[{"author":[{"first_name":"Ilaria","last_name":"Castellano","full_name":"Castellano, Ilaria"},{"full_name":"Giordano Bruno, Anna","first_name":"Anna","last_name":"Giordano Bruno"},{"last_name":"Zava","first_name":"Nicolò","orcid":"0000-0001-8686-1888","id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad","full_name":"Zava, Nicolò"}],"language":[{"iso":"eng"}],"doi":"10.1016/j.tcs.2023.114129","publication_status":"published","oa":1,"intvolume":"       977","year":"2023","date_created":"2023-09-24T22:01:11Z","article_type":"original","day":"25","corr_author":"1","publication":"Theoretical Computer Science","department":[{"_id":"HeEd"}],"_id":"14362","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"isi":["001076934000001"],"arxiv":["2212.08424"]},"quality_controlled":"1","date_updated":"2024-10-09T21:07:00Z","month":"10","volume":977,"title":"Weakly weighted generalised quasi-metric spaces and semilattices","isi":1,"arxiv":1,"date_published":"2023-10-25T00:00:00Z","article_processing_charge":"No","publication_identifier":{"issn":["0304-3975"]},"type":"journal_article","status":"public","oa_version":"Preprint","article_number":"114129","abstract":[{"lang":"eng","text":"Motivated by recent applications to entropy theory in dynamical systems, we generalise notions introduced by Matthews and define weakly weighted and componentwise weakly weighted (generalised) quasi-metrics. We then systematise and extend to full generality the correspondences between these objects and other structures arising in theoretical computer science and dynamics. In particular, we study the correspondences with weak partial metrics and, if the underlying space is a semilattice, with invariant (generalised) quasi-metrics satisfying the descending path condition, and with strictly monotone semi(-co-)valuations.\r\nWe conclude discussing, for endomorphisms of generalised quasi-metric semilattices, a generalisation of both the known intrinsic semilattice entropy and the semigroup entropy."}],"citation":{"ama":"Castellano I, Giordano Bruno A, Zava N. Weakly weighted generalised quasi-metric spaces and semilattices. <i>Theoretical Computer Science</i>. 2023;977. doi:<a href=\"https://doi.org/10.1016/j.tcs.2023.114129\">10.1016/j.tcs.2023.114129</a>","ieee":"I. Castellano, A. Giordano Bruno, and N. Zava, “Weakly weighted generalised quasi-metric spaces and semilattices,” <i>Theoretical Computer Science</i>, vol. 977. Elsevier, 2023.","mla":"Castellano, Ilaria, et al. “Weakly Weighted Generalised Quasi-Metric Spaces and Semilattices.” <i>Theoretical Computer Science</i>, vol. 977, 114129, Elsevier, 2023, doi:<a href=\"https://doi.org/10.1016/j.tcs.2023.114129\">10.1016/j.tcs.2023.114129</a>.","ista":"Castellano I, Giordano Bruno A, Zava N. 2023. Weakly weighted generalised quasi-metric spaces and semilattices. Theoretical Computer Science. 977, 114129.","short":"I. Castellano, A. Giordano Bruno, N. Zava, Theoretical Computer Science 977 (2023).","apa":"Castellano, I., Giordano Bruno, A., &#38; Zava, N. (2023). Weakly weighted generalised quasi-metric spaces and semilattices. <i>Theoretical Computer Science</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.tcs.2023.114129\">https://doi.org/10.1016/j.tcs.2023.114129</a>","chicago":"Castellano, Ilaria, Anna Giordano Bruno, and Nicolò Zava. “Weakly Weighted Generalised Quasi-Metric Spaces and Semilattices.” <i>Theoretical Computer Science</i>. Elsevier, 2023. <a href=\"https://doi.org/10.1016/j.tcs.2023.114129\">https://doi.org/10.1016/j.tcs.2023.114129</a>."},"scopus_import":"1","publisher":"Elsevier","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2212.08424 ","open_access":"1"}]},{"abstract":[{"text":"Given a triangle Δ, we study the problem of determining the smallest enclosing and largest embedded isosceles triangles of Δ with respect to area and perimeter. This problem was initially posed by Nandakumar [17, 22] and was first studied by Kiss, Pach, and Somlai [13], who showed that if Δ′ is the smallest area isosceles triangle containing Δ, then Δ′ and Δ share a side and an angle. In the present paper, we prove that for any triangle Δ, every maximum area isosceles triangle embedded in Δ and every maximum perimeter isosceles triangle embedded in Δ shares a side and an angle with Δ. Somewhat surprisingly, the case of minimum perimeter enclosing triangles is different: there are infinite families of triangles Δ whose minimum perimeter isosceles containers do not share a side and an angle with Δ.","lang":"eng"}],"citation":{"ama":"Ambrus Á, Csikós M, Kiss G, Pach J, Somlai G. Optimal embedded and enclosing isosceles triangles. <i>International Journal of Foundations of Computer Science</i>. 