":"Nicolò","id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad"}],"title":"Epimorphisms and closure operators of categories of semilattices","citation":{"mla":"Dikranjan, D., et al. “Epimorphisms and Closure Operators of Categories of Semilattices.” Quaestiones Mathematicae, vol. 46, no. S1, Taylor & Francis, 2023, pp. 191–221, doi:10.2989/16073606.2023.2247731.","apa":"Dikranjan, D., Giordano Bruno, A., & Zava, N. (2023). Epimorphisms and closure operators of categories of semilattices. Quaestiones Mathematicae. Taylor & Francis. https://doi.org/10.2989/16073606.2023.2247731","ama":"Dikranjan D, Giordano Bruno A, Zava N. Epimorphisms and closure operators of categories of semilattices. Quaestiones Mathematicae. 2023;46(S1):191-221. doi:10.2989/16073606.2023.2247731","short":"D. Dikranjan, A. Giordano Bruno, N. Zava, Quaestiones Mathematicae 46 (2023) 191–221.","ieee":"D. Dikranjan, A. Giordano Bruno, and N. Zava, “Epimorphisms and closure operators of categories of semilattices,” Quaestiones Mathematicae, vol. 46, no. S1. Taylor & Francis, pp. 191–221, 2023.","chicago":"Dikranjan, D., A. Giordano Bruno, and Nicolò Zava. “Epimorphisms and Closure Operators of Categories of Semilattices.” Quaestiones Mathematicae. Taylor & Francis, 2023. https://doi.org/10.2989/16073606.2023.2247731.","ista":"Dikranjan D, Giordano Bruno A, Zava N. 2023. Epimorphisms and closure operators of categories of semilattices. Quaestiones Mathematicae. 46(S1), 191–221."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Taylor & Francis","quality_controlled":"1","acknowledgement":"The first and second named authors are members of GNSAGA – INdAM.\r\nThe third named author was supported by the FWF Grant, Project number I4245–N35","page":"191-221","date_created":"2023-11-19T23:00:55Z","date_published":"2023-11-01T00:00:00Z","doi":"10.2989/16073606.2023.2247731","year":"2023","publication":"Quaestiones Mathematicae","day":"01","article_type":"original","type":"journal_article","status":"public","_id":"14557","department":[{"_id":"HeEd"}],"date_updated":"2023-11-20T09:24:48Z","scopus_import":"1","intvolume":" 46","month":"11","abstract":[{"text":"Motivated by a problem posed in [10], we investigate the closure operators of the category SLatt of join semilattices and its subcategory SLattO of join semilattices with bottom element. In particular, we show that there are only finitely many closure operators of both categories, and provide a complete classification. We use this result to deduce the known fact that epimorphisms of SLatt and SLattO are surjective. We complement the paper with two different proofs of this result using either generators or Isbell’s zigzag theorem.","lang":"eng"}],"oa_version":"None","issue":"S1","volume":46,"publication_status":"published","publication_identifier":{"eissn":["1727-933X"],"issn":["1607-3606"]},"language":[{"iso":"eng"}]},{"scopus_import":"1","main_file_link":[{"url":"https://doi.org/10.1007/s00454-023-00566-1","open_access":"1"}],"month":"09","abstract":[{"lang":"eng","text":"For a locally finite set in R2, the order-k Brillouin tessellations form an infinite sequence of convex face-to-face tilings of the plane. If the set is coarsely dense and generic, then the corresponding infinite sequences of minimum and maximum angles are both monotonic in k. As an example, a stationary Poisson point process in R2 is locally finite, coarsely dense, and generic with probability one. For such a set, the distributions of angles in the Voronoi tessellations, Delaunay mosaics, and Brillouin tessellations are independent of the order and can be derived from the formula for angles in order-1 Delaunay mosaics given by Miles (Math. Biosci. 6, 85–127 (1970))."}],"oa_version":"Published Version","ec_funded":1,"publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"publication_status":"epub_ahead","language":[{"iso":"eng"}],"type":"journal_article","article_type":"original","status":"public","_id":"14345","department":[{"_id":"HeEd"}],"date_updated":"2023-12-13T12:25:06Z","publisher":"Springer Nature","quality_controlled":"1","oa":1,"acknowledgement":"Work by all authors but A. Garber is supported by the European Research Council (ERC), Grant No. 788183, by the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), Grant No. I 02979-N35. Work by A. Garber is partially supported by the Alexander von Humboldt Foundation.","date_published":"2023-09-07T00:00:00Z","doi":"10.1007/s00454-023-00566-1","date_created":"2023-09-17T22:01:10Z","isi":1,"year":"2023","day":"07","publication":"Discrete and Computational Geometry","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183","name":"Alpha Shape Theory Extended"},{"grant_number":"Z00342","name":"The Wittgenstein Prize","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"}],"author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"first_name":"Alexey","last_name":"Garber","full_name":"Garber, Alexey"},{"first_name":"Mohadese","full_name":"Ghafari, Mohadese","last_name":"Ghafari"},{"full_name":"Heiss, Teresa","orcid":"0000-0002-1780-2689","last_name":"Heiss","first_name":"Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Saghafian","full_name":"Saghafian, Morteza","first_name":"Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824"}],"external_id":{"arxiv":["2204.01076"],"isi":["001060727600004"]},"article_processing_charge":"Yes (via OA deal)","title":"On angles in higher order Brillouin tessellations and related tilings in the plane","citation":{"mla":"Edelsbrunner, Herbert, et al. “On Angles in Higher Order Brillouin Tessellations and Related Tilings in the Plane.” Discrete and Computational Geometry, Springer Nature, 2023, doi:10.1007/s00454-023-00566-1.","apa":"Edelsbrunner, H., Garber, A., Ghafari, M., Heiss, T., & Saghafian, M. (2023). On angles in higher order Brillouin tessellations and related tilings in the plane. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-023-00566-1","ama":"Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. On angles in higher order Brillouin tessellations and related tilings in the plane. Discrete and Computational Geometry. 2023. doi:10.1007/s00454-023-00566-1","ieee":"H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, and M. Saghafian, “On angles in higher order Brillouin tessellations and related tilings in the plane,” Discrete and Computational Geometry. Springer Nature, 2023.","short":"H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, Discrete and Computational Geometry (2023).","chicago":"Edelsbrunner, Herbert, Alexey Garber, Mohadese Ghafari, Teresa Heiss, and Morteza Saghafian. “On Angles in Higher Order Brillouin Tessellations and Related Tilings in the Plane.” Discrete and Computational Geometry. Springer Nature, 2023. https://doi.org/10.1007/s00454-023-00566-1.","ista":"Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. 2023. On angles in higher order Brillouin tessellations and related tilings in the plane. Discrete and Computational Geometry."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"citation":{"mla":"Ambrus, Áron, et al. “Optimal Embedded and Enclosing Isosceles Triangles.” International Journal of Foundations of Computer Science, vol. 34, no. 7, World Scientific Publishing, 2023, pp. 737–60, doi:10.1142/S012905412342008X.","ieee":"Á. Ambrus, M. Csikós, G. Kiss, J. Pach, and G. Somlai, “Optimal embedded and enclosing isosceles triangles,” International Journal of Foundations of Computer Science, vol. 34, no. 7. World Scientific Publishing, pp. 737–760, 2023.","short":"Á. Ambrus, M. Csikós, G. Kiss, J. Pach, G. Somlai, International Journal of Foundations of Computer Science 34 (2023) 737–760.","ama":"Ambrus Á, Csikós M, Kiss G, Pach J, Somlai G. Optimal embedded and enclosing isosceles triangles. International Journal of Foundations of Computer Science. 2023;34(7):737-760. doi:10.1142/S012905412342008X","apa":"Ambrus, Á., Csikós, M., Kiss, G., Pach, J., & Somlai, G. (2023). Optimal embedded and enclosing isosceles triangles. International Journal of Foundations of Computer Science. World Scientific Publishing. https://doi.org/10.1142/S012905412342008X","chicago":"Ambrus, Áron, Mónika Csikós, Gergely Kiss, János Pach, and Gábor Somlai. “Optimal Embedded and Enclosing Isosceles Triangles.” International Journal of Foundations of Computer Science. World Scientific Publishing, 2023. https://doi.org/10.1142/S012905412342008X.","ista":"Ambrus Á, Csikós M, Kiss G, Pach J, Somlai G. 2023. Optimal embedded and enclosing isosceles triangles. International Journal of Foundations of Computer Science. 34(7), 737–760."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Ambrus, Áron","last_name":"Ambrus","first_name":"Áron"},{"full_name":"Csikós, Mónika","last_name":"Csikós","first_name":"Mónika"},{"first_name":"Gergely","full_name":"Kiss, Gergely","last_name":"Kiss"},{"id":"E62E3130-B088-11EA-B919-BF823C25FEA4","first_name":"János","last_name":"Pach","full_name":"Pach, János"},{"first_name":"Gábor","full_name":"Somlai, Gábor","last_name":"Somlai"}],"article_processing_charge":"No","external_id":{"arxiv":["2205.11637"],"isi":["001080874400001"]},"title":"Optimal embedded and enclosing isosceles triangles","isi":1,"year":"2023","day":"05","publication":"International Journal of Foundations of Computer Science","page":"737-760","doi":"10.1142/S012905412342008X","date_published":"2023-10-05T00:00:00Z","date_created":"2023-10-29T23:01:18Z","publisher":"World Scientific Publishing","quality_controlled":"1","oa":1,"date_updated":"2023-12-13T13:04:55Z","department":[{"_id":"HeEd"}],"_id":"14464","type":"journal_article","article_type":"original","status":"public","publication_identifier":{"eissn":["1793-6373"],"issn":["0129-0541"]},"publication_status":"published","language":[{"iso":"eng"}],"volume":34,"issue":"7","abstract":[{"lang":"eng","text":"Given a triangle Δ, we study the problem of determining the smallest enclosing and largest embedded isosceles triangles of Δ with respect to area and perimeter. This problem was initially posed by Nandakumar [17, 22] and was first studied by Kiss, Pach, and Somlai [13], who showed that if Δ′ is the smallest area isosceles triangle containing Δ, then Δ′ and Δ share a side and an angle. In the present paper, we prove that for any triangle Δ, every maximum area isosceles triangle embedded in Δ and every maximum perimeter isosceles triangle embedded in Δ shares a side and an angle with Δ. Somewhat surprisingly, the case of minimum perimeter enclosing triangles is different: there are infinite families of triangles Δ whose minimum perimeter isosceles containers do not share a side and an angle with Δ."}],"oa_version":"Preprint","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2205.11637"}],"month":"10","intvolume":" 34"},{"file_date_updated":"2023-04-17T08:10:28Z","department":[{"_id":"KrCh"},{"_id":"HeEd"},{"_id":"UlWa"}],"date_updated":"2024-01-04T12:42:09Z","ddc":["000"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","status":"public","_id":"12833","issue":"2","volume":24,"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"7950"}]},"publication_status":"published","publication_identifier":{"issn":["1462-7264"],"eissn":["1365-8050"]},"language":[{"iso":"eng"}],"file":[{"creator":"dernst","file_size":2072197,"date_updated":"2023-04-17T08:10:28Z","file_name":"2022_DMTCS_Biniaz.pdf","date_created":"2023-04-17T08:10:28Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"file_id":"12844","checksum":"439102ea4f6e2aeefd7107dfb9ccf532"}],"scopus_import":"1","intvolume":" 24","month":"01","abstract":[{"lang":"eng","text":"The input to the token swapping problem is a graph with vertices v1, v2, . . . , vn, and n tokens with labels 1,2, . . . , n, one on each vertex. The goal is to get token i to vertex vi for all i= 1, . . . , n using a minimum number of swaps, where a swap exchanges the tokens on the endpoints of an edge.Token swapping on a tree, also known as “sorting with a transposition tree,” is not known to be in P nor NP-complete. We present some partial results: 1. An optimum swap sequence may need to perform a swap on a leaf vertex that has the correct token (a “happy leaf”), disproving a conjecture of Vaughan. 2. Any algorithm that fixes happy leaves—as all known approximation algorithms for the problem do—has approximation factor at least 4/3. Furthermore, the two best-known 2-approximation algorithms have approximation factor exactly 2. 3. A generalized problem—weighted coloured token swapping—is NP-complete on trees, but solvable in polynomial time on paths and stars. In this version, tokens and vertices have colours, and colours have weights. The goal is to get every token to a vertex of the same colour, and the cost of a swap is the sum of the weights of the two tokens involved."}],"oa_version":"Published Version","external_id":{"arxiv":["1903.06981"]},"article_processing_charge":"No","author":[{"full_name":"Biniaz, Ahmad","last_name":"Biniaz","first_name":"Ahmad"},{"first_name":"Kshitij","full_name":"Jain, Kshitij","last_name":"Jain"},{"last_name":"Lubiw","full_name":"Lubiw, Anna","first_name":"Anna"},{"last_name":"Masárová","orcid":"0000-0002-6660-1322","full_name":"Masárová, Zuzana","first_name":"Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Tillmann","last_name":"Miltzow","full_name":"Miltzow, Tillmann"},{"last_name":"Mondal","full_name":"Mondal, Debajyoti","first_name":"Debajyoti"},{"last_name":"Naredla","full_name":"Naredla, Anurag Murty","first_name":"Anurag Murty"},{"first_name":"Josef","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","last_name":"Tkadlec","orcid":"0000-0002-1097-9684","full_name":"Tkadlec, Josef"},{"full_name":"Turcotte, Alexi","last_name":"Turcotte","first_name":"Alexi"}],"title":"Token swapping on trees","citation":{"short":"A. Biniaz, K. Jain, A. Lubiw, Z. Masárová, T. Miltzow, D. Mondal, A.M. Naredla, J. Tkadlec, A. Turcotte, Discrete Mathematics and Theoretical Computer Science 24 (2023).","ieee":"A. Biniaz et al., “Token swapping on trees,” Discrete Mathematics and Theoretical Computer Science, vol. 24, no. 2. EPI Sciences, 2023.","apa":"Biniaz, A., Jain, K., Lubiw, A., Masárová, Z., Miltzow, T., Mondal, D., … Turcotte, A. (2023). Token swapping on trees. Discrete Mathematics and Theoretical Computer Science. EPI Sciences. https://doi.org/10.46298/DMTCS.8383","ama":"Biniaz A, Jain K, Lubiw A, et al. Token swapping on trees. Discrete Mathematics and Theoretical Computer Science. 2023;24(2). doi:10.46298/DMTCS.8383","mla":"Biniaz, Ahmad, et al. “Token Swapping on Trees.” Discrete Mathematics and Theoretical Computer Science, vol. 24, no. 2, 9, EPI Sciences, 2023, doi:10.46298/DMTCS.8383.","ista":"Biniaz A, Jain K, Lubiw A, Masárová Z, Miltzow T, Mondal D, Naredla AM, Tkadlec J, Turcotte A. 2023. Token swapping on trees. Discrete Mathematics and Theoretical Computer Science. 24(2), 9.","chicago":"Biniaz, Ahmad, Kshitij Jain, Anna Lubiw, Zuzana Masárová, Tillmann Miltzow, Debajyoti Mondal, Anurag Murty Naredla, Josef Tkadlec, and Alexi Turcotte. “Token Swapping on Trees.” Discrete Mathematics and Theoretical Computer Science. EPI Sciences, 2023. https://doi.org/10.46298/DMTCS.8383."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","article_number":"9","date_created":"2023-04-16T22:01:08Z","date_published":"2023-01-18T00:00:00Z","doi":"10.46298/DMTCS.8383","year":"2023","has_accepted_license":"1","publication":"Discrete Mathematics and Theoretical Computer Science","day":"18","oa":1,"quality_controlled":"1","publisher":"EPI Sciences","acknowledgement":"This work was begun at the University of Waterloo and was partially supported by the Natural Sciences and Engineering Council of Canada (NSERC).\r\n"},{"oa_version":"Published Version","abstract":[{"lang":"eng","text":"Attempts to incorporate topological information in supervised learning tasks have resulted in the creation of several techniques for vectorizing persistent homology barcodes. In this paper, we study thirteen such methods. Besides describing an organizational framework for these methods, we comprehensively benchmark them against three well-known classification tasks. Surprisingly, we discover that the best-performing method is a simple vectorization, which consists only of a few elementary summary statistics. Finally, we provide a convenient web application which has been designed to facilitate exploration and experimentation with various vectorization methods."}],"month":"12","intvolume":" 45","file":[{"success":1,"file_id":"14740","checksum":"465c28ef0b151b4b1fb47977ed5581ab","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_name":"2023_IEEEToP_Ali.pdf","date_created":"2024-01-08T10:09:14Z","creator":"dernst","file_size":2370988,"date_updated":"2024-01-08T10:09:14Z"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1939-3539"],"issn":["0162-8828"]},"publication_status":"published","issue":"12","volume":45,"_id":"14739","status":"public","keyword":["Applied Mathematics","Artificial Intelligence","Computational Theory and Mathematics","Computer Vision and Pattern Recognition","Software"],"type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ddc":["000"],"date_updated":"2024-01-08T10:11:46Z","file_date_updated":"2024-01-08T10:09:14Z","department":[{"_id":"HeEd"}],"acknowledgement":"The work of Maria-Jose Jimenez, Eduardo Paluzo-Hidalgo and Manuel Soriano-Trigueros was supported in part by the Spanish grant Ministerio de Ciencia e Innovacion under Grants TED2021-129438B-I00 and PID2019-107339GB-I00, and in part by REXASI-PRO H-EU project, call HORIZON-CL4-2021-HUMAN-01-01 under Grant 101070028. The work of\r\nMaria-Jose Jimenez was supported by a grant of Convocatoria de la Universidad de Sevilla para la recualificacion del sistema universitario español, 2021-23, funded by the European Union, NextGenerationEU. The work of Vidit Nanda was supported in part by EPSRC under Grant EP/R018472/1 and in part by US AFOSR under Grant FA9550-22-1-0462. \r\nWe are grateful to the team of GUDHI and TEASPOON developers, for their work and their support. We are also grateful to Streamlit for providing extra resources to deploy the web app\r\nonline on Streamlit community cloud. We thank the anonymous referees for their helpful suggestions.","publisher":"IEEE","quality_controlled":"1","oa":1,"day":"01","publication":"IEEE Transactions on Pattern Analysis and Machine Intelligence","has_accepted_license":"1","year":"2023","doi":"10.1109/tpami.2023.3308391","date_published":"2023-12-01T00:00:00Z","date_created":"2024-01-08T09:59:46Z","page":"14069-14080","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"apa":"Ali, D., Asaad, A., Jimenez, M.-J., Nanda, V., Paluzo-Hidalgo, E., & Soriano Trigueros, M. (2023). A survey of vectorization methods in topological data analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence. IEEE. https://doi.org/10.1109/tpami.2023.3308391","ama":"Ali D, Asaad A, Jimenez M-J, Nanda V, Paluzo-Hidalgo E, Soriano Trigueros M. A survey of vectorization methods in topological data analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2023;45(12):14069-14080. doi:10.1109/tpami.2023.3308391","short":"D. Ali, A. Asaad, M.-J. Jimenez, V. Nanda, E. Paluzo-Hidalgo, M. Soriano Trigueros, IEEE Transactions on Pattern Analysis and Machine Intelligence 45 (2023) 14069–14080.","ieee":"D. Ali, A. Asaad, M.-J. Jimenez, V. Nanda, E. Paluzo-Hidalgo, and M. Soriano Trigueros, “A survey of vectorization methods in topological data analysis,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 45, no. 12. IEEE, pp. 14069–14080, 2023.","mla":"Ali, Dashti, et al. “A Survey of Vectorization Methods in Topological Data Analysis.” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 45, no. 12, IEEE, 2023, pp. 14069–80, doi:10.1109/tpami.2023.3308391.","ista":"Ali D, Asaad A, Jimenez M-J, Nanda V, Paluzo-Hidalgo E, Soriano Trigueros M. 2023. A survey of vectorization methods in topological data analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence. 45(12), 14069–14080.","chicago":"Ali, Dashti, Aras Asaad, Maria-Jose Jimenez, Vidit Nanda, Eduardo Paluzo-Hidalgo, and Manuel Soriano Trigueros. “A Survey of Vectorization Methods in Topological Data Analysis.” IEEE Transactions on Pattern Analysis and Machine Intelligence. IEEE, 2023. https://doi.org/10.1109/tpami.2023.3308391."