[{"oa":1,"intvolume":"        52","corr_author":"1","month":"04","isi":1,"date_created":"2023-05-14T22:01:00Z","page":"452-486","publication":"SIAM Journal on Computing","doi":"10.1137/21M1412918","external_id":{"isi":["001013183000012"]},"title":"Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations","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. "}],"date_updated":"2025-04-15T06:54:46Z","publication_status":"published","scopus_import":"1","language":[{"iso":"eng"}],"oa_version":"Submitted Version","quality_controlled":"1","project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"},{"grant_number":"M03073","_id":"fc390959-9c52-11eb-aca3-afa58bd282b2","name":"Learning and triangulating manifolds via collapses"}],"type":"journal_article","article_type":"original","citation":{"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.” <i>SIAM Journal on Computing</i>. Society for Industrial and Applied Mathematics, 2023. <a href=\"https://doi.org/10.1137/21M1412918\">https://doi.org/10.1137/21M1412918</a>.","ieee":"J. D. Boissonnat, S. Kachanovich, and M. Wintraecken, “Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations,” <i>SIAM Journal on Computing</i>, vol. 52, no. 2. Society for Industrial and Applied Mathematics, pp. 452–486, 2023.","apa":"Boissonnat, J. D., Kachanovich, S., &#38; Wintraecken, M. (2023). Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations. <i>SIAM Journal on Computing</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/21M1412918\">https://doi.org/10.1137/21M1412918</a>","ama":"Boissonnat JD, Kachanovich S, Wintraecken M. Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations. <i>SIAM Journal on Computing</i>. 2023;52(2):452-486. doi:<a href=\"https://doi.org/10.1137/21M1412918\">10.1137/21M1412918</a>","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.” <i>SIAM Journal on Computing</i>, vol. 52, no. 2, Society for Industrial and Applied Mathematics, 2023, pp. 452–86, doi:<a href=\"https://doi.org/10.1137/21M1412918\">10.1137/21M1412918</a>."},"related_material":{"record":[{"status":"public","relation":"earlier_version","id":"9441"}]},"issue":"2","main_file_link":[{"open_access":"1","url":"https://hal-emse.ccsd.cnrs.fr/3IA-COTEDAZUR/hal-04083489v1"}],"publication_identifier":{"eissn":["1095-7111"],"issn":["0097-5397"]},"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.","volume":52,"ec_funded":1,"status":"public","_id":"12960","author":[{"first_name":"Jean Daniel","full_name":"Boissonnat, Jean Daniel","last_name":"Boissonnat"},{"full_name":"Kachanovich, Siargey","last_name":"Kachanovich","first_name":"Siargey"},{"last_name":"Wintraecken","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","publisher":"Society for Industrial and Applied Mathematics","date_published":"2023-04-30T00:00:00Z","year":"2023","day":"30","department":[{"_id":"HeEd"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"status":"public","ec_funded":1,"arxiv":1,"conference":{"end_date":"2023-06-23","location":"Orlando, FL, United States","start_date":"2023-06-20","name":"STOC: Symposium on Theory of Computing"},"acknowledgement":"We are greatly indebted to Erin Chambers for posing a number of questions that eventually led to this paper. We would also like to thank the other organizers of the workshop on ‘Algorithms\r\nfor the medial axis’. We are also indebted to Tatiana Ezubova for helping with the search for and translation of Russian literature. The second author thanks all members of the Edelsbrunner and Datashape groups for the atmosphere in which the research was conducted.\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). 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.","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","department":[{"_id":"HeEd"}],"date_published":"2023-06-02T00:00:00Z","day":"02","year":"2023","publisher":"Association for Computing Machinery","_id":"13048","article_processing_charge":"No","author":[{"first_name":"André","last_name":"Lieutier","full_name":"Lieutier, André"},{"last_name":"Wintraecken","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs"}],"citation":{"ama":"Lieutier A, Wintraecken M. Hausdorff and Gromov-Hausdorff stable subsets of the medial axis. In: <i>Proceedings of the 55th Annual ACM Symposium on Theory of Computing</i>. Association for Computing Machinery; 2023:1768-1776. doi:<a href=\"https://doi.org/10.1145/3564246.3585113\">10.1145/3564246.3585113</a>","ista":"Lieutier A, Wintraecken M. 2023. Hausdorff and Gromov-Hausdorff stable subsets of the medial axis. Proceedings of the 55th Annual ACM Symposium on Theory of Computing. STOC: Symposium on Theory of Computing, 1768–1776.","short":"A. Lieutier, M. Wintraecken, in:, Proceedings of the 55th Annual ACM Symposium on Theory of Computing, Association for Computing Machinery, 2023, pp. 1768–1776.","chicago":"Lieutier, André, and Mathijs Wintraecken. “Hausdorff and Gromov-Hausdorff Stable Subsets of the Medial Axis.” In <i>Proceedings of the 55th Annual ACM Symposium on Theory of Computing</i>, 1768–76. Association for Computing Machinery, 2023. <a href=\"https://doi.org/10.1145/3564246.3585113\">https://doi.org/10.1145/3564246.3585113</a>.","ieee":"A. Lieutier and M. Wintraecken, “Hausdorff and Gromov-Hausdorff stable subsets of the medial axis,” in <i>Proceedings of the 55th Annual ACM Symposium on Theory of Computing</i>, Orlando, FL, United States, 2023, pp. 1768–1776.","apa":"Lieutier, A., &#38; Wintraecken, M. (2023). Hausdorff and Gromov-Hausdorff stable subsets of the medial axis. In <i>Proceedings of the 55th Annual ACM Symposium on Theory of Computing</i> (pp. 1768–1776). Orlando, FL, United States: Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3564246.3585113\">https://doi.org/10.1145/3564246.3585113</a>","mla":"Lieutier, André, and Mathijs Wintraecken. “Hausdorff and Gromov-Hausdorff Stable Subsets of the Medial Axis.” <i>Proceedings of the 55th Annual ACM Symposium on Theory of Computing</i>, Association for Computing Machinery, 2023, pp. 1768–76, doi:<a href=\"https://doi.org/10.1145/3564246.3585113\">10.1145/3564246.3585113</a>."},"project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"},{"grant_number":"M03073","_id":"fc390959-9c52-11eb-aca3-afa58bd282b2","name":"Learning and triangulating manifolds via collapses"}],"quality_controlled":"1","type":"conference","publication_identifier":{"isbn":["9781450399135"]},"main_file_link":[{"url":"https://arxiv.org/abs/2303.04014","open_access":"1"}],"title":"Hausdorff and Gromov-Hausdorff stable subsets of the medial axis","abstract":[{"lang":"eng","text":"In this paper we introduce a pruning of the medial axis called the (λ,α)-medial axis (axλα). We prove that the (λ,α)-medial axis of a set K is stable in a Gromov-Hausdorff sense under weak assumptions. More formally we prove that if K and K′ are close in the Hausdorff (dH) sense then the (λ,α)-medial axes of K and K′ are close as metric spaces, that is the Gromov-Hausdorff distance (dGH) between the two is 1/4-Hölder in the sense that dGH (axλα(K),axλα(K′)) ≲ dH(K,K′)1/4. The Hausdorff distance between the two medial axes is also bounded, by dH (axλα(K),λα(K′)) ≲ dH(K,K′)1/2. These quantified stability results provide guarantees for practical computations of medial axes from approximations. Moreover, they provide key ingredients for studying the computability of the medial axis in the context of computable analysis."}],"external_id":{"arxiv":["2303.04014"],"isi":["001064640700143"]},"doi":"10.1145/3564246.3585113","language":[{"iso":"eng"}],"oa_version":"Preprint","scopus_import":"1","date_updated":"2025-09-09T12:26:49Z","publication_status":"published","oa":1,"date_created":"2023-05-22T08:02:02Z","publication":"Proceedings of the 55th Annual ACM Symposium on Theory of Computing","page":"1768-1776","month":"06","isi":1,"corr_author":"1"},{"isi":1,"month":"10","corr_author":"1","publication":"Pattern Recognition","date_created":"2023-06-18T22:00:45Z","intvolume":"       142","scopus_import":"1","publication_status":"published","date_updated":"2025-04-15T07:45:32Z","oa_version":"None","language":[{"iso":"eng"}],"doi":"10.1016/j.patcog.2023.109693","title":"Discrete analytical objects in the body-centered cubic grid","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."