[{"title":"Flips in two-dimensional hypertriangulations","project":[{"call_identifier":"H2020","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"},{"call_identifier":"FWF","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342"},{"name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","call_identifier":"FWF"}],"publication_status":"published","fulldoi":"https://doi.org/10.1016/j.ejc.2025.104248","arxiv":1,"isi":1,"status":"public","OA_type":"green","type":"journal_article","ec_funded":1,"OA_place":"repository","corr_author":"1","article_processing_charge":"No","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"doi":"10.1016/j.ejc.2025.104248","date_published":"2026-02-01T00:00:00Z","day":"01","abstract":[{"lang":"eng","text":"We study flips in hypertriangulations of planar points sets. Here a level-k hypertriangulation of n\r\n points in the plane is a subdivision induced by the projection of a k-hypersimplex, which is the convex hull of the barycenters of the (k-1)-dimensional faces of the standard (n-1)-simplex. In particular, we introduce four types of flips and prove that the level-2 hypertriangulations are connected by these flips.\r\n"}],"scopus_import":"1","das_tickbox":"0","date_updated":"2026-07-23T11:58:37Z","author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner"},{"first_name":"Alexey","last_name":"Garber","full_name":"Garber, Alexey"},{"full_name":"Ghafari, Mohadese","first_name":"Mohadese","last_name":"Ghafari"},{"first_name":"Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","last_name":"Heiss","full_name":"Heiss, Teresa","orcid":"0000-0002-1780-2689"},{"full_name":"Saghafian, Morteza","first_name":"Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","last_name":"Saghafian"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2212.11380"}],"publication":"European Journal of Combinatorics","year":"2026","date_created":"2025-10-19T22:01:31Z","citation":{"apa":"Edelsbrunner, H., Garber, A., Ghafari, M., Heiss, T., &#38; Saghafian, M. (2026). Flips in two-dimensional hypertriangulations. <i>European Journal of Combinatorics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.ejc.2025.104248\">https://doi.org/10.1016/j.ejc.2025.104248</a>","ista":"Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. 2026. Flips in two-dimensional hypertriangulations. European Journal of Combinatorics. 132, 104248.","ama":"Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. Flips in two-dimensional hypertriangulations. <i>European Journal of Combinatorics</i>. 2026;132. doi:<a href=\"https://doi.org/10.1016/j.ejc.2025.104248\">10.1016/j.ejc.2025.104248</a>","ieee":"H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, and M. Saghafian, “Flips in two-dimensional hypertriangulations,” <i>European Journal of Combinatorics</i>, vol. 132. Elsevier, 2026.","short":"H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, European Journal of Combinatorics 132 (2026).","mla":"Edelsbrunner, Herbert, et al. “Flips in Two-Dimensional Hypertriangulations.” <i>European Journal of Combinatorics</i>, vol. 132, 104248, Elsevier, 2026, doi:<a href=\"https://doi.org/10.1016/j.ejc.2025.104248\">10.1016/j.ejc.2025.104248</a>.","chicago":"Edelsbrunner, Herbert, Alexey Garber, Mohadese Ghafari, Teresa Heiss, and Morteza Saghafian. “Flips in Two-Dimensional Hypertriangulations.” <i>European Journal of Combinatorics</i>. Elsevier, 2026. <a href=\"https://doi.org/10.1016/j.ejc.2025.104248\">https://doi.org/10.1016/j.ejc.2025.104248</a>."},"article_number":"104248","quality_controlled":"1","volume":132,"publication_identifier":{"issn":["0195-6698"]},"article_type":"original","intvolume":"       132","external_id":{"arxiv":["2212.11380"],"isi":["001599061500002"]},"month":"02","oa_version":"Preprint","publisher":"Elsevier","_id":"20490","department":[{"_id":"HeEd"}],"acknowledgement":"Work by all authors but the second is supported by the European Research Council (ERC), grant no. 788183, by the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), grant no. I 02979-N35. Work by the second author is partially supported by the Alexander von Humboldt Foundation and by the Simons Foundation . The second author thanks Jesús A. De Loera for useful discussions on flips and non-flips and Pavel Galashin and Alexey Balitskiy for useful discussions on plabic graphs."},{"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2505.17858","open_access":"1"}],"publication":"arXiv","citation":{"apa":"Bokor Bleile, Y., Fajstrup, L., Heiss, T., Svane, A. M., &#38; Sørensen, S. S. (n.d.). Identifying cobordisms using kernel persistence. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2505.17858\">https://doi.org/10.48550/arXiv.2505.17858</a>","ama":"Bokor Bleile Y, Fajstrup L, Heiss T, Svane AM, Sørensen SS. Identifying cobordisms using kernel persistence. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2505.17858\">10.48550/arXiv.2505.17858</a>","ista":"Bokor Bleile Y, Fajstrup L, Heiss T, Svane AM, Sørensen SS. Identifying cobordisms using kernel persistence. arXiv, 2505.17858.","mla":"Bokor Bleile, Yossi, et al. “Identifying Cobordisms Using Kernel Persistence.” <i>ArXiv</i>, 2505.17858, doi:<a href=\"https://doi.org/10.48550/arXiv.2505.17858\">10.48550/arXiv.2505.17858</a>.","short":"Y. Bokor Bleile, L. Fajstrup, T. Heiss, A.M. Svane, S.S. Sørensen, ArXiv (n.d.).","ieee":"Y. Bokor Bleile, L. Fajstrup, T. Heiss, A. M. Svane, and S. S. Sørensen, “Identifying cobordisms using kernel persistence,” <i>arXiv</i>. .","chicago":"Bokor Bleile, Yossi, Lisbeth Fajstrup, Teresa Heiss, Anne Marie Svane, and Søren Strandskov Sørensen. “Identifying Cobordisms Using Kernel Persistence.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2505.17858\">https://doi.org/10.48550/arXiv.2505.17858</a>."