},"title":"A survey of vectorization methods in topological data analysis","author":[{"full_name":"Ali, Dashti","last_name":"Ali","first_name":"Dashti"},{"first_name":"Aras","last_name":"Asaad","full_name":"Asaad, Aras"},{"full_name":"Jimenez, Maria-Jose","last_name":"Jimenez","first_name":"Maria-Jose"},{"first_name":"Vidit","full_name":"Nanda, Vidit","last_name":"Nanda"},{"first_name":"Eduardo","full_name":"Paluzo-Hidalgo, Eduardo","last_name":"Paluzo-Hidalgo"},{"orcid":"0000-0003-2449-1433","full_name":"Soriano Trigueros, Manuel","last_name":"Soriano Trigueros","first_name":"Manuel","id":"15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8"}],"article_processing_charge":"Yes (in subscription journal)"},{"oa":1,"quality_controlled":"1","publisher":"Elsevier","date_created":"2023-06-25T22:00:45Z","date_published":"2023-10-01T00:00:00Z","doi":"10.1016/j.jcta.2023.105776","year":"2023","has_accepted_license":"1","publication":"Journal of Combinatorial Theory. Series A","day":"01","article_number":"105776","article_processing_charge":"Yes (in subscription journal)","external_id":{"arxiv":["2206.13592"]},"author":[{"full_name":"Fang, Lixing","last_name":"Fang","first_name":"Lixing"},{"last_name":"Huang","full_name":"Huang, Hao","first_name":"Hao"},{"full_name":"Pach, János","last_name":"Pach","first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4"},{"last_name":"Tardos","full_name":"Tardos, Gábor","first_name":"Gábor"},{"first_name":"Junchi","last_name":"Zuo","full_name":"Zuo, Junchi"}],"title":"Successive vertex orderings of fully regular graphs","citation":{"chicago":"Fang, Lixing, Hao Huang, János Pach, Gábor Tardos, and Junchi Zuo. “Successive Vertex Orderings of Fully Regular Graphs.” Journal of Combinatorial Theory. Series A. Elsevier, 2023. https://doi.org/10.1016/j.jcta.2023.105776.","ista":"Fang L, Huang H, Pach J, Tardos G, Zuo J. 2023. Successive vertex orderings of fully regular graphs. Journal of Combinatorial Theory. Series A. 199(10), 105776.","mla":"Fang, Lixing, et al. “Successive Vertex Orderings of Fully Regular Graphs.” Journal of Combinatorial Theory. Series A, vol. 199, no. 10, 105776, Elsevier, 2023, doi:10.1016/j.jcta.2023.105776.","apa":"Fang, L., Huang, H., Pach, J., Tardos, G., & Zuo, J. (2023). Successive vertex orderings of fully regular graphs. Journal of Combinatorial Theory. Series A. Elsevier. https://doi.org/10.1016/j.jcta.2023.105776","ama":"Fang L, Huang H, Pach J, Tardos G, Zuo J. Successive vertex orderings of fully regular graphs. Journal of Combinatorial Theory Series A. 2023;199(10). doi:10.1016/j.jcta.2023.105776","ieee":"L. Fang, H. Huang, J. Pach, G. Tardos, and J. Zuo, “Successive vertex orderings of fully regular graphs,” Journal of Combinatorial Theory. Series A, vol. 199, no. 10. Elsevier, 2023.","short":"L. Fang, H. Huang, J. Pach, G. Tardos, J. Zuo, Journal of Combinatorial Theory. Series A 199 (2023)."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":"1","intvolume":" 199","month":"10","abstract":[{"text":"A graph G=(V, E) is called fully regular if for every independent set I c V, the number of vertices in V\\I that are not connected to any element of I depends only on the size of I. A linear ordering of the vertices of G is called successive if for every i, the first i vertices induce a connected subgraph of G. We give an explicit formula for the number of successive vertex orderings of a fully regular graph.\r\nAs an application of our results, we give alternative proofs of two theorems of Stanley and Gao & Peng, determining the number of linear edge orderings of complete graphs and complete bipartite graphs, respectively, with the property that the first i edges induce a connected subgraph.\r\nAs another application, we give a simple product formula for the number of linear orderings of the hyperedges of a complete 3-partite 3-uniform hypergraph such that, for every i, the first i hyperedges induce a connected subgraph. We found similar formulas for complete (non-partite) 3-uniform hypergraphs and in another closely related case, but we managed to verify them only when the number of vertices is small.","lang":"eng"}],"oa_version":"Published Version","license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","issue":"10","volume":199,"publication_status":"published","publication_identifier":{"eissn":["1096-0899"],"issn":["0097-3165"]},"language":[{"iso":"eng"}],"file":[{"success":1,"checksum":"9eebc213b4182a66063a99083ff5bd04","file_id":"14902","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_name":"2023_JourCombinatiorialTheory_Fang.pdf","date_created":"2024-01-30T12:03:10Z","file_size":352555,"date_updated":"2024-01-30T12:03:10Z","creator":"dernst"}],"tmp":{"name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","image":"/images/cc_by_nc_sa.png","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","short":"CC BY-NC-SA (4.0)"},"article_type":"original","type":"journal_article","status":"public","_id":"13165","department":[{"_id":"HeEd"}],"file_date_updated":"2024-01-30T12:03:10Z","date_updated":"2024-01-30T12:03:51Z","ddc":["510"]},{"article_number":"114129","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Castellano, Ilaria, et al. “Weakly Weighted Generalised Quasi-Metric Spaces and Semilattices.” Theoretical Computer Science, vol. 977, 114129, Elsevier, 2023, doi:10.1016/j.tcs.2023.114129.","ieee":"I. Castellano, A. Giordano Bruno, and N. Zava, “Weakly weighted generalised quasi-metric spaces and semilattices,” Theoretical Computer Science, vol. 977. Elsevier, 2023.","short":"I. Castellano, A. Giordano Bruno, N. Zava, Theoretical Computer Science 977 (2023).","ama":"Castellano I, Giordano Bruno A, Zava N. Weakly weighted generalised quasi-metric spaces and semilattices. Theoretical Computer Science. 2023;977. doi:10.1016/j.tcs.2023.114129","apa":"Castellano, I., Giordano Bruno, A., & Zava, N. (2023). Weakly weighted generalised quasi-metric spaces and semilattices. Theoretical Computer Science. Elsevier. https://doi.org/10.1016/j.tcs.2023.114129","chicago":"Castellano, Ilaria, Anna Giordano Bruno, and Nicolò Zava. “Weakly Weighted Generalised Quasi-Metric Spaces and Semilattices.” Theoretical Computer Science. Elsevier, 2023. https://doi.org/10.1016/j.tcs.2023.114129.","ista":"Castellano I, Giordano Bruno A, Zava N. 2023. Weakly weighted generalised quasi-metric spaces and semilattices. Theoretical Computer Science. 977, 114129."},"title":"Weakly weighted generalised quasi-metric spaces and semilattices","article_processing_charge":"No","external_id":{"isi":["001076934000001"],"arxiv":["2212.08424"]},"author":[{"first_name":"Ilaria","last_name":"Castellano","full_name":"Castellano, Ilaria"},{"last_name":"Giordano Bruno","full_name":"Giordano Bruno, Anna","first_name":"Anna"},{"last_name":"Zava","full_name":"Zava, Nicolò","orcid":"0000-0001-8686-1888","first_name":"Nicolò","id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad"}],"oa":1,"publisher":"Elsevier","quality_controlled":"1","publication":"Theoretical Computer Science","day":"25","year":"2023","isi":1,"date_created":"2023-09-24T22:01:11Z","doi":"10.1016/j.tcs.2023.114129","date_published":"2023-10-25T00:00:00Z","_id":"14362","status":"public","type":"journal_article","article_type":"original","date_updated":"2024-01-30T13:22:04Z","department":[{"_id":"HeEd"}],"oa_version":"Preprint","abstract":[{"text":"Motivated by recent applications to entropy theory in dynamical systems, we generalise notions introduced by Matthews and define weakly weighted and componentwise weakly weighted (generalised) quasi-metrics. We then systematise and extend to full generality the correspondences between these objects and other structures arising in theoretical computer science and dynamics. In particular, we study the correspondences with weak partial metrics and, if the underlying space is a semilattice, with invariant (generalised) quasi-metrics satisfying the descending path condition, and with strictly monotone semi(-co-)valuations.\r\nWe conclude discussing, for endomorphisms of generalised quasi-metric semilattices, a generalisation of both the known intrinsic semilattice entropy and the semigroup entropy.","lang":"eng"}],"intvolume":" 977","month":"10","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2212.08424 "}],"scopus_import":"1","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0304-3975"]},"volume":977},{"author":[{"id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita","last_name":"Biswas","orcid":"0000-0002-5372-7890","full_name":"Biswas, Ranita"},{"last_name":"Cultrera Di Montesano","orcid":"0000-0001-6249-0832","full_name":"Cultrera Di Montesano, Sebastiano","first_name":"Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"first_name":"Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","full_name":"Saghafian, Morteza","last_name":"Saghafian"}],"article_processing_charge":"Yes (via OA deal)","title":"Geometric characterization of the persistence of 1D maps","citation":{"mla":"Biswas, Ranita, et al. “Geometric Characterization of the Persistence of 1D Maps.” Journal of Applied and Computational Topology, Springer Nature, 2023, doi:10.1007/s41468-023-00126-9.","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian, M. (2023). Geometric characterization of the persistence of 1D maps. Journal of Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-023-00126-9","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Geometric characterization of the persistence of 1D maps. Journal of Applied and Computational Topology. 2023. doi:10.1007/s41468-023-00126-9","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Geometric characterization of the persistence of 1D maps,” Journal of Applied and Computational Topology. Springer Nature, 2023.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology (2023).","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Geometric Characterization of the Persistence of 1D Maps.” Journal of Applied and Computational Topology. Springer Nature, 2023. https://doi.org/10.1007/s41468-023-00126-9.","ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2023. Geometric characterization of the persistence of 1D maps. Journal of Applied and Computational Topology."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended"},{"_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","grant_number":"I4887","name":"Discretization in Geometry and Dynamics"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"Z00342","name":"The Wittgenstein Prize"}],"doi":"10.1007/s41468-023-00126-9","date_published":"2023-06-17T00:00:00Z","date_created":"2023-07-02T22:00:44Z","has_accepted_license":"1","year":"2023","day":"17","publication":"Journal of Applied and Computational Topology","publisher":"Springer Nature","quality_controlled":"1","oa":1,"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. The authors of this paper thank anonymous reviewers for their constructive criticism and Monika Henzinger for detailed comments on an earlier version of this paper.","file_date_updated":"2023-07-03T09:41:05Z","department":[{"_id":"HeEd"}],"date_updated":"2024-03-20T09:36:56Z","ddc":["000"],"type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","_id":"13182","related_material":{"record":[{"id":"15094","status":"public","relation":"dissertation_contains"}]},"ec_funded":1,"publication_identifier":{"issn":["2367-1726"],"eissn":["2367-1734"]},"publication_status":"epub_ahead","file":[{"file_name":"2023_Journal of Applied and Computational Topology_Biswas.pdf","date_created":"2023-07-03T09:41:05Z","creator":"alisjak","file_size":487355,"date_updated":"2023-07-03T09:41:05Z","success":1,"checksum":"697249d5d1c61dea4410b9f021b70fce","file_id":"13185","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"scopus_import":"1","month":"06","abstract":[{"text":"We characterize critical points of 1-dimensional maps paired in persistent homology\r\ngeometrically and this way get elementary proofs of theorems about the symmetry\r\nof persistence diagrams and the variation of such maps. In particular, we identify\r\nbranching points and endpoints of networks as the sole source of asymmetry and\r\nrelate the cycle basis in persistent homology with a version of the stable marriage\r\nproblem. Our analysis provides the foundations of fast algorithms for maintaining a\r\ncollection of sorted lists together with its persistence diagram.","lang":"eng"}],"oa_version":"Published Version"},{"supervisor":[{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"}],"date_updated":"2024-02-26T23:30:04Z","ddc":["500"],"file_date_updated":"2024-02-26T23:30:03Z","department":[{"_id":"GradSch"},{"_id":"HeEd"}],"_id":"14226","type":"dissertation","status":"public","publication_identifier":{"issn":["2791-4585"]},"publication_status":"published","degree_awarded":"MS","file":[{"relation":"source_file","access_level":"closed","embargo_to":"open_access","content_type":"application/x-zip-compressed","file_id":"14227","checksum":"453caf851d75c3478c10ed09bd242a91","creator":"cchlebak","file_size":15501411,"date_updated":"2024-02-26T23:30:03Z","file_name":"documents-export-2023-08-24.zip","date_created":"2023-08-24T13:02:49Z"},{"creator":"cchlebak","date_updated":"2024-02-26T23:30:03Z","file_size":6854783,"date_created":"2023-08-24T13:03:42Z","file_name":"thesis_pdf_a.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"7349d29963d6695e555e171748648d9a","file_id":"14228","embargo":"2024-02-25"}],"language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"We introduce the notion of a Faustian interchange in a 1-parameter family of smooth\r\nfunctions to generalize the medial axis to critical points of index larger than 0.\r\nWe construct and implement a general purpose algorithm for approximating such\r\ngeneralized medial axes."}],"oa_version":"Published Version","alternative_title":["ISTA Master's Thesis"],"month":"08","citation":{"mla":"Stephenson, Elizabeth R. Generalizing Medial Axes with Homology Switches. Institute of Science and Technology Austria, 2023, doi:10.15479/at:ista:14226.","short":"E.R. Stephenson, Generalizing Medial Axes with Homology Switches, Institute of Science and Technology Austria, 2023.","ieee":"E. R. Stephenson, “Generalizing medial axes with homology switches,” Institute of Science and Technology Austria, 2023.","ama":"Stephenson ER. Generalizing medial axes with homology switches. 2023. doi:10.15479/at:ista:14226","apa":"Stephenson, E. R. (2023). Generalizing medial axes with homology switches. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:14226","chicago":"Stephenson, Elizabeth R. “Generalizing Medial Axes with Homology Switches.” Institute of Science and Technology Austria, 2023. https://doi.org/10.15479/at:ista:14226.","ista":"Stephenson ER. 2023. Generalizing medial axes with homology switches. Institute of Science and Technology Austria."},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","author":[{"first_name":"Elizabeth R","id":"2D04F932-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6862-208X","full_name":"Stephenson, Elizabeth R","last_name":"Stephenson"}],"article_processing_charge":"No","title":"Generalizing medial axes with homology switches","has_accepted_license":"1","year":"2023","day":"24","page":"43","doi":"10.15479/at:ista:14226","date_published":"2023-08-24T00:00:00Z","date_created":"2023-08-24T13:01:18Z","publisher":"Institute of Science and Technology Austria","oa":1},{"series_title":"LIPIcs","_id":"11428","status":"public","type":"conference","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"conference":{"start_date":"2022-06-07","location":"Berlin, Germany","end_date":"2022-06-10","name":"SoCG: Symposium on Computational Geometry"},"ddc":["510"],"date_updated":"2023-02-21T09:50:52Z","file_date_updated":"2022-06-07T07:58:30Z","department":[{"_id":"HeEd"}],"oa_version":"Published Version","abstract":[{"text":"The medial axis of a set consists of the points in the ambient space without a unique closest point on the original set. Since its introduction, the medial axis has been used extensively in many applications as a method of computing a topologically equivalent skeleton. Unfortunately, one limiting factor in the use of the medial axis of a smooth manifold is that it is not necessarily topologically stable under small perturbations of the manifold. To counter these instabilities various prunings of the medial axis have been proposed. Here, we examine one type of pruning, called burning. Because of the good experimental results, it was hoped that the burning method of simplifying the medial axis would be stable. In this work we show a simple example that dashes such hopes based on Bing’s house with two rooms, demonstrating an isotopy of a shape where the medial axis goes from collapsible to non-collapsible.","lang":"eng"}],"month":"06","intvolume":" 224","scopus_import":"1","file":[{"file_name":"2022_LIPICs_Chambers.pdf","date_created":"2022-06-07T07:58:30Z","creator":"dernst","file_size":17580705,"date_updated":"2022-06-07T07:58:30Z","success":1,"checksum":"b25ce40fade4ebc0bcaae176db4f5f1f","file_id":"11437","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1868-8969"],"isbn":["978-3-95977-227-3"]},"publication_status":"published","volume":224,"ec_funded":1,"project":[{"name":"Learning and triangulating manifolds via collapses","grant_number":"M03073","_id":"fc390959-9c52-11eb-aca3-afa58bd282b2"},{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183","name":"Alpha Shape Theory Extended"},{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Chambers, Erin, et al. “A Cautionary Tale: Burning the Medial Axis Is Unstable.” 38th International Symposium on Computational Geometry, edited by Xavier Goaoc and Michael Kerber, vol. 224, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022, p. 66:1-66:9, doi:10.4230/LIPIcs.SoCG.2022.66.","ama":"Chambers E, Fillmore CD, Stephenson ER, Wintraecken M. A cautionary tale: Burning the medial axis is unstable. In: Goaoc X, Kerber M, eds. 38th International Symposium on Computational Geometry. Vol 224. LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2022:66:1-66:9. doi:10.4230/LIPIcs.SoCG.2022.66","apa":"Chambers, E., Fillmore, C. D., Stephenson, E. R., & Wintraecken, M. (2022). A cautionary tale: Burning the medial axis is unstable. In X. Goaoc & M. Kerber (Eds.), 38th International Symposium on Computational Geometry (Vol. 224, p. 66:1-66:9). Berlin, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2022.66","short":"E. Chambers, C.D. Fillmore, E.R. Stephenson, M. Wintraecken, in:, X. Goaoc, M. Kerber (Eds.), 38th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022, p. 66:1-66:9.","ieee":"E. Chambers, C. D. Fillmore, E. R. Stephenson, and M. Wintraecken, “A cautionary tale: Burning the medial axis is unstable,” in 38th International Symposium on Computational Geometry, Berlin, Germany, 2022, vol. 224, p. 66:1-66:9.","chicago":"Chambers, Erin, Christopher D Fillmore, Elizabeth R Stephenson, and Mathijs Wintraecken. “A Cautionary Tale: Burning the Medial Axis Is Unstable.” In 38th International Symposium on Computational Geometry, edited by Xavier Goaoc and Michael Kerber, 224:66:1-66:9. LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. https://doi.org/10.4230/LIPIcs.SoCG.2022.66.","ista":"Chambers E, Fillmore CD, Stephenson ER, Wintraecken M. 2022. A cautionary tale: Burning the medial axis is unstable. 38th International Symposium on Computational Geometry. SoCG: Symposium on Computational GeometryLIPIcs vol. 224, 66:1-66:9."},"editor":[{"first_name":"Xavier","full_name":"Goaoc, Xavier","last_name":"Goaoc"},{"first_name":"Michael","last_name":"Kerber","full_name":"Kerber, Michael"}],"title":"A cautionary tale: Burning the medial axis is unstable","author":[{"first_name":"Erin","full_name":"Chambers, Erin","last_name":"Chambers"},{"id":"35638A5C-AAC7-11E9-B0BF-5503E6697425","first_name":"Christopher D","full_name":"Fillmore, Christopher D","last_name":"Fillmore"},{"full_name":"Stephenson, Elizabeth R","orcid":"0000-0002-6862-208X","last_name":"Stephenson","first_name":"Elizabeth R","id":"2D04F932-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","last_name":"Wintraecken","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs"}],"article_processing_charge":"No","acknowledgement":"Partially supported by the DFG Collaborative Research Center TRR 109, “Discretization in Geometry and Dynamics” and the European Research Council (ERC), grant no. 788183, “Alpha Shape Theory Extended”. Erin Chambers: Supported in part by the National Science Foundation through grants DBI-1759807, CCF-1907612, and CCF-2106672. Mathijs Wintraecken: Supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411. The Austrian science fund (FWF) M-3073 Acknowledgements We thank André Lieutier, David Letscher, Ellen Gasparovic, Kathryn Leonard, and Tao Ju for early discussions on this work. We also thank Lu Liu, Yajie Yan and Tao Ju for sharing code to generate the examples.","quality_controlled":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","oa":1,"day":"01","publication":"38th International Symposium on Computational Geometry","has_accepted_license":"1","year":"2022","date_published":"2022-06-01T00:00:00Z","doi":"10.4230/LIPIcs.SoCG.2022.66","date_created":"2022-06-01T14:18:04Z","page":"66:1-66:9"},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2022-06-02T05:56:22Z","citation":{"chicago":"Karimipour, Farid, and Sabine Storandt, eds. Web and Wireless Geographical Information Systems. 