}],"external_id":{"isi":["001013526000001"]},"issue":"10","article_number":"109693","publication_identifier":{"issn":["0031-3203"]},"type":"journal_article","quality_controlled":"1","project":[{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","grant_number":"I02979-N35"},{"grant_number":"I4887","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","name":"Persistent Homology, Algorithms and Stochastic Geometry"}],"citation":{"mla":"Čomić, Lidija, et al. “Discrete Analytical Objects in the Body-Centered Cubic Grid.” <i>Pattern Recognition</i>, vol. 142, no. 10, 109693, Elsevier, 2023, doi:<a href=\"https://doi.org/10.1016/j.patcog.2023.109693\">10.1016/j.patcog.2023.109693</a>.","ieee":"L. Čomić, G. Largeteau-Skapin, R. Zrour, R. Biswas, and E. Andres, “Discrete analytical objects in the body-centered cubic grid,” <i>Pattern Recognition</i>, vol. 142, no. 10. Elsevier, 2023.","apa":"Čomić, L., Largeteau-Skapin, G., Zrour, R., Biswas, R., &#38; Andres, E. (2023). Discrete analytical objects in the body-centered cubic grid. <i>Pattern Recognition</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.patcog.2023.109693\">https://doi.org/10.1016/j.patcog.2023.109693</a>","short":"L. Čomić, G. Largeteau-Skapin, R. Zrour, R. Biswas, E. Andres, Pattern Recognition 142 (2023).","chicago":"Čomić, Lidija, Gaëlle Largeteau-Skapin, Rita Zrour, Ranita Biswas, and Eric Andres. “Discrete Analytical Objects in the Body-Centered Cubic Grid.” <i>Pattern Recognition</i>. Elsevier, 2023. <a href=\"https://doi.org/10.1016/j.patcog.2023.109693\">https://doi.org/10.1016/j.patcog.2023.109693</a>.","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. <i>Pattern Recognition</i>. 2023;142(10). doi:<a href=\"https://doi.org/10.1016/j.patcog.2023.109693\">10.1016/j.patcog.2023.109693</a>"},"article_type":"original","publisher":"Elsevier","_id":"13134","article_processing_charge":"No","author":[{"first_name":"Lidija","last_name":"Čomić","full_name":"Čomić, Lidija"},{"first_name":"Gaëlle","last_name":"Largeteau-Skapin","full_name":"Largeteau-Skapin, Gaëlle"},{"full_name":"Zrour, Rita","last_name":"Zrour","first_name":"Rita"},{"full_name":"Biswas, Ranita","last_name":"Biswas","first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5372-7890"},{"last_name":"Andres","full_name":"Andres, Eric","first_name":"Eric"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"day":"01","year":"2023","date_published":"2023-10-01T00:00:00Z","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.","status":"public","volume":142},{"scopus_import":"1","date_updated":"2025-09-09T12:30:39Z","publication_status":"published","oa_version":"Published Version","language":[{"iso":"eng"}],"doi":"10.1016/j.jcta.2023.105776","abstract":[{"lang":"eng","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."}],"title":"Successive vertex orderings of fully regular graphs","external_id":{"arxiv":["2206.13592"],"isi":["001144487800001"]},"isi":1,"ddc":["510"],"month":"10","corr_author":"1","publication":"Journal of Combinatorial Theory. Series A","date_created":"2023-06-25T22:00:45Z","oa":1,"intvolume":"       199","publisher":"Elsevier","_id":"13165","author":[{"first_name":"Lixing","last_name":"Fang","full_name":"Fang, Lixing"},{"first_name":"Hao","last_name":"Huang","full_name":"Huang, Hao"},{"last_name":"Pach","full_name":"Pach, János","first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4"},{"first_name":"Gábor","last_name":"Tardos","full_name":"Tardos, Gábor"},{"last_name":"Zuo","full_name":"Zuo, Junchi","first_name":"Junchi"}],"article_processing_charge":"Yes (in subscription journal)","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","department":[{"_id":"HeEd"}],"day":"01","year":"2023","date_published":"2023-10-01T00:00:00Z","arxiv":1,"file":[{"date_updated":"2024-01-30T12:03:10Z","access_level":"open_access","date_created":"2024-01-30T12:03:10Z","file_size":352555,"creator":"dernst","success":1,"checksum":"9eebc213b4182a66063a99083ff5bd04","file_name":"2023_JourCombinatiorialTheory_Fang.pdf","content_type":"application/pdf","relation":"main_file","file_id":"14902"}],"license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","status":"public","volume":199,"file_date_updated":"2024-01-30T12:03:10Z","issue":"10","article_number":"105776","publication_identifier":{"eissn":["1096-0899"],"issn":["0097-3165"]},"has_accepted_license":"1","type":"journal_article","quality_controlled":"1","citation":{"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.","ama":"Fang L, Huang H, Pach J, Tardos G, Zuo J. Successive vertex orderings of fully regular graphs. <i>Journal of Combinatorial Theory Series A</i>. 2023;199(10). doi:<a href=\"https://doi.org/10.1016/j.jcta.2023.105776\">10.1016/j.jcta.2023.105776</a>","ieee":"L. Fang, H. Huang, J. Pach, G. Tardos, and J. Zuo, “Successive vertex orderings of fully regular graphs,” <i>Journal of Combinatorial Theory. Series A</i>, vol. 199, no. 10. Elsevier, 2023.","apa":"Fang, L., Huang, H., Pach, J., Tardos, G., &#38; Zuo, J. (2023). Successive vertex orderings of fully regular graphs. <i>Journal of Combinatorial Theory. Series A</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jcta.2023.105776\">https://doi.org/10.1016/j.jcta.2023.105776</a>","short":"L. Fang, H. Huang, J. Pach, G. Tardos, J. Zuo, Journal of Combinatorial Theory. Series A 199 (2023).","chicago":"Fang, Lixing, Hao Huang, János Pach, Gábor Tardos, and Junchi Zuo. “Successive Vertex Orderings of Fully Regular Graphs.” <i>Journal of Combinatorial Theory. Series A</i>. Elsevier, 2023. <a href=\"https://doi.org/10.1016/j.jcta.2023.105776\">https://doi.org/10.1016/j.jcta.2023.105776</a>.","mla":"Fang, Lixing, et al. “Successive Vertex Orderings of Fully Regular Graphs.” <i>Journal of Combinatorial Theory. Series A</i>, vol. 199, no. 10, 105776, Elsevier, 2023, doi:<a href=\"https://doi.org/10.1016/j.jcta.2023.105776\">10.1016/j.jcta.2023.105776</a>."},"tmp":{"short":"CC BY-NC-SA (4.0)","image":"/images/cc_by_nc_sa.png","name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode"},"article_type":"original"},{"alternative_title":["ISTA Master's Thesis"],"publisher":"Institute of Science and Technology Austria","article_processing_charge":"No","_id":"14226","author":[{"orcid":"0000-0002-6862-208X","id":"2D04F932-F248-11E8-B48F-1D18A9856A87","first_name":"Elizabeth R","last_name":"Stephenson","full_name":"Stephenson, Elizabeth R"}],"department":[{"_id":"GradSch"},{"_id":"HeEd"}],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","date_published":"2023-08-24T00:00:00Z","year":"2023","day":"24","status":"public","file":[{"access_level":"closed","date_updated":"2024-02-26T23:30:03Z","date_created":"2023-08-24T13:02:49Z","file_size":15501411,"content_type":"application/x-zip-compressed","file_name":"documents-export-2023-08-24.zip","checksum":"453caf851d75c3478c10ed09bd242a91","creator":"cchlebak","file_id":"14227","embargo_to":"open_access","relation":"source_file"},{"creator":"cchlebak","content_type":"application/pdf","checksum":"7349d29963d6695e555e171748648d9a","file_name":"thesis_pdf_a.pdf","relation":"main_file","file_id":"14228","embargo":"2024-02-25","date_updated":"2024-02-26T23:30:03Z","access_level":"open_access","file_size":6854783,"date_created":"2023-08-24T13:03:42Z"}],"file_date_updated":"2024-02-26T23:30:03Z","has_accepted_license":"1","publication_identifier":{"issn":["2791-4585"]},"type":"dissertation","citation":{"apa":"Stephenson, E. R. (2023). <i>Generalizing medial axes with homology switches</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:14226\">https://doi.org/10.15479/at:ista:14226</a>","ieee":"E. R. Stephenson, “Generalizing medial axes with homology switches,” Institute of Science and Technology Austria, 2023.","chicago":"Stephenson, Elizabeth R. “Generalizing Medial Axes with Homology Switches.” Institute of Science and Technology Austria, 2023. <a href=\"https://doi.org/10.15479/at:ista:14226\">https://doi.org/10.15479/at:ista:14226</a>.","short":"E.R. Stephenson, Generalizing Medial Axes with Homology Switches, Institute of Science and Technology Austria, 2023.","ista":"Stephenson ER. 2023. Generalizing medial axes with homology switches. Institute of Science and Technology Austria.","ama":"Stephenson ER. Generalizing medial axes with homology switches. 2023. doi:<a href=\"https://doi.org/10.15479/at:ista:14226\">10.15479/at:ista:14226</a>","mla":"Stephenson, Elizabeth R. <i>Generalizing Medial Axes with Homology Switches</i>. Institute of Science and Technology Austria, 2023, doi:<a href=\"https://doi.org/10.15479/at:ista:14226\">10.15479/at:ista:14226</a>."},"date_updated":"2026-04-07T14:02:30Z","publication_status":"published","language":[{"iso":"eng"}],"oa_version":"Published Version","OA_place":"publisher","doi":"10.15479/at:ista:14226","title":"Generalizing medial axes with homology switches","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."