},"year":"2025","date_created":"2026-01-20T10:12:21Z","date_updated":"2026-07-22T06:33:07Z","author":[{"orcid":"0000-0002-4861-9174","full_name":"Bleile, Yossi","last_name":"Bleile","first_name":"Yossi","id":"920a7385-7995-11ef-9bfd-8c434cd8f3c2"},{"last_name":"Fajstrup","first_name":"Lisbeth","full_name":"Fajstrup, Lisbeth"},{"orcid":"0000-0002-1780-2689","full_name":"Heiss, Teresa","last_name":"Heiss","first_name":"Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Svane, Anne Marie","last_name":"Svane","first_name":"Anne Marie"},{"last_name":"Sørensen","first_name":"Søren Strandskov","full_name":"Sørensen, Søren Strandskov"}],"das_tickbox":"1","day":"23","date_published":"2025-05-23T00:00:00Z","doi":"10.48550/arXiv.2505.17858","abstract":[{"lang":"eng","text":"Motivated by applications in chemistry, we give a homlogical definition of tunnels, or more generally cobordisms, connecting disjoint parts of a cell complex. For a filtered complex, this defines a persistence module. We give a method for identifying birth and death times using kernel persistence and a matrix reduction algorithm for pairing birth and death times."}],"department":[{"_id":"HeEd"}],"_id":"21016","acknowledgement":"Y. B. B. and L. F. were funded by the Independent Research Fund Denmark, grant\r\nnumber 1026-00037. T. H. was partially supported by the European Research Council\r\n(ERC) Horizon 2020, grant number 788183.","external_id":{"arxiv":["2505.17858"]},"oa_version":"Preprint","month":"05","article_number":"2505.17858","type":"preprint","OA_type":"green","ec_funded":1,"status":"public","arxiv":1,"fulldoi":"https://doi.org/10.48550/arXiv.2505.17858","publication_status":"submitted","title":"Identifying cobordisms using kernel persistence","project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended"}],"language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","oa":1,"OA_place":"repository"},{"date_published":"2024-07-01T00:00:00Z","day":"01","doi":"10.1007/s00454-023-00566-1","abstract":[{"lang":"eng","text":"For a locally finite set in R2, the order-k Brillouin tessellations form an infinite sequence of convex face-to-face tilings of the plane. If the set is coarsely dense and generic, then the corresponding infinite sequences of minimum and maximum angles are both monotonic in k. As an example, a stationary Poisson point process in R2  is locally finite, coarsely dense, and generic with probability one. For such a set, the distributions of angles in the Voronoi tessellations, Delaunay mosaics, and Brillouin tessellations are independent of the order and can be derived from the formula for angles in order-1 Delaunay mosaics given by Miles (Math. Biosci. 6, 85–127 (1970))."}],"scopus_import":"1","das_tickbox":"0","date_updated":"2026-10-02T11:45:50Z","author":[{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Garber","first_name":"Alexey","full_name":"Garber, Alexey"},{"full_name":"Ghafari, Mohadese","first_name":"Mohadese","last_name":"Ghafari"},{"full_name":"Heiss, Teresa","orcid":"0000-0002-1780-2689","first_name":"Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","last_name":"Heiss"},{"full_name":"Saghafian, Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","first_name":"Morteza","last_name":"Saghafian"}],"publication":"Discrete and Computational Geometry","citation":{"chicago":"Edelsbrunner, Herbert, Alexey Garber, Mohadese Ghafari, Teresa Heiss, and Morteza Saghafian. “On Angles in Higher Order Brillouin Tessellations and Related Tilings in the Plane.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00454-023-00566-1\">https://doi.org/10.1007/s00454-023-00566-1</a>.","mla":"Edelsbrunner, Herbert, et al. “On Angles in Higher Order Brillouin Tessellations and Related Tilings in the Plane.” <i>Discrete and Computational Geometry</i>, vol. 72, Springer Nature, 2024, pp. 29–48, doi:<a href=\"https://doi.org/10.1007/s00454-023-00566-1\">10.1007/s00454-023-00566-1</a>.","short":"H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, Discrete and Computational Geometry 72 (2024) 29–48.","ieee":"H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, and M. Saghafian, “On angles in higher order Brillouin tessellations and related tilings in the plane,” <i>Discrete and Computational Geometry</i>, vol. 72. Springer Nature, pp. 29–48, 2024.","ista":"Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. 2024. On angles in higher order Brillouin tessellations and related tilings in the plane. Discrete and Computational Geometry. 72, 29–48.","ama":"Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. On angles in higher order Brillouin tessellations and related tilings in the plane. <i>Discrete and Computational Geometry</i>. 2024;72:29-48. doi:<a href=\"https://doi.org/10.1007/s00454-023-00566-1\">10.1007/s00454-023-00566-1</a>","apa":"Edelsbrunner, H., Garber, A., Ghafari, M., Heiss, T., &#38; Saghafian, M. (2024). On angles in higher order Brillouin tessellations and related tilings in the plane. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-023-00566-1\">https://doi.org/10.1007/s00454-023-00566-1</a>"},"date_created":"2023-09-17T22:01:10Z","year":"2024","pmid":1,"quality_controlled":"1","article_type":"original","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"researchdata_availability":"no","volume":72,"intvolume":"        72","external_id":{"pmid":["39610762"],"isi":["001060727600004"],"arxiv":["2204.01076"]},"publisher":"Springer Nature","month":"07","oa_version":"Published Version","department":[{"_id":"HeEd"}],"_id":"14345","acknowledgement":"Work by all authors but A. Garber is supported by the European Research Council (ERC), Grant No. 788183, by the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), Grant No. I 02979-N35. Work by A. Garber is partially supported by the Alexander von Humboldt Foundation.","publication_status":"published","title":"On angles in higher order Brillouin tessellations and related tilings in the