1st ed. Vol. 13238. Cham: Springer Nature, 2022. https://doi.org/10.1007/978-3-031-06245-2.","ista":"Karimipour F, Storandt S eds. 2022. Web and Wireless Geographical Information Systems 1st ed., Cham: Springer Nature, 153p.","mla":"Karimipour, Farid, and Sabine Storandt, editors. Web and Wireless Geographical Information Systems. 1st ed., vol. 13238, Springer Nature, 2022, doi:10.1007/978-3-031-06245-2.","ieee":"F. Karimipour and S. Storandt, Eds., Web and Wireless Geographical Information Systems, 1st ed., vol. 13238. Cham: Springer Nature, 2022.","short":"F. Karimipour, S. Storandt, eds., Web and Wireless Geographical Information Systems, 1st ed., Springer Nature, Cham, 2022.","apa":"Karimipour, F., & Storandt, S. (Eds.). (2022). Web and Wireless Geographical Information Systems (1st ed., Vol. 13238). Cham: Springer Nature. https://doi.org/10.1007/978-3-031-06245-2","ama":"Karimipour F, Storandt S, eds. Web and Wireless Geographical Information Systems. Vol 13238. 1st ed. Cham: Springer Nature; 2022. doi:10.1007/978-3-031-06245-2"},"department":[{"_id":"HeEd"}],"editor":[{"id":"2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425","first_name":"Farid","last_name":"Karimipour","orcid":"0000-0001-6746-4174","full_name":"Karimipour, Farid"},{"full_name":"Storandt, Sabine","last_name":"Storandt","first_name":"Sabine"}],"title":"Web and Wireless Geographical Information Systems","article_processing_charge":"No","_id":"11429","status":"public","type":"book_editor","language":[{"iso":"eng"}],"day":"01","year":"2022","publication_status":"published","publication_identifier":{"issn":["0302-9743"],"isbn":["9783031062445"],"eissn":["1611-3349"],"eisbn":["9783031062452"]},"date_created":"2022-06-02T05:40:53Z","date_published":"2022-05-01T00:00:00Z","doi":"10.1007/978-3-031-06245-2","volume":13238,"page":"153","oa_version":"None","abstract":[{"lang":"eng","text":"This book constitutes the refereed proceedings of the 18th International Symposium on Web and Wireless Geographical Information Systems, W2GIS 2022, held in Konstanz, Germany, in April 2022.\r\nThe 7 full papers presented together with 6 short papers in the volume were carefully reviewed and selected from 16 submissions. The papers cover topics that range from mobile GIS and Location-Based Services to Spatial Information Retrieval and Wireless Sensor Networks."}],"intvolume":" 13238","place":"Cham","month":"05","edition":"1","publisher":"Springer Nature","alternative_title":["LNCS"],"quality_controlled":"1"},{"abstract":[{"lang":"eng","text":"To compute the persistent homology of a grayscale digital image one needs to build a simplicial or cubical complex from it. For cubical complexes, the two commonly used constructions (corresponding to direct and indirect digital adjacencies) can give different results for the same image. The two constructions are almost dual to each other, and we use this relationship to extend and modify the cubical complexes to become dual filtered cell complexes. We derive a general relationship between the persistent homology of two dual filtered cell complexes, and also establish how various modifications to a filtered complex change the persistence diagram. Applying these results to images, we derive a method to transform the persistence diagram computed using one type of cubical complex into a persistence diagram for the other construction. This means software for computing persistent homology from images can now be easily adapted to produce results for either of the two cubical complex constructions without additional low-level code implementation."}],"oa_version":"Preprint","scopus_import":"1","alternative_title":["Association for Women in Mathematics Series"],"main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2102.11397","open_access":"1"}],"place":"Cham","month":"01","intvolume":" 30","publication_identifier":{"isbn":["9783030955182"],"eisbn":["9783030955199"]},"publication_status":"published","language":[{"iso":"eng"}],"volume":30,"ec_funded":1,"_id":"11440","series_title":"AWMS","type":"book_chapter","status":"public","date_updated":"2022-06-07T08:32:42Z","department":[{"_id":"HeEd"}],"acknowledgement":"This project started during the Women in Computational Topology workshop held in Canberra in July of 2019. All authors are very grateful for its organisation and the financial support for the workshop from the Mathematical Sciences Institute at ANU, the US National Science Foundation through the award CCF-1841455, the Australian Mathematical Sciences Institute and the Association for Women in Mathematics. AG is supported by the Swiss National Science Foundation grant CRSII5_177237. TH is supported by the European Research Council (ERC) Horizon 2020 project “Alpha Shape Theory Extended” No. 788183. KM is supported by the ERC Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 859860. VR was supported by Australian Research Council Future Fellowship FT140100604 during the early stages of this project.","quality_controlled":"1","publisher":"Springer Nature","edition":"1","oa":1,"year":"2022","day":"27","publication":"Research in Computational Topology 2","page":"1-26","doi":"10.1007/978-3-030-95519-9_1","date_published":"2022-01-27T00:00:00Z","date_created":"2022-06-07T08:21:11Z","project":[{"name":"Alpha Shape Theory Extended","grant_number":"788183","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"}],"citation":{"chicago":"Bleile, Bea, Adélie Garin, Teresa Heiss, Kelly Maggs, and Vanessa Robins. “The Persistent Homology of Dual Digital Image Constructions.” In Research in Computational Topology 2, edited by Ellen Gasparovic, Vanessa Robins, and Katharine Turner, 1st ed., 30:1–26. AWMS. Cham: Springer Nature, 2022. https://doi.org/10.1007/978-3-030-95519-9_1.","ista":"Bleile B, Garin A, Heiss T, Maggs K, Robins V. 2022.The persistent homology of dual digital image constructions. In: Research in Computational Topology 2. Association for Women in Mathematics Series, vol. 30, 1–26.","mla":"Bleile, Bea, et al. “The Persistent Homology of Dual Digital Image Constructions.” Research in Computational Topology 2, edited by Ellen Gasparovic et al., 1st ed., vol. 30, Springer Nature, 2022, pp. 1–26, doi:10.1007/978-3-030-95519-9_1.","short":"B. Bleile, A. Garin, T. Heiss, K. Maggs, V. Robins, in:, E. Gasparovic, V. Robins, K. Turner (Eds.), Research in Computational Topology 2, 1st ed., Springer Nature, Cham, 2022, pp. 1–26.","ieee":"B. Bleile, A. Garin, T. Heiss, K. Maggs, and V. Robins, “The persistent homology of dual digital image constructions,” in Research in Computational Topology 2, 1st ed., vol. 30, E. Gasparovic, V. Robins, and K. Turner, Eds. Cham: Springer Nature, 2022, pp. 1–26.","ama":"Bleile B, Garin A, Heiss T, Maggs K, Robins V. The persistent homology of dual digital image constructions. In: Gasparovic E, Robins V, Turner K, eds. Research in Computational Topology 2. Vol 30. 1st ed. AWMS. Cham: Springer Nature; 2022:1-26. doi:10.1007/978-3-030-95519-9_1","apa":"Bleile, B., Garin, A., Heiss, T., Maggs, K., & Robins, V. (2022). The persistent homology of dual digital image constructions. In E. Gasparovic, V. Robins, & K. Turner (Eds.), Research in Computational Topology 2 (1st ed., Vol. 30, pp. 1–26). Cham: Springer Nature. https://doi.org/10.1007/978-3-030-95519-9_1"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Bea","last_name":"Bleile","full_name":"Bleile, Bea"},{"last_name":"Garin","full_name":"Garin, Adélie","first_name":"Adélie"},{"first_name":"Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","last_name":"Heiss","full_name":"Heiss, Teresa","orcid":"0000-0002-1780-2689"},{"full_name":"Maggs, Kelly","last_name":"Maggs","first_name":"Kelly"},{"full_name":"Robins, Vanessa","last_name":"Robins","first_name":"Vanessa"}],"article_processing_charge":"No","external_id":{"arxiv":["2102.11397"]},"title":"The persistent homology of dual digital image constructions","editor":[{"full_name":"Gasparovic, Ellen","last_name":"Gasparovic","first_name":"Ellen"},{"first_name":"Vanessa","full_name":"Robins, Vanessa","last_name":"Robins"},{"first_name":"Katharine","last_name":"Turner","full_name":"Turner, Katharine"}]},{"citation":{"ista":"Shipman BA, Stephenson ER. 2022. Tangible topology through the lens of limits. PRIMUS. 32(5), 593–609.","chicago":"Shipman, Barbara A., and Elizabeth R Stephenson. “Tangible Topology through the Lens of Limits.” PRIMUS. Taylor & Francis, 2022. https://doi.org/10.1080/10511970.2021.1872750.","ieee":"B. A. Shipman and E. R. Stephenson, “Tangible topology through the lens of limits,” PRIMUS, vol. 32, no. 5. Taylor & Francis, pp. 593–609, 2022.","short":"B.A. Shipman, E.R. Stephenson, PRIMUS 32 (2022) 593–609.","ama":"Shipman BA, Stephenson ER. Tangible topology through the lens of limits. PRIMUS. 2022;32(5):593-609. doi:10.1080/10511970.2021.1872750","apa":"Shipman, B. A., & Stephenson, E. R. (2022). Tangible topology through the lens of limits. PRIMUS. Taylor & Francis. https://doi.org/10.1080/10511970.2021.1872750","mla":"Shipman, Barbara A., and Elizabeth R. Stephenson. “Tangible Topology through the Lens of Limits.” PRIMUS, vol. 32, no. 5, Taylor & Francis, 2022, pp. 593–609, doi:10.1080/10511970.2021.1872750."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","author":[{"full_name":"Shipman, Barbara A.","last_name":"Shipman","first_name":"Barbara A."},{"id":"2D04F932-F248-11E8-B48F-1D18A9856A87","first_name":"Elizabeth R","last_name":"Stephenson","full_name":"Stephenson, Elizabeth R","orcid":"0000-0002-6862-208X"}],"title":"Tangible topology through the lens of limits","quality_controlled":"1","publisher":"Taylor & Francis","year":"2022","publication":"PRIMUS","day":"28","page":"593-609","date_created":"2023-01-16T10:07:21Z","doi":"10.1080/10511970.2021.1872750","date_published":"2022-05-28T00:00:00Z","_id":"12307","article_type":"original","type":"journal_article","keyword":["Education","General Mathematics"],"status":"public","date_updated":"2023-01-30T13:02:30Z","department":[{"_id":"HeEd"},{"_id":"GradSch"}],"abstract":[{"text":"Point-set topology is among the most abstract branches of mathematics in that it lacks tangible notions of distance, length, magnitude, order, and size. There is no shape, no geometry, no algebra, and no direction. Everything we are used to visualizing is gone. In the teaching and learning of mathematics, this can present a conundrum. Yet, this very property makes point set topology perfect for teaching and learning abstract mathematical concepts. It clears our minds of preconceived intuitions and expectations and forces us to think in new and creative ways. In this paper, we present guided investigations into topology through questions and thinking strategies that open up fascinating problems. They are intended for faculty who already teach or are thinking about teaching a class in topology or abstract mathematical reasoning for undergraduates. They can be used to build simple to challenging projects in topology, proofs, honors programs, and research experiences.","lang":"eng"}],"oa_version":"None","scopus_import":"1","intvolume":" 32","month":"05","publication_status":"published","publication_identifier":{"issn":["1051-1970"],"eissn":["1935-4053"]},"language":[{"iso":"eng"}],"issue":"5","volume":32},{"citation":{"ista":"Aichholzer O, Arroyo Guevara AM, Masárová Z, Parada I, Perz D, Pilz A, Tkadlec J, Vogtenhuber B. 2022. On compatible matchings. Journal of Graph Algorithms and Applications. 26(2), 225–240.","chicago":"Aichholzer, Oswin, Alan M Arroyo Guevara, Zuzana Masárová, Irene Parada, Daniel Perz, Alexander Pilz, Josef Tkadlec, and Birgit Vogtenhuber. “On Compatible Matchings.” Journal of Graph Algorithms and Applications. Brown University, 2022. https://doi.org/10.7155/jgaa.00591.","apa":"Aichholzer, O., Arroyo Guevara, A. M., Masárová, Z., Parada, I., Perz, D., Pilz, A., … Vogtenhuber, B. (2022). On compatible matchings. Journal of Graph Algorithms and Applications. Brown University. https://doi.org/10.7155/jgaa.00591","ama":"Aichholzer O, Arroyo Guevara AM, Masárová Z, et al. On compatible matchings. Journal of Graph Algorithms and Applications. 2022;26(2):225-240. doi:10.7155/jgaa.00591","short":"O. Aichholzer, A.M. Arroyo Guevara, Z. Masárová, I. Parada, D. Perz, A. Pilz, J. Tkadlec, B. Vogtenhuber, Journal of Graph Algorithms and Applications 26 (2022) 225–240.","ieee":"O. Aichholzer et al., “On compatible matchings,” Journal of Graph Algorithms and Applications, vol. 26, no. 2. Brown University, pp. 225–240, 2022.","mla":"Aichholzer, Oswin, et al. “On Compatible Matchings.” Journal of Graph Algorithms and Applications, vol. 26, no. 2, Brown University, 2022, pp. 225–40, doi:10.7155/jgaa.00591."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Oswin","last_name":"Aichholzer","full_name":"Aichholzer, Oswin"},{"last_name":"Arroyo Guevara","orcid":"0000-0003-2401-8670","full_name":"Arroyo Guevara, Alan M","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87","first_name":"Alan M"},{"last_name":"Masárová","full_name":"Masárová, Zuzana","orcid":"0000-0002-6660-1322","first_name":"Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Irene","full_name":"Parada, Irene","last_name":"Parada"},{"first_name":"Daniel","full_name":"Perz, Daniel","last_name":"Perz"},{"first_name":"Alexander","full_name":"Pilz, Alexander","last_name":"Pilz"},{"full_name":"Tkadlec, Josef","orcid":"0000-0002-1097-9684","last_name":"Tkadlec","first_name":"Josef","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Birgit","full_name":"Vogtenhuber, Birgit","last_name":"Vogtenhuber"}],"external_id":{"arxiv":["2101.03928"]},"article_processing_charge":"No","title":"On compatible matchings","project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"grant_number":"Z00342","name":"The Wittgenstein Prize","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"grant_number":"279307","name":"Quantitative Graph Games: Theory and Applications","call_identifier":"FP7","_id":"2581B60A-B435-11E9-9278-68D0E5697425"},{"name":"Modern Graph Algorithmic Techniques in Formal Verification","grant_number":"P 23499-N23","call_identifier":"FWF","_id":"2584A770-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","_id":"25863FF4-B435-11E9-9278-68D0E5697425","grant_number":"S11407","name":"Game Theory"}],"has_accepted_license":"1","year":"2022","day":"01","publication":"Journal of Graph Algorithms and Applications","page":"225-240","date_published":"2022-06-01T00:00:00Z","doi":"10.7155/jgaa.00591","date_created":"2022-08-21T22:01:56Z","acknowledgement":"A.A. funded by the Marie Sklodowska-Curie grant agreement No 754411. Z.M. partially funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31. I.P., D.P., and B.V. partially supported by FWF within the collaborative DACH project Arrangements and Drawings as FWF project I 3340-N35. A.P. supported by a Schrödinger fellowship of the FWF: J-3847-N35. J.T. partially supported by ERC Start grant no. (279307: Graph Games), FWF grant no. P23499-N23 and S11407-N23 (RiSE).","publisher":"Brown University","quality_controlled":"1","oa":1,"date_updated":"2023-02-23T13:54:21Z","ddc":["000"],"department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"KrCh"}],"file_date_updated":"2022-08-22T06:42:42Z","_id":"11938","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","publication_identifier":{"issn":["1526-1719"]},"publication_status":"published","file":[{"date_created":"2022-08-22T06:42:42Z","file_name":"2022_JourGraphAlgorithmsApplic_Aichholzer.pdf","creator":"dernst","date_updated":"2022-08-22T06:42:42Z","file_size":694538,"file_id":"11940","checksum":"dc6e255e3558faff924fd9e370886c11","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"volume":26,"related_material":{"record":[{"relation":"earlier_version","id":"9296","status":"public"}]},"issue":"2","ec_funded":1,"abstract":[{"text":"A matching is compatible to two or more labeled point sets of size n with labels {1, . . . , n} if its straight-line drawing on each of these point sets is crossing-free. We study the maximum number of edges in a matching compatible to two or more labeled point sets in general position in the plane. We show that for any two labeled sets of n points in convex position there exists a compatible matching with ⌊√2n + 1 − 1⌋ edges. More generally, for any ℓ labeled point sets we construct compatible matchings of size Ω(n1/ℓ). As a corresponding upper bound, we use probabilistic arguments to show that for any ℓ given sets of n points there exists a labeling of each set such that the largest compatible matching has O(n2/(ℓ+1)) edges. Finally, we show that Θ(log n) copies of any set of n points are necessary and sufficient for the existence of labelings of these point sets such that any compatible matching consists only of a single edge.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","month":"06","intvolume":" 26"},{"department":[{"_id":"HeEd"}],"file_date_updated":"2021-07-14T06:44:36Z","date_updated":"2023-08-02T06:49:17Z","ddc":["516"],"type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","_id":"9649","volume":22,"related_material":{"record":[{"status":"public","id":"7952","relation":"earlier_version"}]},"ec_funded":1,"publication_identifier":{"eissn":["1615-3383"]},"publication_status":"published","file":[{"creator":"mwintrae","date_updated":"2021-07-14T06:44:36Z","file_size":1455699,"date_created":"2021-07-14T06:44:36Z","file_name":"Boissonnat-Wintraecken2021_Article_TheTopologicalCorrectnessOfPLA.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"f1d372ec3c08ec22e84f8e93e1126b8c","file_id":"9650"}],"language":[{"iso":"eng"}],"scopus_import":"1","month":"0","intvolume":" 22","abstract":[{"lang":"eng","text":"Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e. manifolds defined as the zero set of some multivariate vector-valued smooth function f : Rd → Rd−n. A natural (and efficient) way to approximate an isomanifold is to consider its Piecewise-Linear (PL) approximation based on a triangulation T of the ambient space Rd. In this paper, we give conditions under which the PL-approximation of an isomanifold is topologically equivalent to the isomanifold. The conditions are easy to satisfy in the sense that they can always be met by taking a sufficiently\r\nfine triangulation T . This contrasts with previous results on the triangulation of manifolds where, in arbitrary dimensions, delicate perturbations are needed to guarantee topological correctness, which leads to strong limitations in practice. We further give a bound on the Fréchet distance between the original isomanifold and its PL-approximation. Finally we show analogous results for the PL-approximation of an isomanifold with boundary."}],"oa_version":"Published Version","author":[{"last_name":"Boissonnat","full_name":"Boissonnat, Jean-Daniel","first_name":"Jean-Daniel"},{"last_name":"Wintraecken","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000673039600001"]},"title":"The topological correctness of PL approximations of isomanifolds","citation":{"ista":"Boissonnat J-D, Wintraecken M. 2022. The topological correctness of PL approximations of isomanifolds. Foundations of Computational Mathematics . 22, 967–1012.","chicago":"Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness of PL Approximations of Isomanifolds.” Foundations of Computational Mathematics . Springer Nature, 2022. https://doi.org/10.1007/s10208-021-09520-0.","apa":"Boissonnat, J.-D., & Wintraecken, M. (2022). The topological correctness of PL approximations of isomanifolds. Foundations of Computational Mathematics . Springer Nature. https://doi.org/10.1007/s10208-021-09520-0","ama":"Boissonnat J-D, Wintraecken M. The topological correctness of PL approximations of isomanifolds. Foundations of Computational Mathematics . 2022;22:967-1012. doi:10.1007/s10208-021-09520-0","short":"J.-D. Boissonnat, M. Wintraecken, Foundations of Computational Mathematics 22 (2022) 967–1012.","ieee":"J.-D. Boissonnat and M. Wintraecken, “The topological correctness of PL approximations of isomanifolds,” Foundations of Computational Mathematics , vol. 22. Springer Nature, pp. 967–1012, 2022.","mla":"Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness of PL Approximations of Isomanifolds.” Foundations of Computational Mathematics , vol. 22, Springer Nature, 2022, pp. 967–1012, doi:10.1007/s10208-021-09520-0."