}],"degree_awarded":"MS","month":"08","ddc":["500"],"supervisor":[{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"corr_author":"1","date_created":"2023-08-24T13:01:18Z","page":"43","oa":1},{"intvolume":"       609","oa":1,"date_created":"2022-07-08T11:40:07Z","page":"145-179","publication":"Journal of Algebra","corr_author":"1","month":"11","isi":1,"ddc":["510"],"external_id":{"isi":["000861841100004"]},"abstract":[{"lang":"eng","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 ."}],"title":"Contravariant pairings between standard Whittaker modules and Verma modules","doi":"10.1016/j.jalgebra.2022.06.017","language":[{"iso":"eng"}],"oa_version":"Published Version","publication_status":"published","date_updated":"2025-04-14T07:43:58Z","scopus_import":"1","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","citation":{"mla":"Brown, Adam, and Anna Romanov. “Contravariant Pairings between Standard Whittaker Modules and Verma Modules.” <i>Journal of Algebra</i>, vol. 609, no. 11, Elsevier, 2022, pp. 145–79, doi:<a href=\"https://doi.org/10.1016/j.jalgebra.2022.06.017\">10.1016/j.jalgebra.2022.06.017</a>.","ista":"Brown A, Romanov A. 2022. Contravariant pairings between standard Whittaker modules and Verma modules. Journal of Algebra. 609(11), 145–179.","ama":"Brown A, Romanov A. Contravariant pairings between standard Whittaker modules and Verma modules. <i>Journal of Algebra</i>. 2022;609(11):145-179. doi:<a href=\"https://doi.org/10.1016/j.jalgebra.2022.06.017\">10.1016/j.jalgebra.2022.06.017</a>","ieee":"A. Brown and A. Romanov, “Contravariant pairings between standard Whittaker modules and Verma modules,” <i>Journal of Algebra</i>, vol. 609, no. 11. Elsevier, pp. 145–179, 2022.","apa":"Brown, A., &#38; Romanov, A. (2022). Contravariant pairings between standard Whittaker modules and Verma modules. <i>Journal of Algebra</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jalgebra.2022.06.017\">https://doi.org/10.1016/j.jalgebra.2022.06.017</a>","chicago":"Brown, Adam, and Anna Romanov. “Contravariant Pairings between Standard Whittaker Modules and Verma Modules.” <i>Journal of Algebra</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.jalgebra.2022.06.017\">https://doi.org/10.1016/j.jalgebra.2022.06.017</a>.","short":"A. Brown, A. Romanov, Journal of Algebra 609 (2022) 145–179."},"quality_controlled":"1","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"type":"journal_article","keyword":["Algebra and Number Theory"],"has_accepted_license":"1","publication_identifier":{"issn":["0021-8693"]},"issue":"11","volume":609,"file_date_updated":"2023-02-02T07:32:48Z","status":"public","ec_funded":1,"file":[{"relation":"main_file","file_id":"12473","success":1,"creator":"dernst","content_type":"application/pdf","file_name":"2022_JournalAlgebra_Brown.pdf","checksum":"82abaee3d7837f703e499a9ecbb25b7c","file_size":582962,"date_created":"2023-02-02T07:32:48Z","date_updated":"2023-02-02T07:32:48Z","access_level":"open_access"}],"license":"https://creativecommons.org/licenses/by/4.0/","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.","date_published":"2022-11-01T00:00:00Z","day":"01","year":"2022","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"HeEd"}],"_id":"11545","author":[{"first_name":"Adam","id":"70B7FDF6-608D-11E9-9333-8535E6697425","full_name":"Brown, Adam","last_name":"Brown"},{"first_name":"Anna","full_name":"Romanov, Anna","last_name":"Romanov"}],"article_processing_charge":"Yes (via OA deal)","publisher":"Elsevier"},{"citation":{"mla":"Shipman, Barbara A., and Elizabeth R. Stephenson. “Tangible Topology through the Lens of Limits.” <i>PRIMUS</i>, vol. 32, no. 5, Taylor &#38; Francis, 2022, pp. 593–609, doi:<a href=\"https://doi.org/10.1080/10511970.2021.1872750\">10.1080/10511970.2021.1872750</a>.","ama":"Shipman BA, Stephenson ER. Tangible topology through the lens of limits. <i>PRIMUS</i>. 2022;32(5):593-609. doi:<a href=\"https://doi.org/10.1080/10511970.2021.1872750\">10.1080/10511970.2021.1872750</a>","ista":"Shipman BA, Stephenson ER. 2022. Tangible topology through the lens of limits. PRIMUS. 32(5), 593–609.","apa":"Shipman, B. A., &#38; Stephenson, E. R. (2022). Tangible topology through the lens of limits. <i>PRIMUS</i>. Taylor &#38; Francis. <a href=\"https://doi.org/10.1080/10511970.2021.1872750\">https://doi.org/10.1080/10511970.2021.1872750</a>","ieee":"B. A. Shipman and E. R. Stephenson, “Tangible topology through the lens of limits,” <i>PRIMUS</i>, vol. 32, no. 5. Taylor &#38; Francis, pp. 593–609, 2022.","chicago":"Shipman, Barbara A., and Elizabeth R Stephenson. “Tangible Topology through the Lens of Limits.” <i>PRIMUS</i>. Taylor &#38; Francis, 2022. <a href=\"https://doi.org/10.1080/10511970.2021.1872750\">https://doi.org/10.1080/10511970.2021.1872750</a>.","short":"B.A. Shipman, E.R. Stephenson, PRIMUS 32 (2022) 593–609."},"article_type":"original","quality_controlled":"1","type":"journal_article","keyword":["Education","General Mathematics"],"publication_identifier":{"issn":["1051-1970"],"eissn":["1935-4053"]},"issue":"5","status":"public","volume":32,"department":[{"_id":"HeEd"},{"_id":"GradSch"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2022-05-28T00:00:00Z","day":"28","year":"2022","publisher":"Taylor & Francis","article_processing_charge":"No","_id":"12307","author":[{"first_name":"Barbara A.","full_name":"Shipman, Barbara A.","last_name":"Shipman"},{"last_name":"Stephenson","full_name":"Stephenson, Elizabeth R","orcid":"0000-0002-6862-208X","first_name":"Elizabeth R","id":"2D04F932-F248-11E8-B48F-1D18A9856A87"}],"intvolume":"        32","date_created":"2023-01-16T10:07:21Z","publication":"PRIMUS","page":"593-609","month":"05","corr_author":"1","title":"Tangible topology through the lens of limits","abstract":[{"lang":"eng","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."}],"doi":"10.1080/10511970.2021.1872750","language":[{"iso":"eng"}],"oa_version":"None","scopus_import":"1","date_updated":"2024-10-09T21:03:58Z","publication_status":"published"},{"author":[{"first_name":"Thomas","last_name":"Weighill","full_name":"Weighill, Thomas"},{"first_name":"Takamitsu","last_name":"Yamauchi","full_name":"Yamauchi, Takamitsu"},{"full_name":"Zava, Nicolò","last_name":"Zava","first_name":"Nicolò","id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad","orcid":"0000-0001-8686-1888"}],"_id":"10608","article_processing_charge":"Yes (via OA deal)","publisher":"Springer Nature","year":"2022","day":"01","date_published":"2022-03-01T00:00:00Z","department":[{"_id":"HeEd"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","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).","file_date_updated":"2024-05-22T11:10:10Z","volume":8,"file":[{"access_level":"open_access","date_updated":"2024-05-22T11:10:10Z","date_created":"2024-05-22T11:10:10Z","file_size":371515,"file_name":"2022_EuJournalMath_Weighill.pdf","checksum":"ce35cbb2d8c889dc7750719972634ed4","content_type":"application/pdf","success":1,"creator":"kschuh","file_id":"17036","relation":"main_file"}],"status":"public","issue":"1","publication_identifier":{"issn":["2199-675X"],"eissn":["2199-6768"]},"has_accepted_license":"1","type":"journal_article","quality_controlled":"1","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)"},"citation":{"apa":"Weighill, T., Yamauchi, T., &#38; Zava, N. (2022). Coarse infinite-dimensionality of hyperspaces of finite subsets. <i>European Journal of Mathematics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s40879-021-00515-3\">https://doi.org/10.1007/s40879-021-00515-3</a>","ieee":"T. Weighill, T. Yamauchi, and N. Zava, “Coarse infinite-dimensionality of hyperspaces of finite subsets,” <i>European Journal of Mathematics</i>, vol. 8, no. 1. Springer Nature, pp. 335–355, 2022.","chicago":"Weighill, Thomas, Takamitsu Yamauchi, and Nicolò Zava. “Coarse Infinite-Dimensionality of Hyperspaces of Finite Subsets.” <i>European Journal of Mathematics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s40879-021-00515-3\">https://doi.org/10.1007/s40879-021-00515-3</a>.","short":"T. Weighill, T. Yamauchi, N. Zava, European Journal of Mathematics 8 (2022) 335–355.","ama":"Weighill T, Yamauchi T, Zava N. Coarse infinite-dimensionality of hyperspaces of finite subsets. <i>European Journal of Mathematics</i>. 2022;8(1):335-355. doi:<a href=\"https://doi.org/10.1007/s40879-021-00515-3\">10.1007/s40879-021-00515-3</a>","ista":"Weighill T, Yamauchi T, Zava N. 2022. Coarse infinite-dimensionality of hyperspaces of finite subsets. European Journal of Mathematics. 8(1), 335–355.","mla":"Weighill, Thomas, et al. “Coarse Infinite-Dimensionality of Hyperspaces of Finite Subsets.” <i>European Journal of Mathematics</i>, vol. 8, no. 1, Springer Nature, 2022, pp. 335–55, doi:<a href=\"https://doi.org/10.1007/s40879-021-00515-3\">10.1007/s40879-021-00515-3</a>."