plane","file":[{"date_updated":"2024-07-22T09:43:19Z","relation":"main_file","success":1,"access_level":"open_access","file_name":"2024_DiscreteComputGeom_Edelsbrunner.pdf","date_created":"2024-07-22T09:43:19Z","content_type":"application/pdf","file_id":"17301","file_size":892019,"checksum":"b207b4e00f904e8ea8a30e24f0251f79","creator":"dernst"}],"project":[{"name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","call_identifier":"H2020"},{"name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342","call_identifier":"FWF"},{"call_identifier":"FWF","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes"}],"arxiv":1,"fulldoi":"https://doi.org/10.1007/s00454-023-00566-1","isi":1,"status":"public","type":"journal_article","ddc":["510"],"ec_funded":1,"license":"https://creativecommons.org/licenses/by/4.0/","supplementarymaterial":"yes","corr_author":"1","file_date_updated":"2024-07-22T09:43:19Z","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"language":[{"iso":"eng"}],"page":"29-48","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345"},{"ec_funded":1,"type":"journal_article","status":"public","isi":1,"fulldoi":"https://doi.org/10.1137/22M1489071","arxiv":1,"project":[{"call_identifier":"H2020","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships"},{"call_identifier":"H2020","name":"Alpha Shape Theory Extended","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"_id":"fc390959-9c52-11eb-aca3-afa58bd282b2","grant_number":"M03073","name":"Learning and triangulating manifolds via collapses"},{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342","call_identifier":"FWF"}],"title":"Brillouin zones of integer lattices and their perturbations","publication_status":"published","page":"1784-1807","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","language":[{"iso":"eng"}],"oa":1,"article_processing_charge":"No","corr_author":"1","supplementarymaterial":"no","year":"2024","date_created":"2024-06-30T22:01:05Z","citation":{"ista":"Edelsbrunner H, Garber A, Ghafaris M, Heiss T, Saghafiant M, Wintraecken M. 2024. Brillouin zones of integer lattices and their perturbations. SIAM Journal on Discrete Mathematics. 38(2), 1784–1807.","ama":"Edelsbrunner H, Garber A, Ghafaris M, Heiss T, Saghafiant M, Wintraecken M. Brillouin zones of integer lattices and their perturbations. <i>SIAM Journal on Discrete Mathematics</i>. 2024;38(2):1784-1807. doi:<a href=\"https://doi.org/10.1137/22M1489071\">10.1137/22M1489071</a>","apa":"Edelsbrunner, H., Garber, A., Ghafaris, M., Heiss, T., Saghafiant, M., &#38; Wintraecken, M. (2024). Brillouin zones of integer lattices and their perturbations. <i>SIAM Journal on Discrete Mathematics</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/22M1489071\">https://doi.org/10.1137/22M1489071</a>","chicago":"Edelsbrunner, Herbert, Alexey Garber, Mohadese Ghafaris, Teresa Heiss, Morteza Saghafiant, and Mathijs Wintraecken. “Brillouin Zones of Integer Lattices and Their Perturbations.” <i>SIAM Journal on Discrete Mathematics</i>. Society for Industrial and Applied Mathematics, 2024. <a href=\"https://doi.org/10.1137/22M1489071\">https://doi.org/10.1137/22M1489071</a>.","short":"H. Edelsbrunner, A. Garber, M. Ghafaris, T. Heiss, M. Saghafiant, M. Wintraecken, SIAM Journal on Discrete Mathematics 38 (2024) 1784–1807.","ieee":"H. Edelsbrunner, A. Garber, M. Ghafaris, T. Heiss, M. Saghafiant, and M. Wintraecken, “Brillouin zones of integer lattices and their perturbations,” <i>SIAM Journal on Discrete Mathematics</i>, vol. 38, no. 2. Society for Industrial and Applied Mathematics, pp. 1784–1807, 2024.","mla":"Edelsbrunner, Herbert, et al. “Brillouin Zones of Integer Lattices and Their Perturbations.” <i>SIAM Journal on Discrete Mathematics</i>, vol. 38, no. 2, Society for Industrial and Applied Mathematics, 2024, pp. 1784–807, doi:<a href=\"https://doi.org/10.1137/22M1489071\">10.1137/22M1489071</a>."},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2204.01077","open_access":"1"}],"publication":"SIAM Journal on Discrete Mathematics","author":[{"last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"last_name":"Garber","first_name":"Alexey","full_name":"Garber, Alexey"},{"full_name":"Ghafaris, Mohadese","first_name":"Mohadese","last_name":"Ghafaris"},{"last_name":"Heiss","first_name":"Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1780-2689","full_name":"Heiss, Teresa"},{"last_name":"Saghafiant","first_name":"Morteza","full_name":"Saghafiant, Morteza"},{"orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","last_name":"Wintraecken","first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"date_updated":"2026-10-02T11:49:10Z","das_tickbox":"0","abstract":[{"lang":"eng","text":"For a locally finite set, 𝐴⊆ℝ𝑑\r\n, the 𝑘\r\nth Brillouin zone of 𝑎∈𝐴\r\n is the region of points 𝑥∈ℝ𝑑\r\n for which ‖𝑥−𝑎‖\r\n is the 𝑘\r\nth smallest among the Euclidean distances between 𝑥\r\n and the points in 𝐴\r\n. If 𝐴\r\n is a lattice, the 𝑘\r\nth Brillouin zones of the points in 𝐴\r\n are translates of each other, and together they tile space. Depending on the value of 𝑘\r\n, they express medium- or long-range order in the set. We study fundamental geometric and combinatorial properties of Brillouin zones, focusing on the integer lattice and its perturbations. Our results include the stability of a Brillouin zone under perturbations, a linear upper bound on the number of chambers in a zone for lattices in ℝ2\r\n, and the convergence of the maximum volume of a chamber to zero for the integer lattice."