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"page":"967-1012","doi":"10.1007/s10208-021-09520-0","date_published":"2022-01-01T00:00:00Z","date_created":"2021-07-14T06:44:53Z","isi":1,"has_accepted_license":"1","year":"2022","day":"01","publication":"Foundations of Computational Mathematics ","quality_controlled":"1","publisher":"Springer Nature","oa":1,"acknowledgement":"First and foremost, we acknowledge Siargey Kachanovich for discussions. We thank Herbert Edelsbrunner and all members of his group, all former and current members of the Datashape team (formerly known as Geometrica), and André Lieutier for encouragement. We further thank the reviewers of Foundations of Computational Mathematics and the reviewers and program committee of the Symposium on Computational Geometry for their feedback, which improved the exposition.\r\nThis work was funded by the European Research Council under the European Union’s ERC Grant Agreement number 339025 GUDHI (Algorithmic Foundations of Geometric Understanding in Higher Dimensions). This work was also 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. Mathijs Wintraecken also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 754411."},{"volume":309,"publication_identifier":{"issn":["0166-8641"]},"publication_status":"published","language":[{"iso":"eng"}],"scopus_import":"1","month":"03","intvolume":" 309","abstract":[{"lang":"eng","text":"Motivated by the recent introduction of the intrinsic semilattice entropy, we study generalized quasi-metric semilattices and their categories. We investigate the relationship between these objects and generalized semivaluations, extending Nakamura and Schellekens' approach. Finally, we use this correspondence to compare the intrinsic semilattice entropy and the semigroup entropy induced in particular situations, like sets, torsion abelian groups and vector spaces."}],"oa_version":"None","department":[{"_id":"HeEd"}],"date_updated":"2023-08-02T13:33:24Z","type":"journal_article","article_type":"original","status":"public","_id":"10413","doi":"10.1016/j.topol.2021.107916","date_published":"2022-03-15T00:00:00Z","date_created":"2021-12-05T23:01:44Z","isi":1,"year":"2022","day":"15","publication":"Topology and its Applications","publisher":"Elsevier","quality_controlled":"1","acknowledgement":"Dedicated to the memory of Hans-Peter Künzi.","author":[{"last_name":"Dikranjan","full_name":"Dikranjan, Dikran","first_name":"Dikran"},{"last_name":"Giordano Bruno","full_name":"Giordano Bruno, Anna","first_name":"Anna"},{"first_name":"Hans Peter","full_name":"Künzi, Hans Peter","last_name":"Künzi"},{"id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad","first_name":"Nicolò","full_name":"Zava, Nicolò","orcid":"0000-0001-8686-1888","last_name":"Zava"},{"last_name":"Toller","full_name":"Toller, Daniele","first_name":"Daniele"}],"external_id":{"isi":["000791838800012"]},"article_processing_charge":"No","title":"Generalized quasi-metric semilattices","citation":{"short":"D. Dikranjan, A. Giordano Bruno, H.P. Künzi, N. Zava, D. Toller, Topology and Its Applications 309 (2022).","ieee":"D. Dikranjan, A. Giordano Bruno, H. P. Künzi, N. Zava, and D. Toller, “Generalized quasi-metric semilattices,” Topology and its Applications, vol. 309. Elsevier, 2022.","apa":"Dikranjan, D., Giordano Bruno, A., Künzi, H. P., Zava, N., & Toller, D. (2022). Generalized quasi-metric semilattices. Topology and Its Applications. Elsevier. https://doi.org/10.1016/j.topol.2021.107916","ama":"Dikranjan D, Giordano Bruno A, Künzi HP, Zava N, Toller D. Generalized quasi-metric semilattices. Topology and its Applications. 2022;309. doi:10.1016/j.topol.2021.107916","mla":"Dikranjan, Dikran, et al. “Generalized Quasi-Metric Semilattices.” Topology and Its Applications, vol. 309, 107916, Elsevier, 2022, doi:10.1016/j.topol.2021.107916.","ista":"Dikranjan D, Giordano Bruno A, Künzi HP, Zava N, Toller D. 2022. Generalized quasi-metric semilattices. Topology and its Applications. 309, 107916.","chicago":"Dikranjan, Dikran, Anna Giordano Bruno, Hans Peter Künzi, Nicolò Zava, and Daniele Toller. “Generalized Quasi-Metric Semilattices.” Topology and Its Applications. Elsevier, 2022. https://doi.org/10.1016/j.topol.2021.107916."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_number":"107916"},{"publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"publication_status":"published","file":[{"creator":"dernst","date_updated":"2022-08-02T06:07:55Z","file_size":2518111,"date_created":"2022-08-02T06:07:55Z","file_name":"2022_DiscreteCompGeometry_Biswas.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"11718","checksum":"9383d3b70561bacee905e335dc922680","success":1}],"language":[{"iso":"eng"}],"volume":67,"abstract":[{"lang":"eng","text":"The Voronoi tessellation in Rd is defined by locally minimizing the power distance to given weighted points. Symmetrically, the Delaunay mosaic can be defined by locally maximizing the negative power distance to other such points. We prove that the average of the two piecewise quadratic functions is piecewise linear, and that all three functions have the same critical points and values. Discretizing the two piecewise quadratic functions, we get the alpha shapes as sublevel sets of the discrete function on the Delaunay mosaic, and analogous shapes as superlevel sets of the discrete function on the Voronoi tessellation. For the same non-critical value, the corresponding shapes are disjoint, separated by a narrow channel that contains no critical points but the entire level set of the piecewise linear function."}],"oa_version":"Published Version","scopus_import":"1","month":"04","intvolume":" 67","date_updated":"2023-08-02T14:31:25Z","ddc":["510"],"department":[{"_id":"HeEd"}],"file_date_updated":"2022-08-02T06:07:55Z","_id":"10773","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","has_accepted_license":"1","isi":1,"year":"2022","day":"01","publication":"Discrete and Computational Geometry","page":"811-842","doi":"10.1007/s00454-022-00371-2","date_published":"2022-04-01T00:00:00Z","date_created":"2022-02-20T23:01:34Z","acknowledgement":"Open access funding provided by the Institute of Science and Technology (IST Austria).","publisher":"Springer Nature","quality_controlled":"1","oa":1,"citation":{"short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Discrete and Computational Geometry 67 (2022) 811–842.","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics,” Discrete and Computational Geometry, vol. 67. Springer Nature, pp. 811–842, 2022.","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics. Discrete and Computational Geometry. 2022;67:811-842. doi:10.1007/s00454-022-00371-2","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian, M. (2022). Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-022-00371-2","mla":"Biswas, Ranita, et al. “Continuous and Discrete Radius Functions on Voronoi Tessellations and Delaunay Mosaics.” Discrete and Computational Geometry, vol. 67, Springer Nature, 2022, pp. 811–42, doi:10.1007/s00454-022-00371-2.","ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2022. Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics. Discrete and Computational Geometry. 67, 811–842.","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Continuous and Discrete Radius Functions on Voronoi Tessellations and Delaunay Mosaics.” Discrete and Computational Geometry. Springer Nature, 2022. https://doi.org/10.1007/s00454-022-00371-2."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"last_name":"Biswas","full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890","first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","last_name":"Cultrera Di Montesano","orcid":"0000-0001-6249-0832","full_name":"Cultrera Di Montesano, Sebastiano"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"full_name":"Saghafian, Morteza","last_name":"Saghafian","first_name":"Morteza"}],"external_id":{"isi":["000752175300002"]},"article_processing_charge":"Yes (via OA deal)","title":"Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics"},{"citation":{"mla":"Heiss, Teresa, et al. “The Impact of Changes in Resolution on the Persistent Homology of Images.” 2021 IEEE International Conference on Big Data, IEEE, 2022, pp. 3824–34, doi:10.1109/BigData52589.2021.9671483.","ama":"Heiss T, Tymochko S, Story B, et al. The impact of changes in resolution on the persistent homology of images. In: 2021 IEEE International Conference on Big Data. IEEE; 2022:3824-3834. doi:10.1109/BigData52589.2021.9671483","apa":"Heiss, T., Tymochko, S., Story, B., Garin, A., Bui, H., Bleile, B., & Robins, V. (2022). The impact of changes in resolution on the persistent homology of images. In 2021 IEEE International Conference on Big Data (pp. 3824–3834). Orlando, FL, United States; Virtuell: IEEE. https://doi.org/10.1109/BigData52589.2021.9671483","short":"T. Heiss, S. Tymochko, B. Story, A. Garin, H. Bui, B. Bleile, V. Robins, in:, 2021 IEEE International Conference on Big Data, IEEE, 2022, pp. 3824–3834.","ieee":"T. Heiss et al., “The impact of changes in resolution on the persistent homology of images,” in 2021 IEEE International Conference on Big Data, Orlando, FL, United States; Virtuell, 2022, pp. 3824–3834.","chicago":"Heiss, Teresa, Sarah Tymochko, Brittany Story, Adélie Garin, Hoa Bui, Bea Bleile, and Vanessa Robins. “The Impact of Changes in Resolution on the Persistent Homology of Images.” In 2021 IEEE International Conference on Big Data, 3824–34. IEEE, 2022. https://doi.org/10.1109/BigData52589.2021.9671483.","ista":"Heiss T, Tymochko S, Story B, Garin A, Bui H, Bleile B, Robins V. 2022. The impact of changes in resolution on the persistent homology of images. 2021 IEEE International Conference on Big Data. Big Data: International Conference on Big Data, 3824–3834."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","external_id":{"arxiv":["2111.05663"],"isi":["000800559503126"]},"author":[{"id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","first_name":"Teresa","last_name":"Heiss","orcid":"0000-0002-1780-2689","full_name":"Heiss, Teresa"},{"first_name":"Sarah","last_name":"Tymochko","full_name":"Tymochko, Sarah"},{"full_name":"Story, Brittany","last_name":"Story","first_name":"Brittany"},{"last_name":"Garin","full_name":"Garin, Adélie","first_name":"Adélie"},{"last_name":"Bui","full_name":"Bui, Hoa","first_name":"Hoa"},{"full_name":"Bleile, Bea","last_name":"Bleile","first_name":"Bea"},{"full_name":"Robins, Vanessa","last_name":"Robins","first_name":"Vanessa"}],"title":"The impact of changes in resolution on the persistent homology of images","oa":1,"publisher":"IEEE","quality_controlled":"1","year":"2022","isi":1,"publication":"2021 IEEE International Conference on Big Data","day":"13","page":"3824-3834","date_created":"2022-03-06T23:01:53Z","doi":"10.1109/BigData52589.2021.9671483","date_published":"2022-01-13T00:00:00Z","_id":"10828","conference":{"start_date":"2021-12-15","location":"Orlando, FL, United States; Virtuell","end_date":"2021-12-18","name":"Big Data: International Conference on Big Data"},"type":"conference","status":"public","date_updated":"2023-08-02T14:44:21Z","department":[{"_id":"HeEd"}],"abstract":[{"text":"Digital images enable quantitative analysis of material properties at micro and macro length scales, but choosing an appropriate resolution when acquiring the image is challenging. A high resolution means longer image acquisition and larger data requirements for a given sample, but if the resolution is too low, significant information may be lost. This paper studies the impact of changes in resolution on persistent homology, a tool from topological data analysis that provides a signature of structure in an image across all length scales. Given prior information about a function, the geometry of an object, or its density distribution at a given resolution, we provide methods to select the coarsest resolution yielding results within an acceptable tolerance. We present numerical case studies for an illustrative synthetic example and samples from porous materials where the theoretical bounds are unknown.","lang":"eng"}],"oa_version":"Preprint","main_file_link":[{"url":"https://arxiv.org/abs/2111.05663","open_access":"1"}],"scopus_import":"1","month":"01","publication_status":"published","publication_identifier":{"isbn":["9781665439022"]},"language":[{"iso":"eng"}]},{"project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"author":[{"id":"70B7FDF6-608D-11E9-9333-8535E6697425","first_name":"Adam","full_name":"Brown, Adam","last_name":"Brown"},{"first_name":"Anna","full_name":"Romanov, Anna","last_name":"Romanov"}],"external_id":{"isi":["000861841100004"]},"article_processing_charge":"Yes (via OA deal)","title":"Contravariant pairings between standard Whittaker modules and Verma modules","citation":{"mla":"Brown, Adam, and Anna Romanov. “Contravariant Pairings between Standard Whittaker Modules and Verma Modules.” Journal of Algebra, vol. 609, no. 11, Elsevier, 2022, pp. 145–79, doi:10.1016/j.jalgebra.2022.06.017.","ama":"Brown A, Romanov A. Contravariant pairings between standard Whittaker modules and Verma modules. Journal of Algebra. 2022;609(11):145-179. doi:10.1016/j.jalgebra.2022.06.017","apa":"Brown, A., & Romanov, A. (2022). Contravariant pairings between standard Whittaker modules and Verma modules. Journal of Algebra. Elsevier. https://doi.org/10.1016/j.jalgebra.2022.06.017","short":"A. Brown, A. Romanov, Journal of Algebra 609 (2022) 145–179.","ieee":"A. Brown and A. Romanov, “Contravariant pairings between standard Whittaker modules and Verma modules,” Journal of Algebra, vol. 609, no. 11. Elsevier, pp. 145–179, 2022.","chicago":"Brown, Adam, and Anna Romanov. “Contravariant Pairings between Standard Whittaker Modules and Verma Modules.” Journal of Algebra. Elsevier, 2022. https://doi.org/10.1016/j.jalgebra.2022.06.017.","ista":"Brown A, Romanov A. 2022. Contravariant pairings between standard Whittaker modules and Verma modules. Journal of Algebra. 609(11), 145–179."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"Elsevier","quality_controlled":"1","oa":1,"acknowledgement":"We thank Catharina Stroppel and Jens Niklas Eberhardt for interesting discussions. The first author acknowledges the support of the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. The second author is supported by the National Science Foundation Award No. 1803059 and the Australian Research Council grant DP170101579.","page":"145-179","date_published":"2022-11-01T00:00:00Z","doi":"10.1016/j.jalgebra.2022.06.017","date_created":"2022-07-08T11:40:07Z","has_accepted_license":"1","isi":1,"year":"2022","day":"01","publication":"Journal of Algebra","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","keyword":["Algebra and Number Theory"],"_id":"11545","file_date_updated":"2023-02-02T07:32:48Z","department":[{"_id":"HeEd"}],"date_updated":"2023-08-03T11:56:30Z","ddc":["510"],"scopus_import":"1","month":"11","intvolume":" 609","abstract":[{"text":"We classify contravariant pairings between standard Whittaker modules and Verma modules over a complex semisimple Lie algebra. These contravariant pairings are useful in extending several classical techniques for category O to the Miličić–Soergel category N . We introduce a class of costandard modules which generalize dual Verma modules, and describe canonical maps from standard to costandard modules in terms of contravariant pairings.\r\nWe show that costandard modules have unique irreducible submodules and share the same composition factors as the corresponding standard Whittaker modules. We show that costandard modules give an algebraic characterization of the global sections of costandard twisted Harish-Chandra sheaves on the associated flag variety, which are defined using holonomic duality of D-modules. We prove that with these costandard modules, blocks of category\r\nN have the structure of highest weight categories and we establish a BGG reciprocity theorem for N .","lang":"eng"}],"oa_version":"Published Version","volume":609,"issue":"11","ec_funded":1,"publication_identifier":{"issn":["0021-8693"]},"publication_status":"published","file":[{"checksum":"82abaee3d7837f703e499a9ecbb25b7c","file_id":"12473","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2023-02-02T07:32:48Z","file_name":"2022_JournalAlgebra_Brown.pdf","date_updated":"2023-02-02T07:32:48Z","file_size":582962,"creator":"dernst"}],"language":[{"iso":"eng"}]},{"publisher":"MDPI","quality_controlled":"1","oa":1,"acknowledgement":"This work was partially supported by grants from National Institutes of Health (NIH) (R01 CA185055, S10OD0252300) and The University of Texas System STARs Award (to Z.P.),\r\nThe University of Texas at Arlington Interdisciplinary Research Program (to B.C., H.V.K. and Z.P.). ","date_published":"2022-02-01T00:00:00Z","doi":"10.3390/ijms23031763","date_created":"2022-02-13T23:01:35Z","isi":1,"has_accepted_license":"1","year":"2022","day":"01","publication":"International Journal of Molecular Sciences","article_number":"1763","author":[{"first_name":"Yan","full_name":"Chang, Yan","last_name":"Chang"},{"last_name":"Funk","full_name":"Funk, Marah","first_name":"Marah"},{"full_name":"Roy, Souvik","last_name":"Roy","first_name":"Souvik"},{"last_name":"Stephenson","orcid":"0000-0002-6862-208X","full_name":"Stephenson, Elizabeth R","first_name":"Elizabeth R","id":"2D04F932-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Choi","full_name":"Choi, Sangyong","first_name":"Sangyong"},{"full_name":"Kojouharov, Hristo V.","last_name":"Kojouharov","first_name":"Hristo V."},{"first_name":"Benito","full_name":"Chen, Benito","last_name":"Chen"},{"first_name":"Zui","full_name":"Pan, Zui","last_name":"Pan"}],"external_id":{"isi":["000754773500001"]},"article_processing_charge":"Yes","title":"Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer","citation":{"mla":"Chang, Yan, et al. “Developing a Mathematical Model of Intracellular Calcium Dynamics for Evaluating Combined Anticancer Effects of Afatinib and RP4010 in Esophageal Cancer.” International Journal of Molecular Sciences, vol. 23, no. 3, 1763, MDPI, 2022, doi:10.3390/ijms23031763.","short":"Y. Chang, M. Funk, S. Roy, E.R. Stephenson, S. Choi, H.V. Kojouharov, B. Chen, Z. Pan, International Journal of Molecular Sciences 23 (2022).","ieee":"Y. Chang et al., “Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer,” International Journal of Molecular Sciences, vol. 23, no. 3. MDPI, 2022.","ama":"Chang Y, Funk M, Roy S, et al. Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer. International Journal of Molecular Sciences. 2022;23(3). doi:10.3390/ijms23031763","apa":"Chang, Y., Funk, M., Roy, S., Stephenson, E. R., Choi, S., Kojouharov, H. V., … Pan, Z. (2022). Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer. International Journal of Molecular Sciences. MDPI. https://doi.org/10.3390/ijms23031763","chicago":"Chang, Yan, Marah Funk, Souvik Roy, Elizabeth R Stephenson, Sangyong Choi, Hristo V. Kojouharov, Benito Chen, and Zui Pan. “Developing a Mathematical Model of Intracellular Calcium Dynamics for Evaluating Combined Anticancer Effects of Afatinib and RP4010 in Esophageal Cancer.” International Journal of Molecular Sciences. MDPI, 2022. https://doi.org/10.3390/ijms23031763.","ista":"Chang Y, Funk M, Roy S, Stephenson ER, Choi S, Kojouharov HV, Chen B, Pan Z. 2022. Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer. International Journal of Molecular Sciences. 23(3), 1763."