},"date_updated":"2024-05-22T11:10:22Z","publication_status":"published","scopus_import":"1","oa_version":"Published Version","language":[{"iso":"eng"}],"doi":"10.1007/s40879-021-00515-3","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."}],"title":"Coarse infinite-dimensionality of hyperspaces of finite subsets","ddc":["500"],"month":"03","page":"335-355","publication":"European Journal of Mathematics","date_created":"2022-01-09T23:01:27Z","oa":1,"intvolume":"         8"},{"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"}],"title":"Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer","external_id":{"isi":["000754773500001"],"pmid":["35163685"]},"doi":"10.3390/ijms23031763","language":[{"iso":"eng"}],"oa_version":"Published Version","scopus_import":"1","date_updated":"2025-06-11T13:46:46Z","publication_status":"published","intvolume":"        23","oa":1,"date_created":"2022-02-13T23:01:35Z","publication":"International Journal of Molecular Sciences","month":"02","isi":1,"ddc":["510","576"],"status":"public","file":[{"date_created":"2022-02-14T07:46:30Z","file_size":24416183,"date_updated":"2022-02-14T07:46:30Z","access_level":"open_access","relation":"main_file","file_id":"10756","creator":"dernst","success":1,"content_type":"application/pdf","file_name":"2022_IJMS_Chang.pdf","checksum":"8890ad20c54e90dc58ad5ea97c902998"}],"file_date_updated":"2022-02-14T07:46:30Z","volume":23,"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.). ","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"date_published":"2022-02-01T00:00:00Z","day":"01","year":"2022","publisher":"MDPI","article_processing_charge":"Yes","_id":"10754","author":[{"first_name":"Yan","last_name":"Chang","full_name":"Chang, Yan"},{"last_name":"Funk","full_name":"Funk, Marah","first_name":"Marah"},{"full_name":"Roy, Souvik","last_name":"Roy","first_name":"Souvik"},{"last_name":"Stephenson","full_name":"Stephenson, Elizabeth R","orcid":"0000-0002-6862-208X","id":"2D04F932-F248-11E8-B48F-1D18A9856A87","first_name":"Elizabeth R"},{"full_name":"Choi, Sangyong","last_name":"Choi","first_name":"Sangyong"},{"first_name":"Hristo V.","last_name":"Kojouharov","full_name":"Kojouharov, Hristo V."},{"first_name":"Benito","last_name":"Chen","full_name":"Chen, Benito"},{"first_name":"Zui","last_name":"Pan","full_name":"Pan, Zui"}],"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.” <i>International Journal of Molecular Sciences</i>, vol. 23, no. 3, 1763, MDPI, 2022, doi:<a href=\"https://doi.org/10.3390/ijms23031763\">10.3390/ijms23031763</a>.","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.” <i>International Journal of Molecular Sciences</i>. MDPI, 2022. <a href=\"https://doi.org/10.3390/ijms23031763\">https://doi.org/10.3390/ijms23031763</a>.","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 <i>et al.</i>, “Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer,” <i>International Journal of Molecular Sciences</i>, vol. 23, no. 3. MDPI, 2022.","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. <i>International Journal of Molecular Sciences</i>. MDPI. <a href=\"https://doi.org/10.3390/ijms23031763\">https://doi.org/10.3390/ijms23031763</a>","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. <i>International Journal of Molecular Sciences</i>. 2022;23(3). doi:<a href=\"https://doi.org/10.3390/ijms23031763\">10.3390/ijms23031763</a>","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."},"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)"},"quality_controlled":"1","type":"journal_article","pmid":1,"has_accepted_license":"1","publication_identifier":{"eissn":["1422-0067"],"issn":["1661-6596"]},"article_number":"1763","issue":"3"},{"intvolume":"        67","oa":1,"page":"811-842","publication":"Discrete and Computational Geometry","date_created":"2022-02-20T23:01:34Z","ddc":["510"],"isi":1,"month":"04","corr_author":"1","abstract":[{"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.","lang":"eng"}],"title":"Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics","external_id":{"isi":["000752175300002"]},"doi":"10.1007/s00454-022-00371-2","oa_version":"Published Version","language":[{"iso":"eng"}],"scopus_import":"1","publication_status":"published","date_updated":"2024-10-09T21:01:38Z","citation":{"mla":"Biswas, Ranita, et al. “Continuous and Discrete Radius Functions on Voronoi Tessellations and Delaunay Mosaics.” <i>Discrete and Computational Geometry</i>, vol. 67, Springer Nature, 2022, pp. 811–42, doi:<a href=\"https://doi.org/10.1007/s00454-022-00371-2\">10.1007/s00454-022-00371-2</a>.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Discrete and Computational Geometry 67 (2022) 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.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00454-022-00371-2\">https://doi.org/10.1007/s00454-022-00371-2</a>.","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., &#38; Saghafian, M. (2022). Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-022-00371-2\">https://doi.org/10.1007/s00454-022-00371-2</a>","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics,” <i>Discrete and Computational Geometry</i>, 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. <i>Discrete and Computational Geometry</i>. 2022;67:811-842. doi:<a href=\"https://doi.org/10.1007/s00454-022-00371-2\">10.1007/s00454-022-00371-2</a>","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."},"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","quality_controlled":"1","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"has_accepted_license":"1","file":[{"access_level":"open_access","date_updated":"2022-08-02T06:07:55Z","file_size":2518111,"date_created":"2022-08-02T06:07:55Z","content_type":"application/pdf","file_name":"2022_DiscreteCompGeometry_Biswas.pdf","checksum":"9383d3b70561bacee905e335dc922680","success":1,"creator":"dernst","file_id":"11718","relation":"main_file"}],"status":"public","file_date_updated":"2022-08-02T06:07:55Z","volume":67,"acknowledgement":"Open access funding provided by the Institute of Science and Technology (IST Austria).","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"HeEd"}],"day":"01","year":"2022","date_published":"2022-04-01T00:00:00Z","publisher":"Springer Nature","author":[{"orcid":"0000-0002-5372-7890","first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","last_name":"Biswas","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"},{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"full_name":"Saghafian, Morteza","last_name":"Saghafian","first_name":"Morteza"}],"_id":"10773","article_processing_charge":"Yes (via OA deal)"},{"oa":1,"intvolume":"       224","corr_author":"1","editor":[{"first_name":"Xavier","last_name":"Goaoc","full_name":"Goaoc, Xavier"},{"first_name":"Michael","full_name":"Kerber, Michael","last_name":"Kerber"}],"ddc":["510"],"month":"06","publication":"38th International Symposium on Computational Geometry","page":"66:1-66:9","date_created":"2022-06-01T14:18:04Z","doi":"10.4230/LIPIcs.SoCG.2022.66","title":"A cautionary tale: Burning the medial axis is unstable","abstract":[{"lang":"eng","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."}],"date_updated":"2025-04-14T07:43:57Z","publication_status":"published","series_title":"LIPIcs","scopus_import":"1","oa_version":"Published Version","language":[{"iso":"eng"}],"type":"conference","quality_controlled":"1","project":[{"grant_number":"M03073","name":"Learning and triangulating manifolds via collapses","_id":"fc390959-9c52-11eb-aca3-afa58bd282b2"},{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","call_identifier":"H2020","grant_number":"788183"},{"name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411"}],"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)"},"citation":{"mla":"Chambers, Erin, et al. “A Cautionary Tale: Burning the Medial Axis Is Unstable.” <i>38th International Symposium on Computational Geometry</i>, edited by Xavier Goaoc and Michael Kerber, vol. 224, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022, p. 66:1-66:9, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2022.66\">10.4230/LIPIcs.SoCG.2022.66</a>.","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.","chicago":"Chambers, Erin, Christopher D Fillmore, Elizabeth R Stephenson, and Mathijs Wintraecken. “A Cautionary Tale: Burning the Medial Axis Is Unstable.” In <i>38th International Symposium on Computational Geometry</i>, edited by Xavier Goaoc and Michael Kerber, 224:66:1-66:9. LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2022.66\">https://doi.org/10.4230/LIPIcs.SoCG.2022.66</a>.","ieee":"E. Chambers, C. D. Fillmore, E. R. Stephenson, and M. Wintraecken, “A cautionary tale: Burning the medial axis is unstable,” in <i>38th International Symposium on Computational Geometry</i>, Berlin, Germany, 2022, vol. 224, p. 66:1-66:9.","apa":"Chambers, E., Fillmore, C. D., Stephenson, E. R., &#38; Wintraecken, M. (2022). A cautionary tale: Burning the medial axis is unstable. In X. Goaoc &#38; M. Kerber (Eds.), <i>38th International Symposium on Computational Geometry</i> (Vol. 224, p. 66:1-66:9). Berlin, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2022.66\">https://doi.org/10.4230/LIPIcs.SoCG.2022.66</a>","ama":"Chambers E, Fillmore CD, Stephenson ER, Wintraecken M. A cautionary tale: Burning the medial axis is unstable. In: Goaoc X, Kerber M, eds. <i>38th International Symposium on Computational Geometry</i>. Vol 224. LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2022:66:1-66:9. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2022.66\">10.4230/LIPIcs.SoCG.2022.66</a>","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."},"publication_identifier":{"isbn":["978-3-95977-227-3"],"issn":["1868-8969"]},"has_accepted_license":"1","conference":{"location":"Berlin, Germany","end_date":"2022-06-10","name":"SoCG: Symposium on Computational Geometry","start_date":"2022-06-07"},"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.","file_date_updated":"2022-06-07T07:58:30Z","volume":224,"file":[{"date_created":"2022-06-07T07:58:30Z","file_size":17580705,"access_level":"open_access","date_updated":"2022-06-07T07:58:30Z","file_id":"11437","relation":"main_file","checksum":"b25ce40fade4ebc0bcaae176db4f5f1f","content_type":"application/pdf","file_name":"2022_LIPICs_Chambers.pdf","success":1,"creator":"dernst"}],"ec_funded":1,"status":"public","_id":"11428","author":[{"last_name":"Chambers","full_name":"Chambers, Erin","first_name":"Erin"},{"id":"35638A5C-AAC7-11E9-B0BF-5503E6697425","first_name":"Christopher D","last_name":"Fillmore","full_name":"Fillmore, Christopher D"},{"orcid":"0000-0002-6862-208X","first_name":"Elizabeth R","id":"2D04F932-F248-11E8-B48F-1D18A9856A87","last_name":"Stephenson","full_name":"Stephenson, Elizabeth R"},{"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","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","year":"2022","day":"01","date_published":"2022-06-01T00:00:00Z","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}]},{"type":"book_editor","quality_controlled":"1","citation":{"apa":"Karimipour, F., &#38; Storandt, S. (Eds.). (2022). <i>Web and Wireless Geographical Information Systems</i> (1st ed., Vol. 13238). Cham: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-031-06245-2\">https://doi.org/10.1007/978-3-031-06245-2</a>","ieee":"F. Karimipour and S. Storandt, Eds., <i>Web and Wireless Geographical Information Systems</i>, 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.","chicago":"Karimipour, Farid, and Sabine Storandt, eds. <i>Web and Wireless Geographical Information Systems</i>. 1st ed. Vol. 13238. Cham: Springer Nature, 2022. <a href=\"https://doi.org/10.1007/978-3-031-06245-2\">https://doi.org/10.1007/978-3-031-06245-2</a>.","ama":"Karimipour F, Storandt S, eds. <i>Web and Wireless Geographical Information Systems</i>. Vol 13238. 1st ed. Cham: Springer Nature; 2022. doi:<a href=\"https://doi.org/10.1007/978-3-031-06245-2\">10.1007/978-3-031-06245-2</a>","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. <i>Web and Wireless Geographical Information Systems</i>. 1st ed., vol. 13238, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/978-3-031-06245-2\">10.1007/978-3-031-06245-2</a>."},"intvolume":"     13238","corr_author":"1","editor":[{"orcid":"0000-0001-6746-4174","first_name":"Farid","id":"2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425","last_name":"Karimipour","full_name":"Karimipour, Farid"},{"first_name":"Sabine","full_name":"Storandt, Sabine","last_name":"Storandt"}],"month":"05","page":"153","date_created":"2022-06-02T05:40:53Z","publication_identifier":{"issn":["0302-9743"],"isbn":["9783031062445"],"eisbn":["9783031062452"],"eissn":["1611-3349"]},"doi":"10.1007/978-3-031-06245-2","volume":13238,"title":"Web and Wireless Geographical Information Systems","abstract":[{"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.","lang":"eng"}],"edition":"1","status":"public","article_processing_charge":"No","_id":"11429","date_updated":"2024-10-09T21:02:30Z","publication_status":"published","publisher":"Springer Nature","alternative_title":["LNCS"],"year":"2022","oa_version":"None","day":"01","date_published":"2022-05-01T00:00:00Z","language":[{"iso":"eng"}],"place":"Cham","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}]},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"HeEd"}],"day":"15","year":"2022","date_published":"2022-03-15T00:00:00Z","publisher":"Elsevier","_id":"10413","article_processing_charge":"No","author":[{"first_name":"Dikran","last_name":"Dikranjan","full_name":"Dikranjan, Dikran"},{"first_name":"Anna","last_name":"Giordano Bruno","full_name":"Giordano Bruno, Anna"},{"first_name":"Hans Peter","last_name":"Künzi","full_name":"Künzi, Hans Peter"},{"last_name":"Zava","full_name":"Zava, Nicolò","orcid":"0000-0001-8686-1888","first_name":"Nicolò","id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad"},{"full_name":"Toller, Daniele","last_name":"Toller","first_name":"Daniele"}],"status":"public","volume":309,"acknowledgement":"Dedicated to the memory of Hans-Peter Künzi.","publication_identifier":{"issn":["0166-8641"]},"article_number":"107916","citation":{"mla":"Dikranjan, Dikran, et al. “Generalized Quasi-Metric Semilattices.” <i>Topology and Its Applications</i>, vol. 309, 107916, Elsevier, 2022, doi:<a href=\"https://doi.org/10.1016/j.topol.2021.107916\">10.1016/j.topol.2021.107916</a>.","ieee":"D. Dikranjan, A. Giordano Bruno, H. P. Künzi, N. Zava, and D. Toller, “Generalized quasi-metric semilattices,” <i>Topology and its Applications</i>, vol. 309. Elsevier, 2022.","apa":"Dikranjan, D., Giordano Bruno, A., Künzi, H. P., Zava, N., &#38; Toller, D. (2022). Generalized quasi-metric semilattices. <i>Topology and Its Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.topol.2021.107916\">https://doi.org/10.1016/j.topol.2021.107916</a>","chicago":"Dikranjan, Dikran, Anna Giordano Bruno, Hans Peter Künzi, Nicolò Zava, and Daniele Toller. “Generalized Quasi-Metric Semilattices.” <i>Topology and Its Applications</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.topol.2021.107916\">https://doi.org/10.1016/j.topol.2021.107916</a>.","short":"D. Dikranjan, A. Giordano Bruno, H.P. Künzi, N. Zava, D. Toller, Topology and Its Applications 309 (2022).","ista":"Dikranjan D, Giordano Bruno A, Künzi HP, Zava N, Toller D. 2022. Generalized quasi-metric semilattices. Topology and its Applications. 309, 107916.","ama":"Dikranjan D, Giordano Bruno A, Künzi HP, Zava N, Toller D. Generalized quasi-metric semilattices. <i>Topology and its Applications</i>. 2022;309. doi:<a href=\"https://doi.org/10.1016/j.topol.2021.107916\">10.1016/j.topol.2021.107916</a>"},"article_type":"original","type":"journal_article","quality_controlled":"1","oa_version":"None","language":[{"iso":"eng"}],"scopus_import":"1","date_updated":"2024-10-09T21:01:16Z","publication_status":"published","abstract":[{"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.","lang":"eng"}],"title":"Generalized quasi-metric semilattices","external_id":{"isi":["000791838800012"]},"doi":"10.1016/j.topol.2021.107916","publication":"Topology and its Applications","date_created":"2021-12-05T23:01:44Z","isi":1,"month":"03","corr_author":"1","intvolume":"       309"},{"language":[{"iso":"eng"}],"oa_version":"Published Version","scopus_import":"1","date_updated":"2025-04-15T07:16:56Z","publication_status":"published","title":"Hardness of token swapping on trees","abstract":[{"lang":"eng","text":"Given a graph where every vertex has exactly one labeled token, how can we most quickly execute a given permutation on the tokens? In (sequential) token swapping, the goal is to use the shortest possible sequence of swaps, each of which exchanges the tokens at the two endpoints of an edge of the graph. In parallel token swapping, the goal is to use the fewest rounds, each of which consists of one or more swaps on the edges of a matching. We prove that both of these problems remain NP-hard when the graph is restricted to be a tree. These token swapping problems have been studied by disparate groups of researchers in discrete mathematics, theoretical computer science, robot motion planning, game theory, and engineering. Previous work establishes NP-completeness on general graphs (for both problems), constant-factor approximation algorithms, and some poly-time exact algorithms for simple graph classes such as cliques, stars, paths, and cycles. Sequential and parallel token swapping on trees were first studied over thirty years ago (as \"sorting with a transposition tree\") and over twenty-five years ago (as \"routing permutations via matchings\"), yet their complexities were previously unknown. We also show limitations on approximation of sequential token swapping on trees: we identify a broad class of algorithms that encompass all three known polynomial-time algorithms that achieve the best known approximation factor (which is 2) and show that no such algorithm can achieve an approximation factor less than 2."