}],"scopus_import":"1","doi":"10.1137/22M1489071","day":"07","date_published":"2024-06-07T00:00:00Z","acknowledgement":"The second author is partially supported by the Alexander von Humboldt Foundation. The sixth author is supported by the European Union's Horizon 2020 research and innovation programme under Marie Sklodowska-Curie grant agreement 754411, and by Austrian Science Fund(FWF) grant M-3073. All other authors are supported by European Research Council (ERC) grant 788183, by the Wittgenstein Prize, by Austrian Science Fund (FWF) grant Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF) grant I 02979-N35.","_id":"17190","department":[{"_id":"HeEd"}],"month":"06","oa_version":"Preprint","publisher":"Society for Industrial and Applied Mathematics","external_id":{"arxiv":["2204.01077"],"isi":["001292728600001"]},"intvolume":"        38","volume":38,"researchdata_availability":"no","article_type":"original","publication_identifier":{"issn":["0895-4801"]},"quality_controlled":"1","issue":"2"},{"acknowledgement":"I was supported by the European Research Council (ERC) Horizon 2020 project\r\n“Alpha Shape Theory Extended” No. 788183 and by the Pöttinger Scholarship. In addition,\r\nI am very thankful for having been able to attend the second Workshop for Women in\r\nComputational Topology in July 2019, funded by the Mathematical Sciences Institute at\r\nANU, the US National Science Foundation through the award CCF-1841455, the Australian\r\nMathematical Sciences Institute and the Association for Women in Mathematics. Two of the\r\nprojects presented in this thesis started there. One of them reached completion thanks to\r\nfunding from the MSRI Summer Research in Mathematics program awarded to me and my\r\ncollaborators in 2020.","alternative_title":["ISTA Thesis"],"department":[{"_id":"GradSch"},{"_id":"HeEd"}],"_id":"18667","publisher":"Institute of Science and Technology Austria","month":"12","oa_version":"Published Version","publication_identifier":{"issn":["2663-337X"],"isbn":["978-3-99078-052-7"]},"researchdata_availability":"no","citation":{"mla":"Heiss, Teresa. <i>New Methods for Applying Topological Data Analysis to Materials Science</i>. Institute of Science and Technology Austria, 2024, doi:<a href=\"https://doi.org/10.15479/at:ista:18667\">10.15479/at:ista:18667</a>.","short":"T. Heiss, New Methods for Applying Topological Data Analysis to Materials Science, Institute of Science and Technology Austria, 2024.","ieee":"T. Heiss, “New methods for applying topological data analysis to materials science,” Institute of Science and Technology Austria, 2024.","chicago":"Heiss, Teresa. “New Methods for Applying Topological Data Analysis to Materials Science.” Institute of Science and Technology Austria, 2024. <a href=\"https://doi.org/10.15479/at:ista:18667\">https://doi.org/10.15479/at:ista:18667</a>.","apa":"Heiss, T. (2024). <i>New methods for applying topological data analysis to materials science</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:18667\">https://doi.org/10.15479/at:ista:18667</a>","ama":"Heiss T. New methods for applying topological data analysis to materials science. 2024. doi:<a href=\"https://doi.org/10.15479/at:ista:18667\">10.15479/at:ista:18667</a>","ista":"Heiss T. 2024. New methods for applying topological data analysis to materials science. Institute of Science and Technology Austria."},"year":"2024","date_created":"2024-12-17T16:17:55Z","supervisor":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner"}],"author":[{"full_name":"Heiss, Teresa","orcid":"0000-0002-1780-2689","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","first_name":"Teresa","last_name":"Heiss"}],"date_updated":"2026-10-02T11:55:42Z","das_tickbox":"0","abstract":[{"lang":"eng","text":"Many chemical and physical properties of materials are determined by the material’s shape,\r\nfor example the size of its pores and the width of its tunnels. This makes materials science\r\na prime application area for geometrical and topological methods. Nevertheless many\r\nmethods in topological data analysis have not been satisfyingly extended to the needs of\r\nmaterials science. This thesis provides new methods and new mathematical theorems\r\ntargeted at those specific needs by answering four different research questions. While the\r\nmotivation for each of the research questions arises from materials science, the methods\r\nare versatile and can be applied in different areas as well. \r\n\r\nThe first research question is concerned with image data, for example a three-dimensional\r\ncomputed tomography (CT) scan of a material, like sand or stone. There are two commonly\r\nused topologies for digital images and depending on the application either of them might be\r\nrequired. However, software for computing the topological data analysis method persistence\r\nhomology, usually supports only one of the two topologies. We answer the question how to\r\ncompute persistent homology of an image with respect to one of the two topologies using\r\nsoftware that is intended for the other topology. \r\n\r\nThe second research question is concerned with image data as well, and asks how much\r\nof the topological information of an image is lost when the resolution is coarsened. As\r\ncomputer tomography scanners are more expensive the higher the resolution, it is an\r\nimportant question in materials science to know which resolution is enough to get satisfying\r\npersistent homology. We give theoretical bounds on the information loss based on different\r\ngeometrical properties of the object to be scanned. In addition, we conduct experiments on\r\nsand and stone CT image data. \r\n\r\nThe third research question is motivated by comparing crystalline materials efficiently. As\r\nthe atoms within a crystal repeat periodically, crystalline materials are either modeled by\r\nunmanageable infinite periodic point sets, or by one of their fundamental domains, which is\r\nunstable under perturbation. Therefore a fingerprint of crystalline materials is needed, with\r\nappropriate properties such that comparing the crystals can be eased by comparing the\r\nfingerprints instead. We define the density fingerprint and prove the necessary properties. \r\n\r\nThe fourth research question is motivated by studying the hole-structure or connectedness,\r\ni.e. persistent homology or merge trees, of crystalline materials. A common way to deal\r\nwith periodicity is to take a fundamental domain and identify opposite boundaries to form a\r\ntorus. However, computing persistent homology or merge trees on that torus loses some\r\nof the information materials scientists are interested in and is additionally not stable under\r\ncertain noise. We therefore decorate the merge tree stemming from the torus with additional\r\ninformation describing the density and growth rate of the periodic copies of a component\r\nwithin a growing spherical window. We prove all desired properties, like stability and efficient\r\ncomputability."