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","scopus_import":"1","month":"02","intvolume":" 23","abstract":[{"text":"Targeting dysregulated Ca2+ signaling in cancer cells is an emerging chemotherapy approach. We previously reported that store-operated Ca2+ entry (SOCE) blockers, such as RP4010, are promising antitumor drugs for esophageal cancer. As a tyrosine kinase inhibitor (TKI), afatinib received FDA approval to be used in targeted therapy for patients with EGFR mutation-positive cancers. While preclinical studies and clinical trials have shown that afatinib has benefits for esophageal cancer patients, it is not known whether a combination of afatinib and RP4010 could achieve better anticancer effects. Since TKI can alter intracellular Ca2+ dynamics through EGFR/phospholipase C-γ pathway, in this study, we evaluated the inhibitory effect of afatinib and RP4010 on intracellular Ca2+ oscillations in KYSE-150, a human esophageal squamous cell carcinoma cell line, using both experimental and mathematical simulations. Our mathematical simulation of Ca2+ oscillations could fit well with experimental data responding to afatinib or RP4010, both separately or in combination. Guided by simulation, we were able to identify a proper ratio of afatinib and RP4010 for combined treatment, and such a combination presented synergistic anticancer-effect evidence by experimental measurement of intracellular Ca2+ and cell proliferation. This intracellular Ca2+ dynamic-based mathematical simulation approach could be useful for a rapid and cost-effective evaluation of combined targeting therapy drugs.","lang":"eng"}],"oa_version":"Published Version","issue":"3","volume":23,"publication_identifier":{"eissn":["14220067"],"issn":["16616596"]},"publication_status":"published","file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"file_id":"10756","checksum":"8890ad20c54e90dc58ad5ea97c902998","file_size":24416183,"date_updated":"2022-02-14T07:46:30Z","creator":"dernst","file_name":"2022_IJMS_Chang.pdf","date_created":"2022-02-14T07:46:30Z"}],"language":[{"iso":"eng"}],"article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","_id":"10754","file_date_updated":"2022-02-14T07:46:30Z","department":[{"_id":"HeEd"}],"date_updated":"2023-08-09T10:17:07Z","ddc":["510","576"]},{"publication":"European Journal of Mathematics","day":"01","year":"2022","has_accepted_license":"1","date_created":"2020-05-03T22:00:48Z","date_published":"2022-12-01T00:00:00Z","doi":"10.1007/s40879-020-00405-0","page":"1309 - 1312","acknowledgement":"AA was supported by European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 78818 Alpha). RK was supported by the Federal professorship program Grant 1.456.2016/1.4 and the Russian Foundation for Basic Research Grants 18-01-00036 and 19-01-00169. Open access funding provided by Institute of Science and Technology (IST Austria). The authors thank Alexey Balitskiy, Milena Radnović, and Serge Tabachnikov for useful discussions.","oa":1,"publisher":"Springer Nature","quality_controlled":"1","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Akopyan, Arseniy, and Roman Karasev. “When Different Norms Lead to Same Billiard Trajectories?” European Journal of Mathematics. Springer Nature, 2022. https://doi.org/10.1007/s40879-020-00405-0.","ista":"Akopyan A, Karasev R. 2022. When different norms lead to same billiard trajectories? European Journal of Mathematics. 8(4), 1309–1312.","mla":"Akopyan, Arseniy, and Roman Karasev. “When Different Norms Lead to Same Billiard Trajectories?” European Journal of Mathematics, vol. 8, no. 4, Springer Nature, 2022, pp. 1309–12, doi:10.1007/s40879-020-00405-0.","apa":"Akopyan, A., & Karasev, R. (2022). When different norms lead to same billiard trajectories? European Journal of Mathematics. Springer Nature. https://doi.org/10.1007/s40879-020-00405-0","ama":"Akopyan A, Karasev R. When different norms lead to same billiard trajectories? European Journal of Mathematics. 2022;8(4):1309-1312. doi:10.1007/s40879-020-00405-0","ieee":"A. Akopyan and R. Karasev, “When different norms lead to same billiard trajectories?,” European Journal of Mathematics, vol. 8, no. 4. Springer Nature, pp. 1309–1312, 2022.","short":"A. Akopyan, R. Karasev, European Journal of Mathematics 8 (2022) 1309–1312."},"title":"When different norms lead to same billiard trajectories?","article_processing_charge":"Yes (via OA deal)","external_id":{"arxiv":["1912.12685"]},"author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan"},{"full_name":"Karasev, Roman","last_name":"Karasev","first_name":"Roman"}],"project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"language":[{"iso":"eng"}],"file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_id":"7796","checksum":"f53e71fd03744075adcd0b8fc1b8423d","creator":"dernst","file_size":263926,"date_updated":"2020-07-14T12:48:03Z","file_name":"2020_EuropMathematics_Akopyan.pdf","date_created":"2020-05-04T10:33:42Z"}],"publication_status":"published","publication_identifier":{"issn":["2199-675X"],"eissn":["2199-6768"]},"ec_funded":1,"volume":8,"issue":"4","oa_version":"Published Version","abstract":[{"text":"Extending a result of Milena Radnovic and Serge Tabachnikov, we establish conditionsfor two different non-symmetric norms to define the same billiard reflection law.","lang":"eng"}],"intvolume":" 8","month":"12","scopus_import":"1","ddc":["510"],"date_updated":"2024-02-22T15:58:42Z","file_date_updated":"2020-07-14T12:48:03Z","department":[{"_id":"HeEd"}],"_id":"7791","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original"},{"publication_status":"submitted","file":[{"checksum":"95903f9d1649e8e437a967b6f2f64730","file_id":"11661","content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2022-07-27T09:30:30Z","file_name":"window 1.pdf","date_updated":"2022-07-27T09:30:30Z","file_size":564836,"creator":"scultrer"}],"language":[{"iso":"eng"}],"related_material":{"record":[{"status":"public","id":"15094","relation":"dissertation_contains"}]},"ec_funded":1,"abstract":[{"text":"We characterize critical points of 1-dimensional maps paired in persistent homology geometrically and this way get elementary proofs of theorems about the symmetry of persistence diagrams and the variation of such maps. In particular, we identify branching points and endpoints of networks as the sole source of asymmetry and relate the cycle basis in persistent homology with a version of the stable marriage problem. Our analysis provides the foundations of fast algorithms for maintaining collections of interrelated sorted lists together with their persistence diagrams. ","lang":"eng"}],"oa_version":"Submitted Version","alternative_title":["LIPIcs"],"month":"07","date_updated":"2024-03-20T09:36:56Z","ddc":["510"],"file_date_updated":"2022-07-27T09:30:30Z","department":[{"_id":"GradSch"},{"_id":"HeEd"}],"_id":"11660","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","has_accepted_license":"1","year":"2022","day":"25","publication":"LIPIcs","date_published":"2022-07-25T00:00:00Z","date_created":"2022-07-27T09:31:15Z","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. ","quality_controlled":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","oa":1,"citation":{"chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “A Window to the Persistence of 1D Maps. I: Geometric Characterization of Critical Point Pairs.” LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, n.d.","ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. A window to the persistence of 1D maps. I: Geometric characterization of critical point pairs. LIPIcs.","mla":"Biswas, Ranita, et al. “A Window to the Persistence of 1D Maps. I: Geometric Characterization of Critical Point Pairs.” LIPIcs, Schloss Dagstuhl - Leibniz-Zentrum für Informatik.","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. A window to the persistence of 1D maps. I: Geometric characterization of critical point pairs. LIPIcs.","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian, M. (n.d.). A window to the persistence of 1D maps. I: Geometric characterization of critical point pairs. LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für Informatik.","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “A window to the persistence of 1D maps. I: Geometric characterization of critical point pairs,” LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für Informatik.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. 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We prove Euler-type relations, which imply extensions of the classic Dehn–Sommerville relations for convex polytopes to sublevel sets of the depth function, and we use the relations to extend the expressions for the number of faces of neighborly polytopes to the number of cells of levels in neighborly arrangements.","lang":"eng"}],"department":[{"_id":"GradSch"},{"_id":"HeEd"}],"file_date_updated":"2022-07-27T09:25:53Z","ddc":["510"],"date_updated":"2024-03-20T09:36:56Z","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","_id":"11658","date_created":"2022-07-27T09:27:34Z","date_published":"2022-07-27T00:00:00Z","publication":"Leibniz International Proceedings on Mathematics","day":"27","year":"2022","has_accepted_license":"1","oa":1,"quality_controlled":"1","publisher":"Schloss Dagstuhl - Leibniz Zentrum für Informatik","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. 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I 02979-N35.","title":"Depth in arrangements: Dehn–Sommerville–Euler relations with applications","article_processing_charge":"No","author":[{"first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5372-7890","full_name":"Biswas, Ranita","last_name":"Biswas"},{"last_name":"Cultrera di Montesano","orcid":"0000-0001-6249-0832","full_name":"Cultrera di Montesano, Sebastiano","first_name":"Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Saghafian","full_name":"Saghafian, Morteza","first_name":"Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Depth in arrangements: Dehn–Sommerville–Euler relations with applications. Leibniz International Proceedings on Mathematics.","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Depth in Arrangements: Dehn–Sommerville–Euler Relations with Applications.” Leibniz International Proceedings on Mathematics. Schloss Dagstuhl - Leibniz Zentrum für Informatik, n.d.","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian, M. (n.d.). Depth in arrangements: Dehn–Sommerville–Euler relations with applications. Leibniz International Proceedings on Mathematics. Schloss Dagstuhl - Leibniz Zentrum für Informatik.","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Depth in arrangements: Dehn–Sommerville–Euler relations with applications. Leibniz International Proceedings on Mathematics.","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Depth in arrangements: Dehn–Sommerville–Euler relations with applications,” Leibniz International Proceedings on Mathematics. Schloss Dagstuhl - Leibniz Zentrum für Informatik.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Leibniz International Proceedings on Mathematics (n.d.).","mla":"Biswas, Ranita, et al. “Depth in Arrangements: Dehn–Sommerville–Euler Relations with Applications.” Leibniz International Proceedings on Mathematics, Schloss Dagstuhl - Leibniz Zentrum für Informatik."},"project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183","name":"Alpha Shape Theory Extended"},{"grant_number":"Z00342","name":"The Wittgenstein Prize","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes"}]},{"related_material":{"record":[{"id":"15094","status":"public","relation":"dissertation_contains"}]},"date_published":"2022-12-06T00:00:00Z","date_created":"2024-03-08T09:54:20Z","ec_funded":1,"day":"06","language":[{"iso":"eng"}],"publication":"arXiv","publication_status":"submitted","year":"2022","month":"12","main_file_link":[{"url":"https://arxiv.org/abs/2212.03121","open_access":"1"}],"oa":1,"oa_version":"Preprint","abstract":[{"lang":"eng","text":"Given a locally finite set A⊆Rd and a coloring χ:A→{0,1,…,s}, we introduce the chromatic Delaunay mosaic of χ, which is a Delaunay mosaic in Rs+d that represents how points of different colors mingle. Our main results are bounds on the size of the chromatic Delaunay mosaic, in which we assume that d and s are constants. For example, if A is finite with n=#A, and the coloring is random, then the chromatic Delaunay mosaic has O(n⌈d/2⌉) cells in expectation. In contrast, for Delone sets and Poisson point processes in Rd, the expected number of cells within a closed ball is only a constant times the number of points in this ball. Furthermore, in R2 all colorings of a dense set of n points have chromatic Delaunay mosaics of size O(n). This encourages the use of chromatic Delaunay mosaics in applications."}],"department":[{"_id":"HeEd"}],"title":"On the size of chromatic Delaunay mosaics","author":[{"first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","last_name":"Biswas","orcid":"0000-0002-5372-7890","full_name":"Biswas, Ranita"},{"first_name":"Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-6249-0832","full_name":"Cultrera di Montesano, Sebastiano","last_name":"Cultrera di Montesano"},{"full_name":"Draganov, Ondrej","last_name":"Draganov","first_name":"Ondrej","id":"2B23F01E-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"full_name":"Saghafian, Morteza","last_name":"Saghafian","id":"f86f7148-b140-11ec-9577-95435b8df824","first_name":"Morteza"}],"external_id":{"arxiv":["2212.03121"]},"article_processing_charge":"No","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","date_updated":"2024-03-20T09:36:56Z","citation":{"mla":"Biswas, Ranita, et al. “On the Size of Chromatic Delaunay Mosaics.” ArXiv, 2212.03121.","apa":"Biswas, R., Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., & Saghafian, M. (n.d.). On the size of chromatic Delaunay mosaics. arXiv.","ama":"Biswas R, Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. On the size of chromatic Delaunay mosaics. arXiv.","short":"R. Biswas, S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.).","ieee":"R. Biswas, S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian, “On the size of chromatic Delaunay mosaics,” arXiv. .","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Ondrej Draganov, Herbert Edelsbrunner, and Morteza Saghafian. “On the Size of Chromatic Delaunay Mosaics.” ArXiv, n.d.","ista":"Biswas R, Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. On the size of chromatic Delaunay mosaics. arXiv, 2212.03121."},"project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","name":"Discretization in Geometry and Dynamics","grant_number":"I4887"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"Z00342","name":"The Wittgenstein Prize"}],"status":"public","type":"preprint","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_number":"2212.03121","_id":"15090"},{"scopus_import":"1","month":"05","intvolume":" 13","abstract":[{"text":"It is practical to collect a huge amount of movement data and environmental context information along with the health signals of individuals because there is the emergence of new generations of positioning and tracking technologies and rapid advancements of health sensors. The study of the relations between these datasets and their sequence similarity analysis is of interest to many applications such as health monitoring and recommender systems. However, entering all movement parameters and health signals can lead to the complexity of the problem and an increase in its computational load. In this situation, dimension reduction techniques can be used to avoid consideration of simultaneous dependent parameters in the process of similarity measurement of the trajectories. The present study provides a framework, named CaDRAW, to use spatial–temporal data and movement parameters along with independent context information in the process of measuring the similarity of trajectories. In this regard, the omission of dependent movement characteristic signals is conducted by using an unsupervised feature selection dimension reduction technique. To evaluate the effectiveness of the proposed framework, it was applied to a real contextualized movement and related health signal datasets of individuals. The results indicated the capability of the proposed framework in measuring the similarity and in decreasing the characteristic signals in such a way that the similarity results -before and after reduction of dependent characteristic signals- have small differences. The mean differences between the obtained results before and after reducing the dimension were 0.029 and 0.023 for the round path, respectively.","lang":"eng"}],"oa_version":"Submitted Version","volume":13,"publication_identifier":{"issn":["1868-5137"],"eissn":["1868-5145"]},"publication_status":"published","file":[{"embargo":"2022-11-12","file_id":"10279","checksum":"0a8961416a9bb2be5a1cebda65468bcf","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_name":"A Context‑aware Dimension Reduction Framework - Journal of Ambient Intelligence 2021 (Preprint version).pdf","date_created":"2021-11-12T19:38:05Z","creator":"fkarimip","file_size":1634958,"date_updated":"2022-12-20T23:30:08Z"}],"language":[{"iso":"eng"}],"article_type":"original","type":"journal_article","status":"public","keyword":["general computer science"],"_id":"10208","file_date_updated":"2022-12-20T23:30:08Z","department":[{"_id":"HeEd"}],"date_updated":"2023-08-02T13:31:48Z","ddc":["000"],"publisher":"Springer Nature","quality_controlled":"1","oa":1,"acknowledgement":"The third author acknowledges the funding received from the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. 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A context-aware dimension reduction framework for trajectory and health signal analyses. Journal of Ambient Intelligence and Humanized Computing. 2022;13:2621–2635. doi:10.1007/s12652-021-03569-z","apa":"Goudarzi, S., Sharif, M., & Karimipour, F. (2022). A context-aware dimension reduction framework for trajectory and health signal analyses. Journal of Ambient Intelligence and Humanized Computing. Springer Nature. https://doi.org/10.1007/s12652-021-03569-z"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"},{"volume":68,"issue":"9","publication_status":"published","publication_identifier":{"eissn":["1088-9477"],"issn":["0002-9920"]},"language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"http://www.ams.org/notices/"}],"alternative_title":["Early Career"],"scopus_import":"1","intvolume":" 68","month":"10","oa_version":"Published Version","department":[{"_id":"HeEd"}],"date_updated":"2021-12-03T07:31:26Z","article_type":"letter_note","type":"journal_article","status":"public","_id":"10071","page":"1511-1514","date_created":"2021-10-03T22:01:22Z","date_published":"2021-10-01T00:00:00Z","doi":"10.1090/noti2349","year":"2021","publication":"Notices of the American Mathematical Society","day":"01","oa":1,"quality_controlled":"1","publisher":"American Mathematical Society","article_processing_charge":"No","author":[{"full_name":"Adams, Henry","last_name":"Adams","first_name":"Henry"},{"full_name":"Kourimska, Hana","last_name":"Kourimska","first_name":"Hana","id":"D9B8E14C-3C26-11EA-98F5-1F833DDC885E"},{"last_name":"Heiss","orcid":"0000-0002-1780-2689","full_name":"Heiss, Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","first_name":"Teresa"},{"last_name":"Percival","full_name":"Percival, Sarah","first_name":"Sarah"},{"full_name":"Ziegelmeier, Lori","last_name":"Ziegelmeier","first_name":"Lori"}],"title":"How to tutorial-a-thon","citation":{"ama":"Adams H, Kourimska H, Heiss T, Percival S, Ziegelmeier L. 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Notices of the American Mathematical Society. 68(9), 1511–1514.","chicago":"Adams, Henry, Hana Kourimska, Teresa Heiss, Sarah Percival, and Lori Ziegelmeier. “How to Tutorial-a-Thon.” Notices of the American Mathematical Society. American Mathematical Society, 2021. https://doi.org/10.1090/noti2349."},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9"},{"year":"2021","has_accepted_license":"1","publication":"59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, Tutorial Abstracts","day":"01","page":"29-30","date_created":"2021-11-28T23:01:30Z","date_published":"2021-08-01T00:00:00Z","doi":"10.18653/v1/2021.acl-tutorials.6","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.","oa":1,"publisher":"Association for Computational Linguistics","quality_controlled":"1","citation":{"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.","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","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","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.","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.","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.","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."},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","article_processing_charge":"No","author":[{"first_name":"Cesar","last_name":"Ilharco","full_name":"Ilharco, Cesar"},{"first_name":"Afsaneh","last_name":"Shirazi","full_name":"Shirazi, Afsaneh"},{"first_name":"Arjun","last_name":"Gopalan","full_name":"Gopalan, Arjun"},{"first_name":"Arsha","full_name":"Nagrani, Arsha","last_name":"Nagrani"},{"full_name":"Bratanič, Blaž","last_name":"Bratanič","first_name":"Blaž"},{"first_name":"Chris","full_name":"Bregler, Chris","last_name":"Bregler"},{"full_name":"Liu, Christina","last_name":"Liu","first_name":"Christina"},{"full_name":"Ferreira, Felipe","last_name":"Ferreira","first_name":"Felipe"},{"last_name":"Barcik","full_name":"Barcik, Gabriek","first_name":"Gabriek"},{"full_name":"Ilharco, Gabriel","last_name":"Ilharco","first_name":"Gabriel"},{"id":"464B40D6-F248-11E8-B48F-1D18A9856A87","first_name":"Georg F","full_name":"Osang, Georg F","last_name":"Osang"},{"last_name":"Bulian","full_name":"Bulian, Jannis","first_name":"Jannis"},{"first_name":"Jared","full_name":"Frank, Jared","last_name":"Frank"},{"full_name":"Smaira, Lucas","last_name":"Smaira","first_name":"Lucas"},{"last_name":"Cao","full_name":"Cao, Qin","first_name":"Qin"},{"last_name":"Marino","full_name":"Marino, Ricardo","first_name":"Ricardo"},{"full_name":"Patel, Roma","last_name":"Patel","first_name":"Roma"},{"first_name":"Thomas","full_name":"Leung, Thomas","last_name":"Leung"},{"last_name":"Imbrasaite","full_name":"Imbrasaite, Vaiva","first_name":"Vaiva"}],"title":"Recognizing multimodal entailment","publication_status":"published","publication_identifier":{"isbn":["9-781-9540-8557-2"]},"language":[{"iso":"eng"}],"file":[{"file_id":"10368","checksum":"b14052a025a6ecf675bdfe51db98c0d7","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2021-11-29T08:41:00Z","file_name":"2021_ACL_Ilharco.pdf","date_updated":"2021-11-29T08:41:00Z","file_size":1227703,"creator":"cchlebak"}],"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."