}],"external_id":{"arxiv":["2103.06707"]},"doi":"10.4230/LIPIcs.ESA.2022.3","date_created":"2024-05-29T06:27:16Z","publication":"30th Annual European Symposium on Algorithms","month":"09","ddc":["510"],"corr_author":"1","intvolume":"       244","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"},{"_id":"UlWa"}],"date_published":"2022-09-01T00:00:00Z","year":"2022","day":"01","alternative_title":["LIPIcs"],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","article_processing_charge":"Yes","_id":"17084","author":[{"first_name":"Oswin","last_name":"Aichholzer","full_name":"Aichholzer, Oswin"},{"last_name":"Demaine","full_name":"Demaine, Erik D.","first_name":"Erik D."},{"full_name":"Korman, Matias","last_name":"Korman","first_name":"Matias"},{"first_name":"Anna","full_name":"Lubiw, Anna","last_name":"Lubiw"},{"first_name":"Jayson","full_name":"Lynch, Jayson","last_name":"Lynch"},{"id":"45CFE238-F248-11E8-B48F-1D18A9856A87","first_name":"Zuzana","orcid":"0000-0002-6660-1322","full_name":"Masárová, Zuzana","last_name":"Masárová"},{"first_name":"Mikhail","last_name":"Rudoy","full_name":"Rudoy, Mikhail"},{"full_name":"Vassilevska Williams, Virginia","last_name":"Vassilevska Williams","first_name":"Virginia"},{"first_name":"Nicole","last_name":"Wein","full_name":"Wein, Nicole"}],"status":"public","file":[{"file_size":1406071,"date_created":"2024-08-12T08:51:44Z","access_level":"open_access","date_updated":"2024-08-12T08:51:44Z","file_id":"17420","relation":"main_file","file_name":"2022_LIPIcS_Aichholzer.pdf","checksum":"a1fbd3e7baad510fbcb998cf4a7d9f7f","content_type":"application/pdf","creator":"dernst","success":1}],"file_date_updated":"2024-08-12T08:51:44Z","volume":244,"acknowledgement":"g Anna Lubiw: Supported by the Natural Sciences and Engineering Research Council of\r\nCanada (NSERC). Jayson Lynch: Supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). Zuzana Masárová: Supported by Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31. Virginia Vassilevska Williams: Supported by an NSF CAREER Award, NSF Grants CCF-1528078, CCF-1514339 and CCF-1909429, a BSF Grant BSF:2012338, a Google Research Fellowship and a Sloan Research Fellowship.\r\nNicole Wein: Supported by a grant to DIMACS from the Simons Foundation (820931). This work was done while the author was at MIT.\r\nThis research was initiated at the 34th Bellairs Winter Workshop on Computational Geometry, co-organized by Erik Demaine and Godfried Toussaint, held on March 22–29,\r\n2019 in Holetown, Barbados. We thank the other participants of that workshop for providing a\r\nstimulating research environment.","arxiv":1,"conference":{"end_date":"2022-09-09","location":"Berlin/Potsdam, Germany","name":"ESA: European Symposium on Algorithms","start_date":"2022-09-05"},"has_accepted_license":"1","article_number":"3","citation":{"mla":"Aichholzer, Oswin, et al. “Hardness of Token Swapping on Trees.” <i>30th Annual European Symposium on Algorithms</i>, vol. 244, 3, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022, doi:<a href=\"https://doi.org/10.4230/LIPIcs.ESA.2022.3\">10.4230/LIPIcs.ESA.2022.3</a>.","ista":"Aichholzer O, Demaine ED, Korman M, Lubiw A, Lynch J, Masárová Z, Rudoy M, Vassilevska Williams V, Wein N. 2022. Hardness of token swapping on trees. 30th Annual European Symposium on Algorithms. ESA: European Symposium on Algorithms, LIPIcs, vol. 244, 3.","ama":"Aichholzer O, Demaine ED, Korman M, et al. Hardness of token swapping on trees. In: <i>30th Annual European Symposium on Algorithms</i>. Vol 244. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2022. doi:<a href=\"https://doi.org/10.4230/LIPIcs.ESA.2022.3\">10.4230/LIPIcs.ESA.2022.3</a>","short":"O. Aichholzer, E.D. Demaine, M. Korman, A. Lubiw, J. Lynch, Z. Masárová, M. Rudoy, V. Vassilevska Williams, N. Wein, in:, 30th Annual European Symposium on Algorithms, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022.","chicago":"Aichholzer, Oswin, Erik D. Demaine, Matias Korman, Anna Lubiw, Jayson Lynch, Zuzana Masárová, Mikhail Rudoy, Virginia Vassilevska Williams, and Nicole Wein. “Hardness of Token Swapping on Trees.” In <i>30th Annual European Symposium on Algorithms</i>, Vol. 244. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. <a href=\"https://doi.org/10.4230/LIPIcs.ESA.2022.3\">https://doi.org/10.4230/LIPIcs.ESA.2022.3</a>.","ieee":"O. Aichholzer <i>et al.</i>, “Hardness of token swapping on trees,” in <i>30th Annual European Symposium on Algorithms</i>, Berlin/Potsdam, Germany, 2022, vol. 244.","apa":"Aichholzer, O., Demaine, E. D., Korman, M., Lubiw, A., Lynch, J., Masárová, Z., … Wein, N. (2022). Hardness of token swapping on trees. In <i>30th Annual European Symposium on Algorithms</i> (Vol. 244). Berlin/Potsdam, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.ESA.2022.3\">https://doi.org/10.4230/LIPIcs.ESA.2022.3</a>"},"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)"},"project":[{"grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science"}],"quality_controlled":"1","type":"conference"},{"intvolume":"         8","oa":1,"publication":"European Journal of Mathematics","page":"1309 - 1312","date_created":"2020-05-03T22:00:48Z","ddc":["510"],"month":"12","corr_author":"1","title":"When different norms lead to same billiard trajectories?","abstract":[{"lang":"eng","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."}],"external_id":{"arxiv":["1912.12685"]},"doi":"10.1007/s40879-020-00405-0","oa_version":"Published Version","language":[{"iso":"eng"}],"scopus_import":"1","publication_status":"published","date_updated":"2025-04-14T07:48:36Z","citation":{"mla":"Akopyan, Arseniy, and Roman Karasev. “When Different Norms Lead to Same Billiard Trajectories?” <i>European Journal of Mathematics</i>, vol. 8, no. 4, Springer Nature, 2022, pp. 1309–12, doi:<a href=\"https://doi.org/10.1007/s40879-020-00405-0\">10.1007/s40879-020-00405-0</a>.","short":"A. Akopyan, R. Karasev, European Journal of Mathematics 8 (2022) 1309–1312.","chicago":"Akopyan, Arseniy, and Roman Karasev. “When Different Norms Lead to Same Billiard Trajectories?” <i>European Journal of Mathematics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s40879-020-00405-0\">https://doi.org/10.1007/s40879-020-00405-0</a>.","ieee":"A. Akopyan and R. Karasev, “When different norms lead to same billiard trajectories?,” <i>European Journal of Mathematics</i>, vol. 8, no. 4. Springer Nature, pp. 1309–1312, 2022.","apa":"Akopyan, A., &#38; Karasev, R. (2022). When different norms lead to same billiard trajectories? <i>European Journal of Mathematics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s40879-020-00405-0\">https://doi.org/10.1007/s40879-020-00405-0</a>","ama":"Akopyan A, Karasev R. When different norms lead to same billiard trajectories? <i>European Journal of Mathematics</i>. 2022;8(4):1309-1312. doi:<a href=\"https://doi.org/10.1007/s40879-020-00405-0\">10.1007/s40879-020-00405-0</a>","ista":"Akopyan A, Karasev R. 2022. When different norms lead to same billiard trajectories? European Journal of Mathematics. 8(4), 1309–1312."