[{"doi":"10.1007/s00454-023-00484-2","language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["000948148000001"]},"oa":1,"project":[{"grant_number":"I04245","_id":"26AD5D90-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Algebraic Footprints of Geometric Features in Homology"}],"isi":1,"quality_controlled":"1","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"month":"07","author":[{"full_name":"Kourimska, Hana","orcid":"0000-0001-7841-0091","id":"D9B8E14C-3C26-11EA-98F5-1F833DDC885E","last_name":"Kourimska","first_name":"Hana"}],"volume":70,"date_created":"2023-03-26T22:01:09Z","date_updated":"2023-10-04T11:46:48Z","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.","year":"2023","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"publication_status":"published","file_date_updated":"2023-10-04T11:46:24Z","date_published":"2023-07-01T00:00:00Z","citation":{"ama":"Kourimska H. Discrete yamabe problem for polyhedral surfaces. Discrete and Computational Geometry. 2023;70:123-153. doi:10.1007/s00454-023-00484-2","ista":"Kourimska H. 2023. Discrete yamabe problem for polyhedral surfaces. Discrete and Computational Geometry. 70, 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","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.","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."},"publication":"Discrete and Computational Geometry","page":"123-153","article_type":"original","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"01","scopus_import":"1","oa_version":"Published Version","file":[{"checksum":"cdbf90ba4a7ddcb190d37b9e9d4cb9d3","success":1,"date_updated":"2023-10-04T11:46:24Z","date_created":"2023-10-04T11:46:24Z","relation":"main_file","file_id":"14396","content_type":"application/pdf","file_size":1026683,"creator":"dernst","access_level":"open_access","file_name":"2023_DiscreteGeometry_Kourimska.pdf"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"12764","intvolume":" 70","status":"public","title":"Discrete yamabe problem for polyhedral surfaces","ddc":["510"],"abstract":[{"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.","lang":"eng"}],"type":"journal_article"},{"file_date_updated":"2023-03-07T14:40:14Z","year":"2023","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.","department":[{"_id":"HeEd"}],"publisher":"Springer Nature","publication_status":"published","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"9605"}]},"author":[{"first_name":"René","last_name":"Corbet","full_name":"Corbet, René"},{"full_name":"Kerber, Michael","orcid":"0000-0002-8030-9299","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","last_name":"Kerber","first_name":"Michael"},{"full_name":"Lesnick, Michael","first_name":"Michael","last_name":"Lesnick"},{"orcid":"0000-0002-8882-5116","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","last_name":"Osang","first_name":"Georg F","full_name":"Osang, Georg F"}],"volume":70,"date_created":"2023-03-05T23:01:06Z","date_updated":"2023-10-04T12:03:40Z","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"month":"09","external_id":{"arxiv":["2103.07823"],"isi":["000936496800001"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"isi":1,"quality_controlled":"1","doi":"10.1007/s00454-022-00476-8","language":[{"iso":"eng"}],"type":"journal_article","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"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"12709","intvolume":" 70","ddc":["000"],"status":"public","title":"Computing the multicover bifiltration","oa_version":"Published Version","file":[{"file_id":"12715","relation":"main_file","success":1,"checksum":"71ce7e59f7ee4620acc704fecca620c2","date_updated":"2023-03-07T14:40:14Z","date_created":"2023-03-07T14:40:14Z","access_level":"open_access","file_name":"2023_DisCompGeo_Corbet.pdf","creator":"cchlebak","file_size":1359323,"content_type":"application/pdf"}],"scopus_import":"1","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"01","citation":{"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.","short":"R. Corbet, M. Kerber, M. Lesnick, G.F. Osang, Discrete and Computational Geometry 70 (2023) 376–405.","mla":"Corbet, René, et al. “Computing the Multicover Bifiltration.” Discrete and Computational Geometry, vol. 70, Springer Nature, 2023, pp. 376–405, doi:10.1007/s00454-022-00476-8.","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.","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","ista":"Corbet R, Kerber M, Lesnick M, Osang GF. 2023. Computing the multicover bifiltration. Discrete and Computational Geometry. 70, 376–405.","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"},"publication":"Discrete and Computational Geometry","page":"376-405","article_type":"original","date_published":"2023-09-01T00:00:00Z"},{"ec_funded":1,"year":"2023","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.","publication_status":"published","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"author":[{"full_name":"Boissonnat, Jean Daniel","last_name":"Boissonnat","first_name":"Jean Daniel"},{"id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","first_name":"Mathijs","last_name":"Wintraecken","full_name":"Wintraecken, Mathijs"}],"date_updated":"2023-10-04T12:07:18Z","date_created":"2023-03-26T22:01:08Z","volume":7,"month":"09","publication_identifier":{"issn":["2367-1726"],"eissn":["2367-1734"]},"oa":1,"main_file_link":[{"url":"https://inserm.hal.science/INRIA-SACLAY/hal-04083524v1","open_access":"1"}],"quality_controlled":"1","project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"},{"_id":"fc390959-9c52-11eb-aca3-afa58bd282b2","grant_number":"M03073","name":"Learning and triangulating manifolds via collapses"}],"doi":"10.1007/s41468-023-00116-x","language":[{"iso":"eng"}],"type":"journal_article","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."