}],"oa_version":"Published Version","main_file_link":[{"url":"https://aclanthology.org/2021.acl-tutorials.6/","open_access":"1"}],"scopus_import":"1","month":"08","date_updated":"2022-01-26T14:26:36Z","ddc":["000"],"department":[{"_id":"HeEd"}],"file_date_updated":"2021-11-29T08:41:00Z","_id":"10367","conference":{"start_date":"2021-08-01","end_date":"2021-08-06","location":"Bangkok, Thailand","name":"ACL: Association for Computational Linguistics ; IJCNLP: International Joint Conference on Natural Language Processing"},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"conference","status":"public"},{"publication_status":"published","publication_identifier":{"issn":["2199-675X"],"eissn":["2199-6768"]},"language":[{"iso":"eng"}],"file":[{"success":1,"checksum":"c435dcfa1ad3aadc5cdd7366bc7f4e98","file_id":"10610","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_name":"2021_EuJournalMath_Weighill.pdf","date_created":"2022-01-10T08:33:22Z","creator":"cchlebak","file_size":384908,"date_updated":"2022-01-10T08:33:22Z"}],"abstract":[{"lang":"eng","text":"We consider infinite-dimensional properties in coarse geometry for hyperspaces consisting of finite subsets of metric spaces with the Hausdorff metric. We see that several infinite-dimensional properties are preserved by taking the hyperspace of subsets with at most n points. On the other hand, we prove that, if a metric space contains a sequence of long intervals coarsely, then its hyperspace of finite subsets is not coarsely embeddable into any uniformly convex Banach space. As a corollary, the hyperspace of finite subsets of the real line is not coarsely embeddable into any uniformly convex Banach space. It is also shown that every (not necessarily bounded geometry) metric space with straight finite decomposition complexity has metric sparsification property."}],"oa_version":"Published Version","scopus_import":"1","month":"12","date_updated":"2022-01-10T08:36:55Z","ddc":["500"],"file_date_updated":"2022-01-10T08:33:22Z","department":[{"_id":"HeEd"}],"_id":"10608","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","status":"public","year":"2021","has_accepted_license":"1","publication":"European Journal of Mathematics","day":"30","date_created":"2022-01-09T23:01:27Z","doi":"10.1007/s40879-021-00515-3","date_published":"2021-12-30T00:00:00Z","acknowledgement":"We would like to thank the referees for their careful reading and the comments that improved our work. The third named author would like to thank the Division of Mathematics, Physics and Earth Sciences of the Graduate School of Science and Engineering of Ehime University and the second named author for hosting his visit in June 2018. Open access funding provided by Institute of Science and Technology (IST Austria).","oa":1,"publisher":"Springer Nature","quality_controlled":"1","citation":{"mla":"Weighill, Thomas, et al. “Coarse Infinite-Dimensionality of Hyperspaces of Finite Subsets.” European Journal of Mathematics, Springer Nature, 2021, doi:10.1007/s40879-021-00515-3.","ama":"Weighill T, Yamauchi T, Zava N. Coarse infinite-dimensionality of hyperspaces of finite subsets. European Journal of Mathematics. 2021. doi:10.1007/s40879-021-00515-3","apa":"Weighill, T., Yamauchi, T., & Zava, N. (2021). Coarse infinite-dimensionality of hyperspaces of finite subsets. European Journal of Mathematics. Springer Nature. https://doi.org/10.1007/s40879-021-00515-3","ieee":"T. Weighill, T. Yamauchi, and N. Zava, “Coarse infinite-dimensionality of hyperspaces of finite subsets,” European Journal of Mathematics. Springer Nature, 2021.","short":"T. Weighill, T. Yamauchi, N. Zava, European Journal of Mathematics (2021).","chicago":"Weighill, Thomas, Takamitsu Yamauchi, and Nicolò Zava. “Coarse Infinite-Dimensionality of Hyperspaces of Finite Subsets.” European Journal of Mathematics. Springer Nature, 2021. https://doi.org/10.1007/s40879-021-00515-3.","ista":"Weighill T, Yamauchi T, Zava N. 2021. Coarse infinite-dimensionality of hyperspaces of finite subsets. European Journal of Mathematics."},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","article_processing_charge":"Yes (via OA deal)","author":[{"first_name":"Thomas","full_name":"Weighill, Thomas","last_name":"Weighill"},{"first_name":"Takamitsu","last_name":"Yamauchi","full_name":"Yamauchi, Takamitsu"},{"first_name":"Nicolò","id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad","full_name":"Zava, Nicolò","last_name":"Zava"}],"title":"Coarse infinite-dimensionality of hyperspaces of finite subsets"},{"department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"KrCh"}],"date_updated":"2023-02-21T16:33:44Z","type":"conference","conference":{"end_date":"2021-03-02","location":"Yangon, Myanmar","start_date":"2021-02-28","name":"WALCOM: Algorithms and Computation"},"status":"public","_id":"9296","volume":12635,"related_material":{"record":[{"relation":"later_version","id":"11938","status":"public"}]},"ec_funded":1,"publication_identifier":{"eissn":["16113349"],"isbn":["9783030682101"],"issn":["03029743"]},"publication_status":"published","language":[{"iso":"eng"}],"alternative_title":["LNCS"],"scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2101.03928"}],"month":"02","intvolume":" 12635","abstract":[{"lang":"eng","text":" matching is compatible to two or more labeled point sets of size n with labels {1,…,n} if its straight-line drawing on each of these point sets is crossing-free. We study the maximum number of edges in a matching compatible to two or more labeled point sets in general position in the plane. We show that for any two labeled convex sets of n points there exists a compatible matching with ⌊2n−−√⌋ edges. More generally, for any ℓ labeled point sets we construct compatible matchings of size Ω(n1/ℓ) . As a corresponding upper bound, we use probabilistic arguments to show that for any ℓ given sets of n points there exists a labeling of each set such that the largest compatible matching has O(n2/(ℓ+1)) edges. Finally, we show that Θ(logn) copies of any set of n points are necessary and sufficient for the existence of a labeling such that any compatible matching consists only of a single edge."}],"oa_version":"Preprint","author":[{"first_name":"Oswin","full_name":"Aichholzer, Oswin","last_name":"Aichholzer"},{"full_name":"Arroyo Guevara, Alan M","orcid":"0000-0003-2401-8670","last_name":"Arroyo Guevara","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87","first_name":"Alan M"},{"first_name":"Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","last_name":"Masárová","full_name":"Masárová, Zuzana","orcid":"0000-0002-6660-1322"},{"first_name":"Irene","last_name":"Parada","full_name":"Parada, Irene"},{"first_name":"Daniel","last_name":"Perz","full_name":"Perz, Daniel"},{"full_name":"Pilz, Alexander","last_name":"Pilz","first_name":"Alexander"},{"id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","first_name":"Josef","orcid":"0000-0002-1097-9684","full_name":"Tkadlec, Josef","last_name":"Tkadlec"},{"last_name":"Vogtenhuber","full_name":"Vogtenhuber, Birgit","first_name":"Birgit"}],"article_processing_charge":"No","external_id":{"arxiv":["2101.03928"]},"title":"On compatible matchings","citation":{"mla":"Aichholzer, Oswin, et al. “On Compatible Matchings.” 15th International Conference on Algorithms and Computation, vol. 12635, Springer Nature, 2021, pp. 221–33, doi:10.1007/978-3-030-68211-8_18.","short":"O. Aichholzer, A.M. Arroyo Guevara, Z. Masárová, I. Parada, D. Perz, A. Pilz, J. Tkadlec, B. Vogtenhuber, in:, 15th International Conference on Algorithms and Computation, Springer Nature, 2021, pp. 221–233.","ieee":"O. Aichholzer et al., “On compatible matchings,” in 15th International Conference on Algorithms and Computation, Yangon, Myanmar, 2021, vol. 12635, pp. 221–233.","ama":"Aichholzer O, Arroyo Guevara AM, Masárová Z, et al. On compatible matchings. In: 15th International Conference on Algorithms and Computation. Vol 12635. Springer Nature; 2021:221-233. doi:10.1007/978-3-030-68211-8_18","apa":"Aichholzer, O., Arroyo Guevara, A. M., Masárová, Z., Parada, I., Perz, D., Pilz, A., … Vogtenhuber, B. (2021). On compatible matchings. In 15th International Conference on Algorithms and Computation (Vol. 12635, pp. 221–233). Yangon, Myanmar: Springer Nature. https://doi.org/10.1007/978-3-030-68211-8_18","chicago":"Aichholzer, Oswin, Alan M Arroyo Guevara, Zuzana Masárová, Irene Parada, Daniel Perz, Alexander Pilz, Josef Tkadlec, and Birgit Vogtenhuber. “On Compatible Matchings.” In 15th International Conference on Algorithms and Computation, 12635:221–33. Springer Nature, 2021. https://doi.org/10.1007/978-3-030-68211-8_18.","ista":"Aichholzer O, Arroyo Guevara AM, Masárová Z, Parada I, Perz D, Pilz A, Tkadlec J, Vogtenhuber B. 2021. On compatible matchings. 15th International Conference on Algorithms and Computation. WALCOM: Algorithms and Computation, LNCS, vol. 12635, 221–233."},"user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"grant_number":"Z00342","name":"The Wittgenstein Prize","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"_id":"2581B60A-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Quantitative Graph Games: Theory and Applications","grant_number":"279307"},{"name":"Modern Graph Algorithmic Techniques in Formal Verification","grant_number":"P 23499-N23","call_identifier":"FWF","_id":"2584A770-B435-11E9-9278-68D0E5697425"},{"name":"Game Theory","grant_number":"S11407","call_identifier":"FWF","_id":"25863FF4-B435-11E9-9278-68D0E5697425"}],"page":"221-233","doi":"10.1007/978-3-030-68211-8_18","date_published":"2021-02-16T00:00:00Z","date_created":"2021-03-28T22:01:41Z","year":"2021","day":"16","publication":"15th International Conference on Algorithms and Computation","quality_controlled":"1","publisher":"Springer Nature","oa":1,"acknowledgement":"A.A. funded by the Marie Skłodowska-Curie grant agreement No. 754411. Z.M. partially funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31. I.P., D.P., and B.V. partially supported by FWF within the collaborative DACH project Arrangements and Drawings as FWF project I 3340-N35. A.P. supported by a Schrödinger fellowship of the FWF: J-3847-N35. J.T. partially supported by ERC Start grant no. (279307: Graph Games), FWF grant no. P23499-N23 and S11407-N23 (RiSE)."},{"_id":"9465","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","ddc":["510"],"date_updated":"2022-05-12T11:41:45Z","department":[{"_id":"HeEd"}],"file_date_updated":"2021-06-11T13:16:26Z","oa_version":"Published Version","abstract":[{"text":"Given a locally finite set 𝑋⊆ℝ𝑑 and an integer 𝑘≥0, we consider the function 𝐰𝑘:Del𝑘(𝑋)→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.","lang":"eng"}],"intvolume":" 112","month":"04","scopus_import":"1","language":[{"iso":"eng"}],"file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"9544","checksum":"e52a832f1def52a2b23d21bcc09e646f","success":1,"creator":"kschuh","date_updated":"2021-06-11T13:16:26Z","file_size":694706,"date_created":"2021-06-11T13:16:26Z","file_name":"2021_Geometry_Edelsbrunner.pdf"}],"publication_status":"published","publication_identifier":{"eissn":["14208997"],"issn":["00472468"]},"issue":"1","volume":112,"article_number":"15","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Edelsbrunner H, Nikitenko A, Osang GF. 2021. A step in the Delaunay mosaic of order k. Journal of Geometry. 112(1), 15.","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.","short":"H. Edelsbrunner, A. Nikitenko, G.F. Osang, Journal of Geometry 112 (2021).","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","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","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."},"title":"A step in the Delaunay mosaic of order k","article_processing_charge":"Yes (via OA deal)","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"first_name":"Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","full_name":"Nikitenko, Anton","last_name":"Nikitenko"},{"first_name":"Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","full_name":"Osang, Georg F","last_name":"Osang"}],"oa":1,"quality_controlled":"1","publisher":"Springer Nature","publication":"Journal of Geometry","day":"01","year":"2021","has_accepted_license":"1","date_created":"2021-06-06T22:01:29Z","date_published":"2021-04-01T00:00:00Z","doi":"10.1007/s00022-021-00577-4"},{"day":"02","publication":"37th International Symposium on Computational Geometry (SoCG 2021)","has_accepted_license":"1","year":"2021","doi":"10.4230/LIPIcs.SoCG.2021.32","date_published":"2021-06-02T00:00:00Z","date_created":"2021-04-22T08:09:58Z","page":"32:1-32:16","acknowledgement":"The authors thank Janos Pach for insightful discussions on the topic of thispaper, Morteza Saghafian for finding the one-dimensional counterexample mentioned in Section 5,and Larry Andrews for generously sharing his crystallographic perspective.","quality_controlled":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","oa":1,"user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","citation":{"ama":"Edelsbrunner H, Heiss T, Kurlin V, Smith P, Wintraecken M. The density fingerprint of a periodic point set. In: 37th International Symposium on Computational Geometry (SoCG 2021). Vol 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021:32:1-32:16. doi:10.4230/LIPIcs.SoCG.2021.32","apa":"Edelsbrunner, H., Heiss, T., Kurlin , V., Smith, P., & Wintraecken, M. (2021). The density fingerprint of a periodic point set. In 37th International Symposium on Computational Geometry (SoCG 2021) (Vol. 189, p. 32:1-32:16). Virtual: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.32","ieee":"H. Edelsbrunner, T. Heiss, V. Kurlin , P. Smith, and M. Wintraecken, “The density fingerprint of a periodic point set,” in 37th International Symposium on Computational Geometry (SoCG 2021), Virtual, 2021, vol. 189, p. 32:1-32:16.","short":"H. Edelsbrunner, T. Heiss, V. Kurlin , P. Smith, M. Wintraecken, in:, 37th International Symposium on Computational Geometry (SoCG 2021), Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, p. 32:1-32:16.","mla":"Edelsbrunner, Herbert, et al. “The Density Fingerprint of a Periodic Point Set.” 37th International Symposium on Computational Geometry (SoCG 2021), vol. 189, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, p. 32:1-32:16, doi:10.4230/LIPIcs.SoCG.2021.32.","ista":"Edelsbrunner H, Heiss T, Kurlin V, Smith P, Wintraecken M. 2021. The density fingerprint of a periodic point set. 37th International Symposium on Computational Geometry (SoCG 2021). SoCG: Symposium on Computational Geometry, LIPIcs, vol. 189, 32:1-32:16.","chicago":"Edelsbrunner, Herbert, Teresa Heiss, Vitaliy Kurlin , Philip Smith, and Mathijs Wintraecken. “The Density Fingerprint of a Periodic Point Set.” In 37th International Symposium on Computational Geometry (SoCG 2021), 189:32:1-32:16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.32."},"title":"The density fingerprint of a periodic point set","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"first_name":"Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","last_name":"Heiss","full_name":"Heiss, Teresa","orcid":"0000-0002-1780-2689"},{"last_name":" Kurlin ","full_name":" Kurlin , Vitaliy","first_name":"Vitaliy"},{"first_name":"Philip","full_name":"Smith, Philip","last_name":"Smith"},{"orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","last_name":"Wintraecken","first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"name":"Discretization in Geometry and Dynamics","grant_number":"I4887","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316"},{"grant_number":"Z00312","name":"The Wittgenstein Prize","_id":"25C5A090-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"file_id":"9346","checksum":"1787baef1523d6d93753b90d0c109a6d","file_size":3117435,"date_updated":"2021-04-22T08:08:14Z","creator":"mwintrae","file_name":"df_socg_final_version.pdf","date_created":"2021-04-22T08:08:14Z"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1868-8969"]},"publication_status":"published","volume":189,"ec_funded":1,"oa_version":"Published Version","abstract":[{"lang":"eng","text":"Modeling a crystal as a periodic point set, we present a fingerprint consisting of density functionsthat facilitates the efficient search for new materials and material properties. We prove invarianceunder isometries, continuity, and completeness in the generic case, which are necessary featuresfor the reliable comparison of crystals. The proof of continuity integrates methods from discretegeometry and lattice theory, while the proof of generic completeness combines techniques fromgeometry with analysis. The fingerprint has a fast algorithm based on Brillouin zones and relatedinclusion-exclusion formulae. We have implemented the algorithm and describe its application tocrystal structure prediction."}],"month":"06","intvolume":" 189","alternative_title":["LIPIcs"],"ddc":["004","516"],"date_updated":"2023-02-23T13:55:40Z","department":[{"_id":"HeEd"}],"file_date_updated":"2021-04-22T08:08:14Z","_id":"9345","status":"public","type":"conference","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"conference":{"name":"SoCG: Symposium on Computational Geometry","location":"Virtual","end_date":"2021-06-11","start_date":"2021-06-07"}},{"article_number":"16","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"The Wittgenstein Prize","grant_number":"Z00342"},{"grant_number":"I4887","name":"Discretization in Geometry and Dynamics","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316"}],"citation":{"mla":"Biswas, Ranita, et al. “Counting Cells of Order-k Voronoi Tessellations in ℝ3 with Morse Theory.” Leibniz International Proceedings in Informatics, vol. 189, 16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, doi:10.4230/LIPIcs.SoCG.2021.16.","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian, M. (2021). Counting cells of order-k voronoi tessellations in ℝ3 with morse theory. In Leibniz International Proceedings in Informatics (Vol. 189). Online: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2021.16","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Counting cells of order-k voronoi tessellations in ℝ3 with morse theory. In: Leibniz International Proceedings in Informatics. Vol 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021. doi:10.4230/LIPIcs.SoCG.2021.16","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Counting cells of order-k voronoi tessellations in ℝ3 with morse theory,” in Leibniz International Proceedings in Informatics, Online, 2021, vol. 189.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, in:, Leibniz International Proceedings in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021.","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Counting Cells of Order-k Voronoi Tessellations in ℝ3 with Morse Theory.” In Leibniz International Proceedings in Informatics, Vol. 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.SoCG.2021.16.","ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2021. Counting cells of order-k voronoi tessellations in ℝ3 with morse theory. Leibniz International Proceedings in Informatics. SoCG: International Symposium on Computational Geometry, LIPIcs, vol. 189, 16."