},"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)"},"type":"journal_article","project":[{"name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"quality_controlled":"1","publication_identifier":{"eissn":["2199-6768"],"issn":["2199-675X"]},"has_accepted_license":"1","issue":"4","file":[{"file_name":"2020_EuropMathematics_Akopyan.pdf","content_type":"application/pdf","checksum":"f53e71fd03744075adcd0b8fc1b8423d","creator":"dernst","file_id":"7796","relation":"main_file","access_level":"open_access","date_updated":"2020-07-14T12:48:03Z","file_size":263926,"date_created":"2020-05-04T10:33:42Z"}],"status":"public","ec_funded":1,"volume":8,"file_date_updated":"2020-07-14T12:48:03Z","arxiv":1,"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.","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"day":"01","year":"2022","date_published":"2022-12-01T00:00:00Z","publisher":"Springer Nature","article_processing_charge":"Yes (via OA deal)","_id":"7791","author":[{"last_name":"Akopyan","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Karasev, Roman","last_name":"Karasev","first_name":"Roman"}]},{"publisher":"Springer Nature","author":[{"orcid":"0000-0002-2548-617X","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","full_name":"Akopyan, Arseniy"},{"first_name":"Richard","full_name":"Schwartz, Richard","last_name":"Schwartz"},{"first_name":"Serge","full_name":"Tabachnikov, Serge","last_name":"Tabachnikov"}],"_id":"8538","article_processing_charge":"No","department":[{"_id":"HeEd"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","date_published":"2022-12-01T00:00:00Z","day":"01","year":"2022","arxiv":1,"acknowledgement":" This paper would not be written if not for Dan Reznik’s curiosity and persistence; we are very grateful to him. We also thank R. Garcia and J. Koiller for interesting discussions. It is a pleasure to thank the Mathematical Institute of the University of Heidelberg for its stimulating atmosphere. ST thanks M. Bialy for interesting discussions and the Tel Aviv\r\nUniversity for its invariable hospitality. AA was supported by European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 78818 Alpha). RS is supported by NSF Grant DMS-1807320. ST was supported by NSF grant DMS-1510055 and SFB/TRR 191.","ec_funded":1,"status":"public","volume":8,"issue":"4","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2001.02934"}],"publication_identifier":{"issn":["2199-675X"],"eissn":["2199-6768"]},"quality_controlled":"1","project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"type":"journal_article","citation":{"mla":"Akopyan, Arseniy, et al. “Billiards in Ellipses Revisited.” <i>European Journal of Mathematics</i>, vol. 8, no. 4, Springer Nature, 2022, pp. 1313–27, doi:<a href=\"https://doi.org/10.1007/s40879-020-00426-9\">10.1007/s40879-020-00426-9</a>.","ama":"Akopyan A, Schwartz R, Tabachnikov S. Billiards in ellipses revisited. <i>European Journal of Mathematics</i>. 2022;8(4):1313-1327. doi:<a href=\"https://doi.org/10.1007/s40879-020-00426-9\">10.1007/s40879-020-00426-9</a>","ista":"Akopyan A, Schwartz R, Tabachnikov S. 2022. Billiards in ellipses revisited. European Journal of Mathematics. 8(4), 1313–1327.","apa":"Akopyan, A., Schwartz, R., &#38; Tabachnikov, S. (2022). Billiards in ellipses revisited. <i>European Journal of Mathematics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s40879-020-00426-9\">https://doi.org/10.1007/s40879-020-00426-9</a>","ieee":"A. Akopyan, R. Schwartz, and S. Tabachnikov, “Billiards in ellipses revisited,” <i>European Journal of Mathematics</i>, vol. 8, no. 4. Springer Nature, pp. 1313–1327, 2022.","chicago":"Akopyan, Arseniy, Richard Schwartz, and Serge Tabachnikov. “Billiards in Ellipses Revisited.” <i>European Journal of Mathematics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s40879-020-00426-9\">https://doi.org/10.1007/s40879-020-00426-9</a>.","short":"A. Akopyan, R. Schwartz, S. Tabachnikov, European Journal of Mathematics 8 (2022) 1313–1327."},"article_type":"original","scopus_import":"1","publication_status":"published","date_updated":"2025-04-14T07:48:34Z","language":[{"iso":"eng"}],"oa_version":"Preprint","doi":"10.1007/s40879-020-00426-9","abstract":[{"lang":"eng","text":"We prove some recent experimental observations of Dan Reznik concerning periodic billiard orbits in ellipses. For example, the sum of cosines of the angles of a periodic billiard polygon remains constant in the 1-parameter family of such polygons (that exist due to the Poncelet porism). In our proofs, we use geometric and complex analytic methods."}],"title":"Billiards in ellipses revisited","external_id":{"arxiv":["2001.02934"]},"month":"12","date_created":"2020-09-20T22:01:38Z","page":"1313-1327","publication":"European Journal of Mathematics","oa":1,"intvolume":"         8"},{"month":"01","isi":1,"ddc":["516"],"corr_author":"1","date_created":"2021-07-14T06:44:53Z","publication":"Foundations of Computational Mathematics ","page":"967-1012","oa":1,"intvolume":"        22","scopus_import":"1","publication_status":"published","date_updated":"2025-04-22T13:45:18Z","language":[{"iso":"eng"}],"oa_version":"Published Version","doi":"10.1007/s10208-021-09520-0","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."}],"title":"The topological correctness of PL approximations of isomanifolds","external_id":{"isi":["000673039600001"]},"related_material":{"record":[{"id":"7952","relation":"earlier_version","status":"public"}]},"has_accepted_license":"1","publication_identifier":{"eissn":["1615-3383"]},"quality_controlled":"1","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"type":"journal_article","citation":{"mla":"Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness of PL Approximations of Isomanifolds.” <i>Foundations of Computational Mathematics </i>, vol. 22, Springer Nature, 2022, pp. 967–1012, doi:<a href=\"https://doi.org/10.1007/s10208-021-09520-0\">10.1007/s10208-021-09520-0</a>.","ieee":"J.-D. Boissonnat and M. Wintraecken, “The topological correctness of PL approximations of isomanifolds,” <i>Foundations of Computational Mathematics </i>, vol. 22. Springer Nature, pp. 967–1012, 2022.","apa":"Boissonnat, J.-D., &#38; Wintraecken, M. (2022). The topological correctness of PL approximations of isomanifolds. <i>Foundations of Computational Mathematics </i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10208-021-09520-0\">https://doi.org/10.1007/s10208-021-09520-0</a>","chicago":"Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness of PL Approximations of Isomanifolds.” <i>Foundations of Computational Mathematics </i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s10208-021-09520-0\">https://doi.org/10.1007/s10208-021-09520-0</a>.","short":"J.-D. Boissonnat, M. Wintraecken, Foundations of Computational Mathematics  22 (2022) 967–1012.","ista":"Boissonnat J-D, Wintraecken M. 2022. The topological correctness of PL approximations of isomanifolds. Foundations of Computational Mathematics . 22, 967–1012.","ama":"Boissonnat J-D, Wintraecken M. The topological correctness of PL approximations of isomanifolds. <i>Foundations of Computational Mathematics </i>. 2022;22:967-1012. doi:<a href=\"https://doi.org/10.1007/s10208-021-09520-0\">10.1007/s10208-021-09520-0</a>"},"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","publisher":"Springer Nature","author":[{"full_name":"Boissonnat, Jean-Daniel","last_name":"Boissonnat","first_name":"Jean-Daniel"},{"first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","last_name":"Wintraecken"}],"_id":"9649","article_processing_charge":"Yes (via OA deal)","department":[{"_id":"HeEd"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2022-01-01T00:00:00Z","day":"01","year":"2022","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.","status":"public","ec_funded":1,"file":[{"relation":"main_file","file_id":"9650","creator":"mwintrae","file_name":"Boissonnat-Wintraecken2021_Article_TheTopologicalCorrectnessOfPLA.pdf","checksum":"f1d372ec3c08ec22e84f8e93e1126b8c","content_type":"application/pdf","file_size":1455699,"date_created":"2021-07-14T06:44:36Z","date_updated":"2021-07-14T06:44:36Z","access_level":"open_access"}],"volume":22,"file_date_updated":"2021-07-14T06:44:36Z"},{"quality_controlled":"1","project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","call_identifier":"H2020"}],"type":"book_chapter","citation":{"mla":"Bleile, Bea, et al. “The Persistent Homology of Dual Digital Image Constructions.” <i>Research in Computational Topology 2</i>, edited by Ellen Gasparovic et al., 1st ed., vol. 30, Springer Nature, 2022, pp. 1–26, doi:<a href=\"https://doi.org/10.1007/978-3-030-95519-9_1\">10.1007/978-3-030-95519-9_1</a>.","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.","chicago":"Bleile, Bea, Adélie Garin, Teresa Heiss, Kelly Maggs, and Vanessa Robins. “The Persistent Homology of Dual Digital Image Constructions.” In <i>Research in Computational Topology 2</i>, edited by Ellen Gasparovic, Vanessa Robins, and Katharine Turner, 1st ed., 30:1–26. AWMS. Cham: Springer Nature, 2022. <a href=\"https://doi.org/10.1007/978-3-030-95519-9_1\">https://doi.org/10.1007/978-3-030-95519-9_1</a>.","ieee":"B. Bleile, A. Garin, T. Heiss, K. Maggs, and V. Robins, “The persistent homology of dual digital image constructions,” in <i>Research in Computational Topology 2</i>, 1st ed., vol. 30, E. Gasparovic, V. Robins, and K. Turner, Eds. Cham: Springer Nature, 2022, pp. 1–26.","apa":"Bleile, B., Garin, A., Heiss, T., Maggs, K., &#38; Robins, V. (2022). The persistent homology of dual digital image constructions. In E. Gasparovic, V. Robins, &#38; K. Turner (Eds.), <i>Research in Computational Topology 2</i> (1st ed., Vol. 30, pp. 1–26). Cham: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-030-95519-9_1\">https://doi.org/10.1007/978-3-030-95519-9_1</a>","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. <i>Research in Computational Topology 2</i>. Vol 30. 