}],"date_published":"2024-12-17T00:00:00Z","day":"17","doi":"10.15479/at:ista:18667","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"language":[{"iso":"eng"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","page":"111","related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"10828"},{"id":"11440","status":"public","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","status":"public","id":"9345"},{"status":"public","id":"18673","relation":"part_of_dissertation"}]},"oa":1,"has_accepted_license":"1","article_processing_charge":"No","file_date_updated":"2024-12-19T10:24:50Z","keyword":["persistent homology","topological data analysis","periodic","crystalline materials","images","fingerprint"],"corr_author":"1","OA_place":"publisher","supplementarymaterial":"no","degree_awarded":"PhD","ec_funded":1,"ddc":["514","516","004"],"type":"dissertation","status":"public","fulldoi":"https://doi.org/10.15479/at:ista:18667","publication_status":"published","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020"}],"title":"New methods for applying topological data analysis to materials science","file":[{"date_updated":"2024-12-19T10:24:46Z","relation":"main_file","success":1,"content_type":"application/pdf","date_created":"2024-12-19T10:24:46Z","access_level":"open_access","file_name":"Teresa_Heiss_PhD_Thesis_final.pdf","file_size":7752253,"file_id":"18686","creator":"theiss","checksum":"247bb057aed2fba1cd4711917aaa2d77"},{"file_id":"18687","file_size":17197731,"creator":"theiss","checksum":"9648b45c07a008ee11a07f99856a139d","relation":"source_file","date_updated":"2024-12-19T10:24:50Z","date_created":"2024-12-19T10:24:50Z","content_type":"application/zip","file_name":"PhD_Thesis.zip","access_level":"closed"}],"doi_confirm":"1"},{"corr_author":"1","OA_place":"repository","supplementarymaterial":"no","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"language":[{"iso":"eng"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","related_material":{"record":[{"status":"public","id":"18667","relation":"dissertation_contains"}]},"oa":1,"article_processing_charge":"No","arxiv":1,"fulldoi":"https://doi.org/10.48550/arXiv.2408.16575","publication_status":"draft","title":"Merge trees of periodic filtrations","project":[{"call_identifier":"H2020","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended"},{"call_identifier":"FWF","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes"}],"ec_funded":1,"type":"preprint","status":"public","researchdata_availability":"no","acknowledgement":"Both authors are partially supported by the European Research Council (ERC) Horizon 2020 project\r\n‘Alpha Shape Theory Extended’, grant no. 788183. The first author is also partially supported by the DFG\r\nCollaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund\r\n(FWF), grant no. I 02979-N35.","department":[{"_id":"HeEd"}],"_id":"18673","month":"08","oa_version":"Preprint","external_id":{"arxiv":["2408.16575"]},"das_tickbox":"0","abstract":[{"text":"Motivated by applications to crystalline materials, we generalize the merge tree and the related barcode of a filtered complex to the periodic setting in Euclidean space. They are invariant under isometries, changing bases, and indeed changing lattices. In addition, we prove stability under perturbations and provide an algorithm that under mild geometric conditions typically satisfied by crystalline materials takes O((n+m)logn) time, in which n and m are the numbers of vertices and edges in the quotient complex, respectively.\r\n","lang":"eng"}],"day":"29","date_published":"2024-08-29T00:00:00Z","doi":"10.48550/arXiv.2408.16575","citation":{"chicago":"Edelsbrunner, Herbert, and Teresa Heiss. “Merge Trees of Periodic Filtrations.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2408.16575\">https://doi.org/10.48550/arXiv.2408.16575</a>.","ieee":"H. Edelsbrunner and T. Heiss, “Merge trees of periodic filtrations,” <i>arXiv</i>. .","short":"H. Edelsbrunner, T. Heiss, ArXiv (n.d.).","mla":"Edelsbrunner, Herbert, and Teresa Heiss. “Merge Trees of Periodic Filtrations.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/arXiv.2408.16575\">10.48550/arXiv.2408.16575</a>.","ama":"Edelsbrunner H, Heiss T. Merge trees of periodic filtrations. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2408.16575\">10.48550/arXiv.2408.16575</a>","ista":"Edelsbrunner H, Heiss T. Merge trees of periodic filtrations. arXiv, <a href=\"https://doi.org/10.48550/arXiv.2408.16575\">10.48550/arXiv.2408.16575</a>.","apa":"Edelsbrunner, H., &#38; Heiss, T. (n.d.). Merge trees of periodic filtrations. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2408.16575\">https://doi.org/10.48550/arXiv.2408.16575</a>"},"date_created":"2024-12-18T14:06:57Z","year":"2024","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2408.16575"}],"publication":"arXiv","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"last_name":"Heiss","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","first_name":"Teresa","orcid":"0000-0002-1780-2689","full_name":"Heiss, Teresa"}],"date_updated":"2026-10-02T11:55:43Z"},{"scopus_import":"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."