}],"_id":"12763","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"The reach of subsets of manifolds","status":"public","intvolume":" 7","oa_version":"Submitted Version","scopus_import":"1","day":"01","article_processing_charge":"No","publication":"Journal of Applied and Computational Topology","citation":{"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.","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","ista":"Boissonnat JD, Wintraecken M. 2023. The reach of subsets of manifolds. Journal of Applied and Computational Topology. 7, 619–641.","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","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.","short":"J.D. Boissonnat, M. Wintraecken, Journal of Applied and Computational Topology 7 (2023) 619–641.","mla":"Boissonnat, Jean Daniel, and Mathijs Wintraecken. “The Reach of Subsets of Manifolds.” Journal of Applied and Computational Topology, vol. 7, Springer Nature, 2023, pp. 619–41, doi:10.1007/s41468-023-00116-x."},"article_type":"original","page":"619-641","date_published":"2023-09-01T00:00:00Z"},{"doi":"10.1137/21M1412918","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://hal-emse.ccsd.cnrs.fr/3IA-COTEDAZUR/hal-04083489v1","open_access":"1"}],"external_id":{"isi":["001013183000012"]},"oa":1,"project":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"name":"Learning and triangulating manifolds via collapses","grant_number":"M03073","_id":"fc390959-9c52-11eb-aca3-afa58bd282b2"}],"quality_controlled":"1","isi":1,"publication_identifier":{"issn":["0097-5397"],"eissn":["1095-7111"]},"month":"04","related_material":{"record":[{"id":"9441","relation":"earlier_version","status":"public"}]},"author":[{"last_name":"Boissonnat","first_name":"Jean Daniel","full_name":"Boissonnat, Jean Daniel"},{"first_name":"Siargey","last_name":"Kachanovich","full_name":"Kachanovich, Siargey"},{"id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","first_name":"Mathijs","last_name":"Wintraecken","full_name":"Wintraecken, Mathijs"}],"volume":52,"date_created":"2023-05-14T22:01:00Z","date_updated":"2023-10-10T07:34:35Z","year":"2023","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"}],"publisher":"Society for Industrial and Applied Mathematics","publication_status":"published","ec_funded":1,"date_published":"2023-04-30T00:00:00Z","citation":{"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","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.","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.","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","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.","short":"J.D. Boissonnat, S. Kachanovich, M. Wintraecken, SIAM Journal on Computing 52 (2023) 452–486.","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."},"publication":"SIAM Journal on Computing","page":"452-486","article_type":"original","article_processing_charge":"No","day":"30","scopus_import":"1","oa_version":"Submitted Version","_id":"12960","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 52","title":"Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations","status":"public","issue":"2","abstract":[{"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. ","lang":"eng"}],"type":"journal_article"},{"volume":142,"date_updated":"2023-10-10T07:37:16Z","date_created":"2023-06-18T22:00:45Z","author":[{"first_name":"Lidija","last_name":"Čomić","full_name":"Čomić, Lidija"},{"last_name":"Largeteau-Skapin","first_name":"Gaëlle","full_name":"Largeteau-Skapin, Gaëlle"},{"last_name":"Zrour","first_name":"Rita","full_name":"Zrour, Rita"},{"last_name":"Biswas","first_name":"Ranita","orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","full_name":"Biswas, Ranita"},{"full_name":"Andres, Eric","first_name":"Eric","last_name":"Andres"}],"department":[{"_id":"HeEd"}],"publisher":"Elsevier","publication_status":"published","year":"2023","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.","article_number":"109693","language":[{"iso":"eng"}],"doi":"10.1016/j.patcog.2023.109693","project":[{"call_identifier":"FWF","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"},{"name":"Discretization in Geometry and Dynamics","grant_number":"I4887","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316"}],"isi":1,"quality_controlled":"1","external_id":{"isi":["001013526000001"]},"publication_identifier":{"issn":["0031-3203"]},"month":"10","oa_version":"None","intvolume":" 142","title":"Discrete analytical objects in the body-centered cubic grid","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"13134","issue":"10","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."}],"type":"journal_article","date_published":"2023-10-01T00:00:00Z","article_type":"original","citation":{"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.","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","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.","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","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.","short":"L. Čomić, G. Largeteau-Skapin, R. Zrour, R. Biswas, E. Andres, Pattern Recognition 142 (2023).","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."},"publication":"Pattern Recognition","article_processing_charge":"No","day":"01","scopus_import":"1"}]