1st ed. AWMS. Cham: Springer Nature; 2022:1-26. doi:<a href=\"https://doi.org/10.1007/978-3-030-95519-9_1\">10.1007/978-3-030-95519-9_1</a>","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."},"related_material":{"record":[{"id":"18667","status":"public","relation":"dissertation_contains"}]},"main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2102.11397","open_access":"1"}],"publication_identifier":{"eisbn":["9783030955199"],"isbn":["9783030955182"]},"arxiv":1,"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.","volume":30,"status":"public","ec_funded":1,"author":[{"first_name":"Bea","last_name":"Bleile","full_name":"Bleile, Bea"},{"first_name":"Adélie","last_name":"Garin","full_name":"Garin, Adélie"},{"full_name":"Heiss, Teresa","last_name":"Heiss","first_name":"Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1780-2689"},{"last_name":"Maggs","full_name":"Maggs, Kelly","first_name":"Kelly"},{"last_name":"Robins","full_name":"Robins, Vanessa","first_name":"Vanessa"}],"_id":"11440","article_processing_charge":"No","alternative_title":["Association for Women in Mathematics Series"],"publisher":"Springer Nature","date_published":"2022-01-27T00:00:00Z","year":"2022","day":"27","department":[{"_id":"HeEd"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","place":"Cham","oa":1,"intvolume":"        30","month":"01","editor":[{"first_name":"Ellen","last_name":"Gasparovic","full_name":"Gasparovic, Ellen"},{"first_name":"Vanessa","full_name":"Robins, Vanessa","last_name":"Robins"},{"first_name":"Katharine","last_name":"Turner","full_name":"Turner, Katharine"}],"date_created":"2022-06-07T08:21:11Z","publication":"Research in Computational Topology 2","page":"1-26","doi":"10.1007/978-3-030-95519-9_1","external_id":{"arxiv":["2102.11397"]},"title":"The persistent homology of dual digital image constructions","edition":"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."}],"publication_status":"published","series_title":"AWMS","date_updated":"2026-04-07T12:54:09Z","scopus_import":"1","language":[{"iso":"eng"}],"oa_version":"Preprint"},{"date_created":"2022-03-06T23:01:53Z","publication":"2021 IEEE International Conference on Big Data","page":"3824-3834","month":"01","isi":1,"oa":1,"language":[{"iso":"eng"}],"oa_version":"Preprint","scopus_import":"1","publication_status":"published","date_updated":"2026-04-07T12:54:09Z","title":"The impact of changes in resolution on the persistent homology of images","abstract":[{"lang":"eng","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."}],"external_id":{"isi":["000800559503126"],"arxiv":["2111.05663"]},"doi":"10.1109/BigData52589.2021.9671483","publication_identifier":{"isbn":["9781665439022"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2111.05663"}],"related_material":{"record":[{"id":"18667","relation":"dissertation_contains","status":"public"}]},"citation":{"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.","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 <i>2021 IEEE International Conference on Big Data</i>, 3824–34. IEEE, 2022. <a href=\"https://doi.org/10.1109/BigData52589.2021.9671483\">https://doi.org/10.1109/BigData52589.2021.9671483</a>.","ieee":"T. Heiss <i>et al.</i>, “The impact of changes in resolution on the persistent homology of images,” in <i>2021 IEEE International Conference on Big Data</i>, Orlando, FL, United States; Virtuell, 2022, pp. 3824–3834.","apa":"Heiss, T., Tymochko, S., Story, B., Garin, A., Bui, H., Bleile, B., &#38; Robins, V. (2022). The impact of changes in resolution on the persistent homology of images. In <i>2021 IEEE International Conference on Big Data</i> (pp. 3824–3834). Orlando, FL, United States; Virtuell: IEEE. <a href=\"https://doi.org/10.1109/BigData52589.2021.9671483\">https://doi.org/10.1109/BigData52589.2021.9671483</a>","ama":"Heiss T, Tymochko S, Story B, et al. The impact of changes in resolution on the persistent homology of images. In: <i>2021 IEEE International Conference on Big Data</i>. IEEE; 2022:3824-3834. doi:<a href=\"https://doi.org/10.1109/BigData52589.2021.9671483\">10.1109/BigData52589.2021.9671483</a>","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.","mla":"Heiss, Teresa, et al. “The Impact of Changes in Resolution on the Persistent Homology of Images.” <i>2021 IEEE International Conference on Big Data</i>, IEEE, 2022, pp. 3824–34, doi:<a href=\"https://doi.org/10.1109/BigData52589.2021.9671483\">10.1109/BigData52589.2021.9671483</a>."},"quality_controlled":"1","type":"conference","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"HeEd"}],"date_published":"2022-01-13T00:00:00Z","day":"13","year":"2022","publisher":"IEEE","article_processing_charge":"No","_id":"10828","author":[{"orcid":"0000-0002-1780-2689","first_name":"Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","last_name":"Heiss","full_name":"Heiss, Teresa"},{"first_name":"Sarah","full_name":"Tymochko, Sarah","last_name":"Tymochko"},{"first_name":"Brittany","last_name":"Story","full_name":"Story, Brittany"},{"last_name":"Garin","full_name":"Garin, Adélie","first_name":"Adélie"},{"first_name":"Hoa","last_name":"Bui","full_name":"Bui, Hoa"},{"last_name":"Bleile","full_name":"Bleile, Bea","first_name":"Bea"},{"last_name":"Robins","full_name":"Robins, Vanessa","first_name":"Vanessa"}],"status":"public","conference":{"end_date":"2021-12-18","location":"Orlando, FL, United States; Virtuell","name":"Big Data: International Conference on Big Data","start_date":"2021-12-15"},"arxiv":1},{"abstract":[{"lang":"eng","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. "}],"title":"A window to the persistence of 1D maps. I: Geometric characterization of critical point pairs","publication_status":"submitted","date_updated":"2026-04-07T12:58:47Z","oa_version":"Submitted Version","language":[{"iso":"eng"}],"oa":1,"corr_author":"1","ddc":["510"],"month":"07","publication":"LIPIcs","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. ","file_date_updated":"2022-07-27T09:30:30Z","file":[{"relation":"main_file","file_id":"11661","creator":"scultrer","file_name":"window 1.pdf","content_type":"application/pdf","checksum":"95903f9d1649e8e437a967b6f2f64730","date_created":"2022-07-27T09:30:30Z","file_size":564836,"date_updated":"2022-07-27T09:30:30Z","access_level":"open_access"}],"status":"public","ec_funded":1,"_id":"11660","author":[{"last_name":"Biswas","full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita"},{"full_name":"Cultrera di Montesano, Sebastiano","last_name":"Cultrera di Montesano","first_name":"Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-6249-0832"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"last_name":"Saghafian","full_name":"Saghafian, Morteza","first_name":"Morteza"}],"article_processing_charge":"No","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","alternative_title":["LIPIcs"],"year":"2022","day":"25","date_published":"2022-07-25T00:00:00Z","department":[{"_id":"GradSch"},{"_id":"HeEd"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","project":[{"name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183"},{"grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science","call_identifier":"FWF"},{"grant_number":"I02979-N35","call_identifier":"FWF","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","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)"},"citation":{"mla":"Biswas, Ranita, et al. “A Window to the Persistence of 1D Maps. I: Geometric Characterization of Critical Point Pairs.” <i>LIPIcs</i>, Schloss Dagstuhl - Leibniz-Zentrum für Informatik.","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., &#38; Saghafian, M. (n.d.). A window to the persistence of 1D maps. I: Geometric characterization of critical point pairs. <i>LIPIcs</i>. 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,” <i>LIPIcs</i>. Schloss Dagstuhl - Leibniz-Zentrum für Informatik.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, LIPIcs (n.d.).","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.” <i>LIPIcs</i>. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, n.d.","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. <i>LIPIcs</i>.","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."},"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"15094"}]},"has_accepted_license":"1"}]