}],"editor":[{"last_name":"Gasparovic","first_name":"Ellen","full_name":"Gasparovic, Ellen"},{"last_name":"Robins","first_name":"Vanessa","full_name":"Robins, Vanessa"},{"last_name":"Turner","first_name":"Katharine","full_name":"Turner, Katharine"}],"day":"27","date_published":"2022-01-27T00:00:00Z","doi":"10.1007/978-3-030-95519-9_1","author":[{"first_name":"Bea","last_name":"Bleile","full_name":"Bleile, Bea"},{"last_name":"Garin","first_name":"Adélie","full_name":"Garin, Adélie"},{"orcid":"0000-0002-1780-2689","full_name":"Heiss, Teresa","last_name":"Heiss","first_name":"Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Maggs, Kelly","first_name":"Kelly","last_name":"Maggs"},{"full_name":"Robins, Vanessa","last_name":"Robins","first_name":"Vanessa"}],"date_updated":"2026-10-02T11:24:32Z","citation":{"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>.","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.","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.","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.","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>","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>"},"year":"2022","series_title":"AWMS","date_created":"2022-06-07T08:21:11Z","publication":"Research in Computational Topology 2","main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2102.11397"}],"quality_controlled":"1","intvolume":"        30","place":"Cham","publication_identifier":{"isbn":["9783030955182"],"eisbn":["9783030955199"]},"volume":30,"publisher":"Springer Nature","oa_version":"Preprint","month":"01","external_id":{"arxiv":["2102.11397"]},"edition":"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.","alternative_title":["Association for Women in Mathematics Series"],"department":[{"_id":"HeEd"}],"_id":"11440","publication_status":"published","project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","call_identifier":"H2020"}],"title":"The persistent homology of dual digital image constructions","arxiv":1,"fulldoi":"https://doi.org/10.1007/978-3-030-95519-9_1","status":"public","ec_funded":1,"type":"book_chapter","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"18667"}]},"oa":1,"article_processing_charge":"No","language":[{"iso":"eng"}],"page":"1-26","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"page":"3824-3834","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","language":[{"iso":"eng"}],"article_processing_charge":"No","oa":1,"related_material":{"record":[{"status":"public","id":"18667","relation":"dissertation_contains"}]},"fulldoi":"https://doi.org/10.1109/BigData52589.2021.9671483","arxiv":1,"isi":1,"title":"The impact of changes in resolution on the persistent homology of images","publication_status":"published","type":"conference","status":"public","publication_identifier":{"isbn":["9781665439022"]},"quality_controlled":"1","_id":"10828","department":[{"_id":"HeEd"}],"conference":{"name":"Big Data: International Conference on Big Data","end_date":"2021-12-18","start_date":"2021-12-15","location":"Orlando, FL, United States; Virtuell"},"external_id":{"isi":["000800559503126"],"arxiv":["2111.05663"]},"month":"01","oa_version":"Preprint","publisher":"IEEE","doi":"10.1109/BigData52589.2021.9671483","day":"13","date_published":"2022-01-13T00:00:00Z","scopus_import":"1","abstract":[{"text":"Digital images enable quantitative analysis of material properties at micro and macro length scales, but choosing an appropriate resolution when acquiring the image is challenging. A high resolution means longer image acquisition and larger data requirements for a given sample, but if the resolution is too low, significant information may be lost. This paper studies the impact of changes in resolution on persistent homology, a tool from topological data analysis that provides a signature of structure in an image across all length scales. Given prior information about a function, the geometry of an object, or its density distribution at a given resolution, we provide methods to select the coarsest resolution yielding results within an acceptable tolerance. We present numerical case studies for an illustrative synthetic example and samples from porous materials where the theoretical bounds are unknown.","lang":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/2111.05663","open_access":"1"}],"publication":"2021 IEEE International Conference on Big Data","year":"2022","date_created":"2022-03-06T23:01:53Z","citation":{"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>","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.","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>","short":"T. Heiss, S. Tymochko, B. Story, A. Garin, H. Bui, B. Bleile, V. Robins, in:, 2021 IEEE International Conference on Big Data, IEEE, 2022, pp. 3824–3834.","ieee":"T. Heiss <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.","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>.","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>."},"date_updated":"2026-10-02T11:24:32Z","author":[{"full_name":"Heiss, Teresa","orcid":"0000-0002-1780-2689","first_name":"Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","last_name":"Heiss"},{"full_name":"Tymochko, Sarah","last_name":"Tymochko","first_name":"Sarah"},{"full_name":"Story, Brittany","last_name":"Story","first_name":"Brittany"},{"last_name":"Garin","first_name":"Adélie","full_name":"Garin, Adélie"},{"first_name":"Hoa","last_name":"Bui","full_name":"Bui, Hoa"},{"last_name":"Bleile","first_name":"Bea","full_name":"Bleile, Bea"},{"first_name":"Vanessa","last_name":"Robins","full_name":"Robins, Vanessa"}]},{"citation":{"chicago":"Adams, Henry, Hana Kourimska, Teresa Heiss, Sarah Percival, and Lori Ziegelmeier. “How to Tutorial-a-Thon.” <i>Notices of the American Mathematical Society</i>. American Mathematical Society, 2021. <a href=\"https://doi.org/10.1090/noti2349\">https://doi.org/10.1090/noti2349</a>.","mla":"Adams, Henry, et al. “How to Tutorial-a-Thon.” <i>Notices of the American Mathematical Society</i>, vol. 68, no. 9, American Mathematical Society, 2021, pp. 1511–14, doi:<a href=\"https://doi.org/10.1090/noti2349\">10.1090/noti2349</a>.","ieee":"H. Adams, H. Kourimska, T. Heiss, S. Percival, and L. Ziegelmeier, “How to tutorial-a-thon,” <i>Notices of the American Mathematical Society</i>, vol. 68, no. 9. American Mathematical Society, pp. 1511–1514, 2021.","short":"H. Adams, H. Kourimska, T. Heiss, S. Percival, L. Ziegelmeier, Notices of the American Mathematical Society 68 (2021) 1511–1514.","ama":"Adams H, Kourimska H, Heiss T, Percival S, Ziegelmeier L. How to tutorial-a-thon. <i>Notices of the American Mathematical Society</i>. 