},"user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","article_processing_charge":"No","author":[{"id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita","orcid":"0000-0002-5372-7890","full_name":"Biswas, Ranita","last_name":"Biswas"},{"first_name":"Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","last_name":"Cultrera di Montesano","orcid":"0000-0001-6249-0832","full_name":"Cultrera di Montesano, Sebastiano"},{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"full_name":"Saghafian, Morteza","last_name":"Saghafian","first_name":"Morteza"}],"title":"Counting cells of order-k voronoi tessellations in ℝ3 with morse theory","oa":1,"quality_controlled":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","year":"2021","has_accepted_license":"1","publication":"Leibniz International Proceedings in Informatics","day":"02","date_created":"2021-06-27T22:01:48Z","date_published":"2021-06-02T00:00:00Z","doi":"10.4230/LIPIcs.SoCG.2021.16","_id":"9604","conference":{"start_date":"2021-06-07","end_date":"2021-06-11","location":"Online","name":"SoCG: International Symposium on Computational Geometry"},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"conference","status":"public","date_updated":"2023-02-23T14:02:28Z","ddc":["516"],"file_date_updated":"2021-06-28T13:11:39Z","department":[{"_id":"HeEd"}],"abstract":[{"text":"Generalizing Lee’s inductive argument for counting the cells of higher order Voronoi tessellations in ℝ² to ℝ³, we get precise relations in terms of Morse theoretic quantities for piecewise constant functions on planar arrangements. Specifically, we prove that for a generic set of n ≥ 5 points in ℝ³, the number of regions in the order-k Voronoi tessellation is N_{k-1} - binom(k,2)n + n, for 1 ≤ k ≤ n-1, in which N_{k-1} is the sum of Euler characteristics of these function’s first k-1 sublevel sets. We get similar expressions for the vertices, edges, and polygons of the order-k Voronoi tessellation.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","alternative_title":["LIPIcs"],"intvolume":" 189","month":"06","publication_status":"published","publication_identifier":{"isbn":["9783959771849"],"issn":["18688969"]},"language":[{"iso":"eng"}],"file":[{"creator":"asandaue","date_updated":"2021-06-28T13:11:39Z","file_size":727817,"date_created":"2021-06-28T13:11:39Z","file_name":"2021_LIPIcs_Biswas.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"22b11a719018b22ecba2471b51f2eb40","file_id":"9611","success":1}],"ec_funded":1,"volume":189},{"year":"2021","day":"16","publication":"Discrete Geometry and Mathematical Morphology","page":"152-163","doi":"10.1007/978-3-030-76657-3_10","date_published":"2021-05-16T00:00:00Z","date_created":"2021-08-08T22:01:29Z","acknowledgement":"This work has been partially supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia through the project no. 451-03-68/2020-14/200156: “Innovative scientific and artistic research from the FTS (activity) domain” (LČ), the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant no. 788183 (RB), and the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35 (RB).","quality_controlled":"1","publisher":"Springer Nature","citation":{"mla":"Čomić, Lidija, et al. “Body Centered Cubic Grid - Coordinate System and Discrete Analytical Plane Definition.” Discrete Geometry and Mathematical Morphology, vol. 12708, Springer Nature, 2021, pp. 152–63, doi:10.1007/978-3-030-76657-3_10.","ama":"Čomić L, Zrour R, Largeteau-Skapin G, Biswas R, Andres E. Body centered cubic grid - coordinate system and discrete analytical plane definition. In: Discrete Geometry and Mathematical Morphology. Vol 12708. Springer Nature; 2021:152-163. doi:10.1007/978-3-030-76657-3_10","apa":"Čomić, L., Zrour, R., Largeteau-Skapin, G., Biswas, R., & Andres, E. (2021). Body centered cubic grid - coordinate system and discrete analytical plane definition. In Discrete Geometry and Mathematical Morphology (Vol. 12708, pp. 152–163). Uppsala, Sweden: Springer Nature. https://doi.org/10.1007/978-3-030-76657-3_10","short":"L. Čomić, R. Zrour, G. Largeteau-Skapin, R. Biswas, E. Andres, in:, Discrete Geometry and Mathematical Morphology, Springer Nature, 2021, pp. 152–163.","ieee":"L. Čomić, R. Zrour, G. Largeteau-Skapin, R. Biswas, and E. Andres, “Body centered cubic grid - coordinate system and discrete analytical plane definition,” in Discrete Geometry and Mathematical Morphology, Uppsala, Sweden, 2021, vol. 12708, pp. 152–163.","chicago":"Čomić, Lidija, Rita Zrour, Gaëlle Largeteau-Skapin, Ranita Biswas, and Eric Andres. “Body Centered Cubic Grid - Coordinate System and Discrete Analytical Plane Definition.” In Discrete Geometry and Mathematical Morphology, 12708:152–63. Springer Nature, 2021. https://doi.org/10.1007/978-3-030-76657-3_10.","ista":"Čomić L, Zrour R, Largeteau-Skapin G, Biswas R, Andres E. 2021. Body centered cubic grid - coordinate system and discrete analytical plane definition. Discrete Geometry and Mathematical Morphology. DGMM: International Conference on Discrete Geometry and Mathematical Morphology, LNCS, vol. 12708, 152–163."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Lidija","last_name":"Čomić","full_name":"Čomić, Lidija"},{"last_name":"Zrour","full_name":"Zrour, Rita","first_name":"Rita"},{"full_name":"Largeteau-Skapin, Gaëlle","last_name":"Largeteau-Skapin","first_name":"Gaëlle"},{"id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita","orcid":"0000-0002-5372-7890","full_name":"Biswas, Ranita","last_name":"Biswas"},{"last_name":"Andres","full_name":"Andres, Eric","first_name":"Eric"}],"article_processing_charge":"No","title":"Body centered cubic grid - coordinate system and discrete analytical plane definition","project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"}],"publication_identifier":{"issn":["03029743"],"isbn":["9783030766566"],"eissn":["16113349"]},"publication_status":"published","language":[{"iso":"eng"}],"volume":12708,"ec_funded":1,"abstract":[{"lang":"eng","text":"We define a new compact coordinate system in which each integer triplet addresses a voxel in the BCC grid, and we investigate some of its properties. We propose a characterization of 3D discrete analytical planes with their topological features (in the Cartesian and in the new coordinate system) such as the interrelation between the thickness of the plane and the separability constraint we aim to obtain."}],"oa_version":"None","scopus_import":"1","alternative_title":["LNCS"],"month":"05","intvolume":" 12708","date_updated":"2022-05-31T06:58:21Z","department":[{"_id":"HeEd"}],"_id":"9824","type":"conference","conference":{"name":"DGMM: International Conference on Discrete Geometry and Mathematical Morphology","start_date":"2021-05-24","end_date":"2021-05-27","location":"Uppsala, Sweden"},"status":"public"},{"quality_controlled":"1","publisher":"Elsevier","oa":1,"acknowledgement":"This research was performed in part at the 33rd Bellairs Winter Workshop on Computational Geometry. We thank all other participants for a fruitful atmosphere. H. Akitaya was supported by NSF CCF-1422311 & 1423615. Z. Masárová was partially funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31.","date_published":"2021-02-01T00:00:00Z","doi":"10.1016/j.comgeo.2020.101700","date_created":"2020-08-30T22:01:09Z","day":"01","publication":"Computational Geometry: Theory and Applications","isi":1,"year":"2021","project":[{"name":"The Wittgenstein Prize","grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"}],"article_number":"101700","title":"Folding polyominoes with holes into a cube","author":[{"first_name":"Oswin","full_name":"Aichholzer, Oswin","last_name":"Aichholzer"},{"first_name":"Hugo A.","full_name":"Akitaya, Hugo A.","last_name":"Akitaya"},{"first_name":"Kenneth C.","full_name":"Cheung, Kenneth C.","last_name":"Cheung"},{"first_name":"Erik D.","last_name":"Demaine","full_name":"Demaine, Erik D."},{"last_name":"Demaine","full_name":"Demaine, Martin L.","first_name":"Martin L."},{"last_name":"Fekete","full_name":"Fekete, Sándor P.","first_name":"Sándor P."},{"first_name":"Linda","last_name":"Kleist","full_name":"Kleist, Linda"},{"full_name":"Kostitsyna, Irina","last_name":"Kostitsyna","first_name":"Irina"},{"first_name":"Maarten","last_name":"Löffler","full_name":"Löffler, Maarten"},{"first_name":"Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","last_name":"Masárová","full_name":"Masárová, Zuzana","orcid":"0000-0002-6660-1322"},{"first_name":"Klara","full_name":"Mundilova, Klara","last_name":"Mundilova"},{"first_name":"Christiane","last_name":"Schmidt","full_name":"Schmidt, Christiane"}],"article_processing_charge":"No","external_id":{"isi":["000579185100004"],"arxiv":["1910.09917"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"mla":"Aichholzer, Oswin, et al. “Folding Polyominoes with Holes into a Cube.” Computational Geometry: Theory and Applications, vol. 93, 101700, Elsevier, 2021, doi:10.1016/j.comgeo.2020.101700.","short":"O. Aichholzer, H.A. Akitaya, K.C. Cheung, E.D. Demaine, M.L. Demaine, S.P. Fekete, L. Kleist, I. Kostitsyna, M. Löffler, Z. Masárová, K. Mundilova, C. Schmidt, Computational Geometry: Theory and Applications 93 (2021).","ieee":"O. Aichholzer et al., “Folding polyominoes with holes into a cube,” Computational Geometry: Theory and Applications, vol. 93. Elsevier, 2021.","apa":"Aichholzer, O., Akitaya, H. A., Cheung, K. C., Demaine, E. D., Demaine, M. L., Fekete, S. P., … Schmidt, C. (2021). Folding polyominoes with holes into a cube. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2020.101700","ama":"Aichholzer O, Akitaya HA, Cheung KC, et al. Folding polyominoes with holes into a cube. Computational Geometry: Theory and Applications. 2021;93. doi:10.1016/j.comgeo.2020.101700","chicago":"Aichholzer, Oswin, Hugo A. Akitaya, Kenneth C. Cheung, Erik D. Demaine, Martin L. Demaine, Sándor P. Fekete, Linda Kleist, et al. “Folding Polyominoes with Holes into a Cube.” Computational Geometry: Theory and Applications. Elsevier, 2021. https://doi.org/10.1016/j.comgeo.2020.101700.","ista":"Aichholzer O, Akitaya HA, Cheung KC, Demaine ED, Demaine ML, Fekete SP, Kleist L, Kostitsyna I, Löffler M, Masárová Z, Mundilova K, Schmidt C. 2021. Folding polyominoes with holes into a cube. Computational Geometry: Theory and Applications. 93, 101700."},"month":"02","intvolume":" 93","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1910.09917v3","open_access":"1"}],"oa_version":"Preprint","abstract":[{"text":"When can a polyomino piece of paper be folded into a unit cube? Prior work studied tree-like polyominoes, but polyominoes with holes remain an intriguing open problem. We present sufficient conditions for a polyomino with one or several holes to fold into a cube, and conditions under which cube folding is impossible. In particular, we show that all but five special “basic” holes guarantee foldability.","lang":"eng"}],"volume":93,"related_material":{"record":[{"id":"6989","status":"public","relation":"shorter_version"}]},"language":[{"iso":"eng"}],"publication_identifier":{"issn":["09257721"]},"publication_status":"published","status":"public","article_type":"original","type":"journal_article","_id":"8317","department":[{"_id":"HeEd"}],"date_updated":"2023-08-04T10:57:42Z"},{"type":"journal_article","article_type":"original","status":"public","keyword":["Applied Mathematics","General Mathematics"],"_id":"8773","department":[{"_id":"HeEd"}],"date_updated":"2023-08-04T11:11:47Z","main_file_link":[{"url":"https://arxiv.org/abs/1910.08286","open_access":"1"}],"month":"01","intvolume":" 149","abstract":[{"text":"Let g be a complex semisimple Lie algebra. We give a classification of contravariant forms on the nondegenerate Whittaker g-modules Y(χ,η) introduced by Kostant. We prove that the set of all contravariant forms on Y(χ,η) forms a vector space whose dimension is given by the cardinality of the Weyl group of g. We also describe a procedure for parabolically inducing contravariant forms. As a corollary, we deduce the existence of the Shapovalov form on a Verma module, and provide a formula for the dimension of the space of contravariant forms on the degenerate Whittaker modules M(χ,η) introduced by McDowell.","lang":"eng"}],"oa_version":"Preprint","issue":"1","volume":149,"ec_funded":1,"publication_identifier":{"issn":["0002-9939"],"eissn":["1088-6826"]},"publication_status":"published","language":[{"iso":"eng"}],"project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"author":[{"full_name":"Brown, Adam","last_name":"Brown","first_name":"Adam","id":"70B7FDF6-608D-11E9-9333-8535E6697425"},{"last_name":"Romanov","full_name":"Romanov, Anna","first_name":"Anna"}],"article_processing_charge":"No","external_id":{"isi":["000600416300004"],"arxiv":["1910.08286"]},"title":"Contravariant forms on Whittaker modules","citation":{"ista":"Brown A, Romanov A. 2021. Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. 149(1), 37–52.","chicago":"Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.” Proceedings of the American Mathematical Society. American Mathematical Society, 2021. https://doi.org/10.1090/proc/15205.","short":"A. Brown, A. Romanov, Proceedings of the American Mathematical Society 149 (2021) 37–52.","ieee":"A. Brown and A. Romanov, “Contravariant forms on Whittaker modules,” Proceedings of the American Mathematical Society, vol. 149, no. 1. American Mathematical Society, pp. 37–52, 2021.","apa":"Brown, A., & Romanov, A. (2021). Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/15205","ama":"Brown A, Romanov A. Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. 2021;149(1):37-52. doi:10.1090/proc/15205","mla":"Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.” Proceedings of the American Mathematical Society, vol. 149, no. 1, American Mathematical Society, 2021, pp. 37–52, doi:10.1090/proc/15205."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"American Mathematical Society","quality_controlled":"1","oa":1,"acknowledgement":"We would like to thank Peter Trapa for useful discussions, and Dragan Milicic and Arun Ram for valuable feedback on the structure of the paper. The first author acknowledges the support of the European Unions Horizon 2020 research and innovation programme under the Marie Skodowska-Curie Grant Agreement No. 754411. The second author is\r\nsupported by the National Science Foundation Award No. 1803059.","page":"37-52","date_published":"2021-01-01T00:00:00Z","doi":"10.1090/proc/15205","date_created":"2020-11-19T10:17:40Z","isi":1,"year":"2021","day":"01","publication":"Proceedings of the American Mathematical Society"},{"publication_identifier":{"isbn":["9781728162515"]},"publication_status":"published","language":[{"iso":"eng"}],"scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/2008.10064","open_access":"1"}],"month":"03","abstract":[{"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.","lang":"eng"}],"oa_version":"Preprint","department":[{"_id":"HeEd"}],"date_updated":"2023-08-07T14:00:13Z","type":"conference","conference":{"end_date":"2020-12-13","location":"Atlanta, GA, United States","start_date":"2020-12-10","name":"Big Data: International Conference on Big Data"},"status":"public","_id":"9253","page":"3123-3132","doi":"10.1109/bigdata50022.2020.9378374","date_published":"2021-03-19T00:00:00Z","date_created":"2021-03-21T11:34:07Z","isi":1,"year":"2021","day":"19","publication":"2020 IEEE International Conference on Big Data","publisher":"IEEE","quality_controlled":"1","oa":1,"author":[{"last_name":"Heiler","full_name":"Heiler, Georg","first_name":"Georg"},{"last_name":"Reisch","full_name":"Reisch, Tobias","first_name":"Tobias"},{"last_name":"Hurt","full_name":"Hurt, Jan","first_name":"Jan"},{"first_name":"Mohammad","last_name":"Forghani","full_name":"Forghani, Mohammad"},{"first_name":"Aida","last_name":"Omani","full_name":"Omani, Aida"},{"last_name":"Hanbury","full_name":"Hanbury, Allan","first_name":"Allan"},{"id":"2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425","first_name":"Farid","full_name":"Karimipour, Farid","orcid":"0000-0001-6746-4174","last_name":"Karimipour"}],"external_id":{"isi":["000662554703032"],"arxiv":["2008.10064"]},"article_processing_charge":"No","title":"Country-wide mobility changes observed using mobile phone data during COVID-19 pandemic","citation":{"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.","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.","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","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","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.","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.","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"},{"date_updated":"2023-08-07T14:35:44Z","ddc":["516"],"department":[{"_id":"HeEd"}],"file_date_updated":"2021-12-01T10:56:53Z","_id":"9317","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","status":"public","publication_status":"published","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"language":[{"iso":"eng"}],"file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"10394","checksum":"59b4e1e827e494209bcb4aae22e1d347","success":1,"creator":"cchlebak","date_updated":"2021-12-01T10:56:53Z","file_size":677704,"date_created":"2021-12-01T10:56:53Z","file_name":"2021_DisCompGeo_Edelsbrunner_Osang.pdf"}],"ec_funded":1,"volume":65,"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"187"}]},"abstract":[{"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.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 65","month":"03","citation":{"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","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","short":"H. Edelsbrunner, G.F. Osang, Discrete and Computational Geometry 65 (2021) 1296–1313.","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.","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.","ista":"Edelsbrunner H, Osang GF. 2021. The multi-cover persistence of Euclidean balls. Discrete and Computational Geometry. 65, 1296–1313.","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","external_id":{"isi":["000635460400001"]},"article_processing_charge":"Yes (via OA deal)","author":[{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"last_name":"Osang","full_name":"Osang, Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","first_name":"Georg F"}],"title":"The multi-cover persistence of Euclidean balls","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183","name":"Alpha Shape Theory Extended"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"year":"2021","isi":1,"has_accepted_license":"1","publication":"Discrete and Computational Geometry","day":"31","page":"1296–1313","date_created":"2021-04-11T22:01:15Z","date_published":"2021-03-31T00:00:00Z","doi":"10.1007/s00454-021-00281-9","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).","oa":1,"publisher":"Springer Nature","quality_controlled":"1"},{"publication":"Journal of Combinatorial Theory. Series B","day":"09","year":"2021","has_accepted_license":"1","isi":1,"date_created":"2021-06-27T22:01:47Z","date_published":"2021-06-09T00:00:00Z","doi":"10.1016/j.jctb.2021.05.004","page":"21-37","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.","oa":1,"publisher":"Elsevier","quality_controlled":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Pach J, Tomon I. 2021. Erdős-Hajnal-type results for monotone paths. Journal of Combinatorial Theory. Series B. 151, 21–37.","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.","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","short":"J. Pach, I. Tomon, Journal of Combinatorial Theory. Series B 151 (2021) 21–37.","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.","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."},"title":"Erdős-Hajnal-type results for monotone paths","external_id":{"isi":["000702280800002"]},"article_processing_charge":"No","author":[{"first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4","last_name":"Pach","full_name":"Pach, János"},{"full_name":"Tomon, István","last_name":"Tomon","first_name":"István"}],"project":[{"_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"The Wittgenstein Prize","grant_number":"Z00342"}],"language":[{"iso":"eng"}],"file":[{"creator":"asandaue","date_updated":"2021-06-28T13:33:23Z","file_size":418168,"date_created":"2021-06-28T13:33:23Z","file_name":"2021_JournalOfCombinatorialTheory_Pach.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"15fbc9064cd9d1c777ac0043b78c8f12","file_id":"9612","success":1}],"publication_status":"published","publication_identifier":{"issn":["0095-8956"]},"volume":151,"oa_version":"Published Version","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."}],"intvolume":" 151","month":"06","scopus_import":"1","ddc":["510"],"date_updated":"2023-08-10T13:38:00Z","department":[{"_id":"HeEd"}],"file_date_updated":"2021-06-28T13:33:23Z","_id":"9602","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original"},{"year":"2021","isi":1,"has_accepted_license":"1","publication":"PLoS ONE","day":"01","date_created":"2021-08-08T22:01:28Z","doi":"10.1371/journal.pone.0253851","date_published":"2021-07-01T00:00:00Z","acknowledgement":"We express our gratitude to the anonymous referees who provided constructive comments that helped us improve the quality of the paper.","oa":1,"publisher":"Public Library of Science","quality_controlled":"1","citation":{"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","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","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.","short":"G. Graff, B. Graff, P. Pilarczyk, G. Jablonski, D. Gąsecki, K. Narkiewicz, PLoS ONE 16 (2021).","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.","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.","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","external_id":{"isi":["000678124900050"],"pmid":["34292957"]},"article_processing_charge":"Yes","author":[{"first_name":"Grzegorz","full_name":"Graff, Grzegorz","last_name":"Graff"},{"full_name":"Graff, Beata","last_name":"Graff","first_name":"Beata"},{"last_name":"Pilarczyk","full_name":"Pilarczyk, Pawel","id":"3768D56A-F248-11E8-B48F-1D18A9856A87","first_name":"Pawel"},{"id":"4483EF78-F248-11E8-B48F-1D18A9856A87","first_name":"Grzegorz","orcid":"0000-0002-3536-9866","full_name":"Jablonski, Grzegorz","last_name":"Jablonski"},{"last_name":"Gąsecki","full_name":"Gąsecki, Dariusz","first_name":"Dariusz"},{"last_name":"Narkiewicz","full_name":"Narkiewicz, Krzysztof","first_name":"Krzysztof"}],"title":"Persistent homology as a new method of the assessment of heart rate variability","article_number":"e0253851","publication_status":"published","publication_identifier":{"eissn":["19326203"]},"language":[{"iso":"eng"}],"file":[{"file_name":"2021_PLoSONE_Graff.pdf","date_created":"2021-08-09T09:25:41Z","file_size":2706919,"date_updated":"2021-08-09T09:25:41Z","creator":"asandaue","success":1,"checksum":"0277aa155d5db1febd2cb384768bba5f","file_id":"9832","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"issue":"7","volume":16,"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."}],"pmid":1,"oa_version":"Published Version","scopus_import":"1","intvolume":" 16","month":"07","date_updated":"2023-08-10T14:21:42Z","ddc":["006"],"file_date_updated":"2021-08-09T09:25:41Z","department":[{"_id":"HeEd"}],"_id":"9821","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","status":"public"},{"_id":"10222","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","date_updated":"2023-08-14T11:57:07Z","ddc":["510"],"file_date_updated":"2023-08-14T11:55:10Z","department":[{"_id":"HeEd"}],"abstract":[{"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.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","month":"10","publication_identifier":{"issn":["1058-6458"],"eissn":["1944-950X"]},"publication_status":"published","file":[{"creator":"dernst","file_size":1966019,"date_updated":"2023-08-14T11:55:10Z","file_name":"2023_ExperimentalMath_Akopyan.pdf","date_created":"2023-08-14T11:55:10Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"file_id":"14053","checksum":"3514382e3a1eb87fa6c61ad622874415"}],"language":[{"iso":"eng"}],"ec_funded":1,"project":[{"name":"Alpha Shape Theory Extended","grant_number":"788183","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"grant_number":"Z00342","name":"The Wittgenstein Prize","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"grant_number":"I4887","name":"Discretization in Geometry and Dynamics","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316"},{"call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"}],"citation":{"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.","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.","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","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","short":"A. Akopyan, H. Edelsbrunner, A. Nikitenko, Experimental Mathematics (2021) 1–15.","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"first_name":"Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","last_name":"Nikitenko","full_name":"Nikitenko, Anton","orcid":"0000-0002-0659-3201"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000710893500001"],"arxiv":["2007.07783"]},"title":"The beauty of random polytopes inscribed in the 2-sphere","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.","publisher":"Taylor and Francis","quality_controlled":"1","oa":1,"isi":1,"has_accepted_license":"1","year":"2021","day":"25","publication":"Experimental Mathematics","page":"1-15","date_published":"2021-10-25T00:00:00Z","doi":"10.1080/10586458.2021.1980459","date_created":"2021-11-07T23:01:25Z"},{"intvolume":" 66","month":"07","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We quantise Whitney’s construction to prove the existence of a triangulation for any C^2 manifold, so that we get an algorithm with explicit bounds. We also give a new elementary proof, which is completely geometric."}],"ec_funded":1,"issue":"1","volume":66,"language":[{"iso":"eng"}],"file":[{"date_updated":"2021-08-06T09:52:29Z","file_size":983307,"creator":"kschuh","date_created":"2021-08-06T09:52:29Z","file_name":"2021_DescreteCompGeopmetry_Boissonnat.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_id":"9795","checksum":"c848986091e56699dc12de85adb1e39c","success":1}],"publication_status":"published","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"keyword":["Theoretical Computer Science","Computational Theory and Mathematics","Geometry and Topology","Discrete Mathematics and Combinatorics"],"status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","_id":"8940","department":[{"_id":"HeEd"}],"file_date_updated":"2021-08-06T09:52:29Z","ddc":["516"],"date_updated":"2023-09-05T15:02:40Z","oa":1,"publisher":"Springer Nature","quality_controlled":"1","acknowledgement":"This work has been funded by the European Research Council under the European Union’s ERC Grant Agreement Number 339025 GUDHI (Algorithmic Foundations of Geometric Understanding in Higher Dimensions). The third author also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. Open access funding provided by the Institute of Science and Technology (IST Austria).","date_created":"2020-12-12T11:07:02Z","date_published":"2021-07-01T00:00:00Z","doi":"10.1007/s00454-020-00250-8","page":"386-434","publication":"Discrete & Computational Geometry","day":"01","year":"2021","has_accepted_license":"1","isi":1,"project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"title":"Triangulating submanifolds: An elementary and quantified version of Whitney’s method","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000597770300001"]},"author":[{"first_name":"Jean-Daniel","last_name":"Boissonnat","full_name":"Boissonnat, Jean-Daniel"},{"first_name":"Siargey","full_name":"Kachanovich, Siargey","last_name":"Kachanovich"},{"id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs","last_name":"Wintraecken","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"mla":"Boissonnat, Jean-Daniel, et al. “Triangulating Submanifolds: An Elementary and Quantified Version of Whitney’s Method.” Discrete & Computational Geometry, vol. 66, no. 1, Springer Nature, 2021, pp. 386–434, doi:10.1007/s00454-020-00250-8.","ieee":"J.-D. Boissonnat, S. Kachanovich, and M. Wintraecken, “Triangulating submanifolds: An elementary and quantified version of Whitney’s method,” Discrete & Computational Geometry, vol. 66, no. 1. Springer Nature, pp. 386–434, 2021.","short":"J.-D. Boissonnat, S. Kachanovich, M. Wintraecken, Discrete & Computational Geometry 66 (2021) 386–434.","ama":"Boissonnat J-D, Kachanovich S, Wintraecken M. Triangulating submanifolds: An elementary and quantified version of Whitney’s method. Discrete & Computational Geometry. 2021;66(1):386-434. doi:10.1007/s00454-020-00250-8","apa":"Boissonnat, J.-D., Kachanovich, S., & Wintraecken, M. (2021). Triangulating submanifolds: An elementary and quantified version of Whitney’s method. Discrete & Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00250-8","chicago":"Boissonnat, Jean-Daniel, Siargey Kachanovich, and Mathijs Wintraecken. “Triangulating Submanifolds: An Elementary and Quantified Version of Whitney’s Method.” Discrete & Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-020-00250-8.","ista":"Boissonnat J-D, Kachanovich S, Wintraecken M. 2021. Triangulating submanifolds: An elementary and quantified version of Whitney’s method. Discrete & Computational Geometry. 66(1), 386–434."}},{"title":"Probabilistic convergence and stability of random mapper graphs","article_processing_charge":"Yes (via OA deal)","external_id":{"arxiv":["1909.03488"]},"author":[{"full_name":"Brown, Adam","last_name":"Brown","first_name":"Adam","id":"70B7FDF6-608D-11E9-9333-8535E6697425"},{"first_name":"Omer","full_name":"Bobrowski, Omer","last_name":"Bobrowski"},{"first_name":"Elizabeth","full_name":"Munch, Elizabeth","last_name":"Munch"},{"full_name":"Wang, Bei","last_name":"Wang","first_name":"Bei"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"mla":"Brown, Adam, et al. “Probabilistic Convergence and Stability of Random Mapper Graphs.” Journal of Applied and Computational Topology, vol. 5, no. 1, Springer Nature, 2021, pp. 99–140, doi:10.1007/s41468-020-00063-x.","apa":"Brown, A., Bobrowski, O., Munch, E., & Wang, B. (2021). Probabilistic convergence and stability of random mapper graphs. Journal of Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-020-00063-x","ama":"Brown A, Bobrowski O, Munch E, Wang B. Probabilistic convergence and stability of random mapper graphs. Journal of Applied and Computational Topology. 2021;5(1):99-140. doi:10.1007/s41468-020-00063-x","short":"A. Brown, O. Bobrowski, E. Munch, B. Wang, Journal of Applied and Computational Topology 5 (2021) 99–140.","ieee":"A. Brown, O. Bobrowski, E. Munch, and B. Wang, “Probabilistic convergence and stability of random mapper graphs,” Journal of Applied and Computational Topology, vol. 5, no. 1. Springer Nature, pp. 99–140, 2021.","chicago":"Brown, Adam, Omer Bobrowski, Elizabeth Munch, and Bei Wang. “Probabilistic Convergence and Stability of Random Mapper Graphs.” Journal of Applied and Computational Topology. Springer Nature, 2021. https://doi.org/10.1007/s41468-020-00063-x.","ista":"Brown A, Bobrowski O, Munch E, Wang B. 2021. Probabilistic convergence and stability of random mapper graphs. Journal of Applied and Computational Topology. 5(1), 99–140."},"project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"date_created":"2021-02-11T14:41:02Z","date_published":"2021-03-01T00:00:00Z","doi":"10.1007/s41468-020-00063-x","page":"99-140","publication":"Journal of Applied and Computational Topology","day":"01","year":"2021","has_accepted_license":"1","oa":1,"quality_controlled":"1","publisher":"Springer Nature","acknowledgement":"AB was supported in part by the European Union’s Horizon 2020 research and innovation\r\nprogramme under the Marie Sklodowska-Curie GrantAgreement No. 754411 and NSF IIS-1513616. OB was supported in part by the Israel Science Foundation, Grant 1965/19. BW was supported in part by NSF IIS-1513616 and DBI-1661375. EM was supported in part by NSF CMMI-1800466, DMS-1800446, and CCF-1907591.We would like to thank the Institute for Mathematics and its Applications for hosting a workshop titled Bridging Statistics and Sheaves in May 2018, where this work was conceived.\r\nOpen Access funding provided by Institute of Science and Technology (IST Austria).","file_date_updated":"2021-02-11T14:43:59Z","department":[{"_id":"HeEd"}],"ddc":["510"],"date_updated":"2023-09-05T15:37:56Z","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","_id":"9111","ec_funded":1,"volume":5,"issue":"1","language":[{"iso":"eng"}],"file":[{"success":1,"checksum":"3f02e9d47c428484733da0f588a3c069","file_id":"9112","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_name":"2020_JourApplCompTopology_Brown.pdf","date_created":"2021-02-11T14:43:59Z","file_size":2090265,"date_updated":"2021-02-11T14:43:59Z","creator":"dernst"}],"publication_status":"published","publication_identifier":{"eissn":["2367-1734"],"issn":["2367-1726"]},"intvolume":" 5","month":"03","scopus_import":"1","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We study the probabilistic convergence between the mapper graph and the Reeb graph of a topological space X equipped with a continuous function f:X→R. We first give a categorification of the mapper graph and the Reeb graph by interpreting them in terms of cosheaves and stratified covers of the real line R. We then introduce a variant of the classic mapper graph of Singh et al. (in: Eurographics symposium on point-based graphics, 2007), referred to as the enhanced mapper graph, and demonstrate that such a construction approximates the Reeb graph of (X,f) when it is applied to points randomly sampled from a probability density function concentrated on (X,f). Our techniques are based on the interleaving distance of constructible cosheaves and topological estimation via kernel density estimates. Following Munch and Wang (In: 32nd international symposium on computational geometry, volume 51 of Leibniz international proceedings in informatics (LIPIcs), Dagstuhl, Germany, pp 53:1–53:16, 2016), we first show that the mapper graph of (X,f), a constructible R-space (with a fixed open cover), approximates the Reeb graph of the same space. We then construct an isomorphism between the mapper of (X,f) to the mapper of a super-level set of a probability density function concentrated on (X,f). Finally, building on the approach of Bobrowski et al. (Bernoulli 23(1):288–328, 2017b), we show that, with high probability, we can recover the mapper of the super-level set given a sufficiently large sample. Our work is the first to consider the mapper construction using the theory of cosheaves in a probabilistic setting. It is part of an ongoing effort to combine sheaf theory, probability, and statistics, to support topological data analysis with random data."}]},{"page":"134","date_published":"2021-02-01T00:00:00Z","doi":"10.15479/AT:ISTA:9056","date_created":"2021-02-02T14:11:06Z","has_accepted_license":"1","year":"2021","day":"01","publisher":"Institute of Science and Technology Austria","oa":1,"author":[{"full_name":"Osang, Georg F","orcid":"0000-0002-8882-5116","last_name":"Osang","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","first_name":"Georg F"}],"article_processing_charge":"No","title":"Multi-cover persistence and Delaunay mosaics","citation":{"mla":"Osang, Georg F. Multi-Cover Persistence and Delaunay Mosaics. Institute of Science and Technology Austria, 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","ama":"Osang GF. Multi-cover persistence and Delaunay mosaics. 2021. doi:10.15479/AT:ISTA:9056","ieee":"G. F. Osang, “Multi-cover persistence and Delaunay mosaics,” Institute of Science and Technology Austria, Klosterneuburg, 2021.","short":"G.F. Osang, Multi-Cover Persistence and Delaunay Mosaics, Institute of Science and Technology Austria, 2021.","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.","ista":"Osang GF. 2021. Multi-cover persistence and Delaunay mosaics. Klosterneuburg: Institute of Science and Technology Austria."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","related_material":{"record":[{"relation":"part_of_dissertation","id":"187","status":"public"},{"id":"8703","status":"public","relation":"part_of_dissertation"}]},"publication_identifier":{"issn":["2663-337X"]},"publication_status":"published","degree_awarded":"PhD","file":[{"file_size":13446994,"date_updated":"2021-02-03T10:37:28Z","creator":"patrickd","file_name":"thesis_source.zip","date_created":"2021-02-02T14:09:25Z","content_type":"application/zip","relation":"source_file","access_level":"closed","checksum":"bcf27986147cab0533b6abadd74e7629","file_id":"9063"},{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"file_id":"9064","checksum":"9cc8af266579a464385bbe2aff6af606","file_size":5210329,"date_updated":"2021-02-02T14:09:18Z","creator":"patrickd","file_name":"thesis_pdfA2b.pdf","date_created":"2021-02-02T14:09:18Z"}],"language":[{"iso":"eng"}],"alternative_title":["ISTA Thesis"],"month":"02","place":"Klosterneuburg","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."}],"oa_version":"Published Version","file_date_updated":"2021-02-03T10:37:28Z","department":[{"_id":"HeEd"},{"_id":"GradSch"}],"supervisor":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"}],"date_updated":"2023-09-07T13:29:01Z","ddc":["006","514","516"],"type":"dissertation","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","_id":"9056"},{"project":[{"name":"Alpha Shape Theory Extended","grant_number":"788183","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"grant_number":"Z00342","name":"The Wittgenstein Prize","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"}],"title":"Topological signatures and stability of hexagonal close packing and Barlow stackings","article_processing_charge":"No","external_id":{"pmid":["34569592"],"isi":["000700090000001"]},"author":[{"first_name":"Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","last_name":"Osang","orcid":"0000-0002-8882-5116","full_name":"Osang, Georg F"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"last_name":"Saadatfar","full_name":"Saadatfar, Mohammad","first_name":"Mohammad"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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.","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","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.","short":"G.F. Osang, H. Edelsbrunner, M. Saadatfar, Soft Matter 17 (2021) 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."},"oa":1,"publisher":"Royal Society of Chemistry ","quality_controlled":"1","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.","date_created":"2021-10-31T23:01:30Z","date_published":"2021-10-20T00:00:00Z","doi":"10.1039/d1sm00774b","page":"9107-9115","publication":"Soft Matter","day":"20","year":"2021","isi":1,"has_accepted_license":"1","status":"public","type":"journal_article","article_type":"original","_id":"10204","department":[{"_id":"HeEd"}],"file_date_updated":"2023-10-03T09:21:42Z","ddc":["540"],"date_updated":"2023-10-03T09:24:27Z","intvolume":" 17","month":"10","scopus_import":"1","oa_version":"Submitted Version","pmid":1,"abstract":[{"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.","lang":"eng"}],"ec_funded":1,"volume":17,"issue":"40","language":[{"iso":"eng"}],"file":[{"date_created":"2023-10-03T09:21:42Z","file_name":"2021_SoftMatter_acceptedversion_Osang.pdf","creator":"dernst","date_updated":"2023-10-03T09:21:42Z","file_size":4678788,"file_id":"14385","checksum":"b4da0c420530295e61b153960f6cb350","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"publication_status":"published","publication_identifier":{"eissn":["1744-6848"],"issn":["1744-683X"]}},{"doi":"10.4230/LIPIcs.SoCG.2021.27","date_published":"2021-06-02T00:00:00Z","date_created":"2021-06-27T22:01:49Z","day":"02","publication":"Leibniz International Proceedings in Informatics","has_accepted_license":"1","year":"2021","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","quality_controlled":"1","oa":1,"acknowledgement":"The authors want to thank the reviewers for many helpful comments and suggestions.","title":"Computing the multicover bifiltration","author":[{"first_name":"René","full_name":"Corbet, René","last_name":"Corbet"},{"full_name":"Kerber, Michael","last_name":"Kerber","first_name":"Michael"},{"first_name":"Michael","full_name":"Lesnick, Michael","last_name":"Lesnick"},{"first_name":"Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","last_name":"Osang","full_name":"Osang, Georg F","orcid":"0000-0002-8882-5116"}],"external_id":{"arxiv":["2103.07823"]},"article_processing_charge":"No","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","citation":{"short":"R. Corbet, M. Kerber, M. Lesnick, G.F. Osang, in:, Leibniz International Proceedings in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021.","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.","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","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.","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.","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."},"article_number":"27","related_material":{"record":[{"relation":"later_version","id":"12709","status":"public"}],"link":[{"relation":"extended_version","url":"https://arxiv.org/abs/2103.07823"}]},"volume":189,"file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"9610","checksum":"0de217501e7ba8b267d58deed0d51761","success":1,"creator":"cziletti","date_updated":"2021-06-28T12:40:47Z","file_size":"1367983","date_created":"2021-06-28T12:40:47Z","file_name":"2021_LIPIcs_Corbet.pdf"}],"language":[{"iso":"eng"}],"publication_identifier":{"isbn":["9783959771849"],"issn":["18688969"]},"publication_status":"published","month":"06","intvolume":" 189","alternative_title":["LIPIcs"],"scopus_import":"1","oa_version":"Published Version","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. "}],"file_date_updated":"2021-06-28T12:40:47Z","department":[{"_id":"HeEd"}],"ddc":["516"],"date_updated":"2023-10-04T12:03:39Z","status":"public","type":"conference","conference":{"start_date":"2021-06-07","end_date":"2021-06-11","location":"Online","name":"SoCG: International Symposium on Computational Geometry"},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"9605"}]