2021;68(9):1511-1514. doi:<a href=\"https://doi.org/10.1090/noti2349\">10.1090/noti2349</a>","ista":"Adams H, Kourimska H, Heiss T, Percival S, Ziegelmeier L. 2021. How to tutorial-a-thon. Notices of the American Mathematical Society. 68(9), 1511–1514.","apa":"Adams, H., Kourimska, H., Heiss, T., Percival, S., &#38; Ziegelmeier, L. (2021). How to tutorial-a-thon. <i>Notices of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/noti2349\">https://doi.org/10.1090/noti2349</a>"},"date_created":"2021-10-03T22:01:22Z","year":"2021","publication":"Notices of the American Mathematical Society","main_file_link":[{"open_access":"1","url":"http://www.ams.org/notices/"}],"author":[{"first_name":"Henry","last_name":"Adams","full_name":"Adams, Henry"},{"last_name":"Kourimska","first_name":"Hana","id":"D9B8E14C-3C26-11EA-98F5-1F833DDC885E","orcid":"0000-0001-7841-0091","full_name":"Kourimska, Hana"},{"orcid":"0000-0002-1780-2689","full_name":"Heiss, Teresa","last_name":"Heiss","first_name":"Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Percival, Sarah","last_name":"Percival","first_name":"Sarah"},{"full_name":"Ziegelmeier, Lori","first_name":"Lori","last_name":"Ziegelmeier"}],"date_updated":"2026-06-18T08:36:13Z","scopus_import":"1","day":"01","date_published":"2021-10-01T00:00:00Z","doi":"10.1090/noti2349","department":[{"_id":"HeEd"}],"alternative_title":["Early Career"],"_id":"10071","publisher":"American Mathematical Society","oa_version":"Published Version","month":"10","intvolume":"        68","publication_identifier":{"eissn":["1088-9477"],"issn":["0002-9920"]},"article_type":"letter_note","volume":68,"quality_controlled":"1","issue":"9","ddc":["500"],"type":"journal_article","status":"public","fulldoi":"https://doi.org/10.1090/noti2349","publication_status":"published","title":"How to tutorial-a-thon","language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"1511-1514","oa":1,"article_processing_charge":"No"},{"page":"32:1-32:16","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"has_accepted_license":"1","article_processing_charge":"No","file_date_updated":"2021-04-22T08:08:14Z","oa":1,"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"18667"}]},"type":"conference","ddc":["004","516"],"ec_funded":1,"status":"public","fulldoi":"https://doi.org/10.4230/LIPIcs.SoCG.2021.32","file":[{"checksum":"1787baef1523d6d93753b90d0c109a6d","creator":"mwintrae","file_size":3117435,"file_id":"9346","file_name":"df_socg_final_version.pdf","access_level":"open_access","date_created":"2021-04-22T08:08:14Z","content_type":"application/pdf","success":1,"relation":"main_file","date_updated":"2021-04-22T08:08:14Z"}],"title":"The density fingerprint of a periodic point set","project":[{"call_identifier":"H2020","name":"Alpha Shape Theory Extended","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"name":"Persistent Homology, Algorithms and Stochastic Geometry","grant_number":"I4887","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316"},{"name":"Synaptic communication in neuronal microcircuits","grant_number":"Z00312","_id":"25C5A090-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}],"publication_status":"published","_id":"9345","alternative_title":["LIPIcs"],"department":[{"_id":"HeEd"}],"acknowledgement":"The authors thank Janos Pach for insightful discussions on the topic of thispaper, Morteza Saghafian for finding the one-dimensional counterexample mentioned in Section 5,and Larry Andrews for generously sharing his crystallographic perspective.","conference":{"start_date":"2021-06-07","name":"SoCG: Symposium on Computational Geometry","end_date":"2021-06-11","location":"Virtual"},"oa_version":"Published Version","month":"06","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","volume":189,"publication_identifier":{"issn":["1868-8969"]},"intvolume":"       189","quality_controlled":"1","publication":"37th International Symposium on Computational Geometry","date_created":"2021-04-22T08:09:58Z","year":"2021","citation":{"ieee":"H. Edelsbrunner, T. Heiss, V.  Kurlin , P. Smith, and M. Wintraecken, “The density fingerprint of a periodic point set,” in <i>37th International Symposium on Computational Geometry</i>, Virtual, 2021, vol. 189, p. 32:1-32:16.","short":"H. Edelsbrunner, T. Heiss, V.  Kurlin , P. Smith, M. Wintraecken, in:, 37th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, p. 32:1-32:16.","mla":"Edelsbrunner, Herbert, et al. “The Density Fingerprint of a Periodic Point Set.” <i>37th International Symposium on Computational Geometry</i>, vol. 189, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, p. 32:1-32:16, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2021.32\">10.4230/LIPIcs.SoCG.2021.32</a>.","chicago":"Edelsbrunner, Herbert, Teresa Heiss, Vitaliy  Kurlin , Philip Smith, and Mathijs Wintraecken. “The Density Fingerprint of a Periodic Point Set.” In <i>37th International Symposium on Computational Geometry</i>, 189:32:1-32:16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2021.32\">https://doi.org/10.4230/LIPIcs.SoCG.2021.32</a>.","apa":"Edelsbrunner, H., Heiss, T.,  Kurlin , V., Smith, P., &#38; Wintraecken, M. (2021). The density fingerprint of a periodic point set. In <i>37th International Symposium on Computational Geometry</i> (Vol. 189, p. 32:1-32:16). Virtual: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2021.32\">https://doi.org/10.4230/LIPIcs.SoCG.2021.32</a>","ama":"Edelsbrunner H, Heiss T,  Kurlin  V, Smith P, Wintraecken M. The density fingerprint of a periodic point set. In: <i>37th International Symposium on Computational Geometry</i>. Vol 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021:32:1-32:16. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2021.32\">10.4230/LIPIcs.SoCG.2021.32</a>","ista":"Edelsbrunner H, Heiss T,  Kurlin  V, Smith P, Wintraecken M. 2021. The density fingerprint of a periodic point set. 37th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 189, 32:1-32:16."},"date_updated":"2026-10-02T11:24:33Z","author":[{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","last_name":"Heiss","full_name":"Heiss, Teresa","orcid":"0000-0002-1780-2689"},{"first_name":"Vitaliy","last_name":" Kurlin ","full_name":" Kurlin , Vitaliy"},{"full_name":"Smith, Philip","last_name":"Smith","first_name":"Philip"},{"last_name":"Wintraecken","first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs"}],"das_tickbox":"1","doi":"10.4230/LIPIcs.SoCG.2021.32","date_published":"2021-06-02T00:00:00Z","day":"02","scopus_import":"1","abstract":[{"lang":"eng","text":"Modeling a crystal as a periodic point set, we present a fingerprint consisting of density functionsthat facilitates the efficient search for new materials and material properties. We prove invarianceunder isometries, continuity, and completeness in the generic case, which are necessary featuresfor the reliable comparison of crystals. The proof of continuity integrates methods from discretegeometry and lattice theory, while the proof of generic completeness combines techniques fromgeometry with analysis. The fingerprint has a fast algorithm based on Brillouin zones and relatedinclusion-exclusion formulae. We have implemented the algorithm and describe its application tocrystal structure prediction."}]},{"publication_identifier":{"issn":["0302-9743"]},"volume":10424,"intvolume":"     10424","quality_controlled":"1","alternative_title":["LNCS"],"department":[{"_id":"HeEd"}],"_id":"833","external_id":{"arxiv":["1705.02045"],"isi":["000432085900032"]},"conference":{"location":"Ystad, Sweden","start_date":"2017-08-22","name":"CAIP: Computer Analysis of Images and Patterns","end_date":"2017-08-24"},"publisher":"Springer","oa_version":"Submitted Version","month":"07","day":"28","editor":[{"full_name":"Felsberg, Michael","last_name":"Felsberg","first_name":"Michael"},{"first_name":"Anders","last_name":"Heyden","full_name":"Heyden, Anders"},{"last_name":"Krüger","first_name":"Norbert","full_name":"Krüger, Norbert"}],"date_published":"2017-07-28T00:00:00Z","doi":"10.1007/978-3-319-64689-3_32","scopus_import":"1","abstract":[{"text":"We present an efficient algorithm to compute Euler characteristic curves of gray scale images of arbitrary dimension. In various applications the Euler characteristic curve is used as a descriptor of an image. Our algorithm is the first streaming algorithm for Euler characteristic curves. The usage of streaming removes the necessity to store the entire image in RAM. Experiments show that our implementation handles terabyte scale images on commodity hardware. Due to lock-free parallelism, it scales well with the number of processor cores. Additionally, we put the concept of the Euler characteristic curve in the wider context of computational topology. In particular, we explain the connection with persistence diagrams.","lang":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/1705.02045","open_access":"1"}],"citation":{"mla":"Heiss, Teresa, and Hubert Wagner. <i>Streaming Algorithm for Euler Characteristic Curves of Multidimensional Images</i>. Edited by Michael Felsberg et al., vol. 10424, Springer, 2017, pp. 397–409, doi:<a href=\"https://doi.org/10.1007/978-3-319-64689-3_32\">10.1007/978-3-319-64689-3_32</a>.","short":"T. Heiss, H. Wagner, in:, M. Felsberg, A. Heyden, N. Krüger (Eds.), Springer, 2017, pp. 397–409.","ieee":"T. Heiss and H. Wagner, “Streaming algorithm for Euler characteristic curves of multidimensional images,” presented at the CAIP: Computer Analysis of Images and Patterns, Ystad, Sweden, 2017, vol. 10424, pp. 397–409.","chicago":"Heiss, Teresa, and Hubert Wagner. “Streaming Algorithm for Euler Characteristic Curves of Multidimensional Images.” edited by Michael Felsberg, Anders Heyden, and Norbert Krüger, 10424:397–409. Springer, 2017. <a href=\"https://doi.org/10.1007/978-3-319-64689-3_32\">https://doi.org/10.1007/978-3-319-64689-3_32</a>.","apa":"Heiss, T., &#38; Wagner, H. (2017). Streaming algorithm for Euler characteristic curves of multidimensional images. In M. Felsberg, A. Heyden, &#38; N. Krüger (Eds.) (Vol. 10424, pp. 397–409). Presented at the CAIP: Computer Analysis of Images and Patterns, Ystad, Sweden: Springer. <a href=\"https://doi.org/10.1007/978-3-319-64689-3_32\">https://doi.org/10.1007/978-3-319-64689-3_32</a>","ista":"Heiss T, Wagner H. 2017. Streaming algorithm for Euler characteristic curves of multidimensional images. CAIP: Computer Analysis of Images and Patterns, LNCS, vol. 10424, 397–409.","ama":"Heiss T, Wagner H. Streaming algorithm for Euler characteristic curves of multidimensional images. In: Felsberg M, Heyden A, Krüger N, eds. Vol 10424. Springer; 2017:397-409. doi:<a href=\"https://doi.org/10.1007/978-3-319-64689-3_32\">10.1007/978-3-319-64689-3_32</a>"},"year":"2017","date_created":"2018-12-11T11:48:45Z","date_updated":"2025-06-04T09:54:22Z","author":[{"last_name":"Heiss","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","first_name":"Teresa","orcid":"0000-0002-1780-2689","full_name":"Heiss, Teresa"},{"first_name":"Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","full_name":"Wagner, Hubert"}],"corr_author":"1","language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"397 - 409","article_processing_charge":"No","oa":1,"arxiv":1,"publist_id":"6815","fulldoi":"https://doi.org/10.1007/978-3-319-64689-3_32","isi":1,"publication_status":"published","title":"Streaming algorithm for Euler characteristic curves of multidimensional images","type":"conference","status":"public"}]