2023;34(7):737-760. doi:<a href=\"https://doi.org/10.1142/S012905412342008X\">10.1142/S012905412342008X</a>","ieee":"Á. Ambrus, M. Csikós, G. Kiss, J. Pach, and G. Somlai, “Optimal embedded and enclosing isosceles triangles,” <i>International Journal of Foundations of Computer Science</i>, vol. 34, no. 7. World Scientific Publishing, pp. 737–760, 2023.","short":"Á. Ambrus, M. Csikós, G. Kiss, J. Pach, G. Somlai, International Journal of Foundations of Computer Science 34 (2023) 737–760.","ista":"Ambrus Á, Csikós M, Kiss G, Pach J, Somlai G. 2023. Optimal embedded and enclosing isosceles triangles. International Journal of Foundations of Computer Science. 34(7), 737–760.","mla":"Ambrus, Áron, et al. “Optimal Embedded and Enclosing Isosceles Triangles.” <i>International Journal of Foundations of Computer Science</i>, vol. 34, no. 7, World Scientific Publishing, 2023, pp. 737–60, doi:<a href=\"https://doi.org/10.1142/S012905412342008X\">10.1142/S012905412342008X</a>.","chicago":"Ambrus, Áron, Mónika Csikós, Gergely Kiss, János Pach, and Gábor Somlai. “Optimal Embedded and Enclosing Isosceles Triangles.” <i>International Journal of Foundations of Computer Science</i>. World Scientific Publishing, 2023. <a href=\"https://doi.org/10.1142/S012905412342008X\">https://doi.org/10.1142/S012905412342008X</a>.","apa":"Ambrus, Á., Csikós, M., Kiss, G., Pach, J., &#38; Somlai, G. (2023). Optimal embedded and enclosing isosceles triangles. <i>International Journal of Foundations of Computer Science</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S012905412342008X\">https://doi.org/10.1142/S012905412342008X</a>"},"scopus_import":"1","oa_version":"Preprint","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2205.11637","open_access":"1"}],"publisher":"World Scientific Publishing","status":"public","type":"journal_article","publication_identifier":{"eissn":["1793-6373"],"issn":["0129-0541"]},"volume":34,"article_processing_charge":"No","arxiv":1,"date_published":"2023-10-05T00:00:00Z","isi":1,"title":"Optimal embedded and enclosing isosceles triangles","quality_controlled":"1","date_updated":"2023-12-13T13:04:55Z","external_id":{"isi":["001080874400001"],"arxiv":["2205.11637"]},"month":"10","_id":"14464","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"issue":"7","page":"737-760","day":"05","publication":"International Journal of Foundations of Computer Science","year":"2023","article_type":"original","date_created":"2023-10-29T23:01:18Z","language":[{"iso":"eng"}],"author":[{"last_name":"Ambrus","first_name":"Áron","full_name":"Ambrus, Áron"},{"first_name":"Mónika","last_name":"Csikós","full_name":"Csikós, Mónika"},{"full_name":"Kiss, Gergely","last_name":"Kiss","first_name":"Gergely"},{"id":"E62E3130-B088-11EA-B919-BF823C25FEA4","full_name":"Pach, János","first_name":"János","last_name":"Pach"},{"first_name":"Gábor","last_name":"Somlai","full_name":"Somlai, Gábor"}],"intvolume":"        34","publication_status":"published","oa":1,"doi":"10.1142/S012905412342008X"},{"page":"191-221","department":[{"_id":"HeEd"}],"issue":"S1","_id":"14557","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication":"Quaestiones Mathematicae","day":"01","date_created":"2023-11-19T23:00:55Z","article_type":"original","year":"2023","doi":"10.2989/16073606.2023.2247731","project":[{"grant_number":"I04245","_id":"26AD5D90-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Algebraic Footprints of Geometric Features in Homology"}],"publication_status":"published","intvolume":"        46","author":[{"first_name":"D.","last_name":"Dikranjan","full_name":"Dikranjan, D."},{"first_name":"A.","last_name":"Giordano Bruno","full_name":"Giordano Bruno, A."},{"id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad","full_name":"Zava, Nicolò","first_name":"Nicolò","last_name":"Zava","orcid":"0000-0001-8686-1888"}],"language":[{"iso":"eng"}],"publisher":"Taylor & Francis","oa_version":"None","abstract":[{"lang":"eng","text":"Motivated by a problem posed in [10], we investigate the closure operators of the category SLatt of join semilattices and its subcategory SLattO of join semilattices with bottom element. In particular, we show that there are only finitely many closure operators of both categories, and provide a complete classification. We use this result to deduce the known fact that epimorphisms of SLatt and SLattO are surjective. We complement the paper with two different proofs of this result using either generators or Isbell’s zigzag theorem."}],"scopus_import":"1","citation":{"ama":"Dikranjan D, Giordano Bruno A, Zava N. Epimorphisms and closure operators of categories of semilattices. <i>Quaestiones Mathematicae</i>. 2023;46(S1):191-221. doi:<a href=\"https://doi.org/10.2989/16073606.2023.2247731\">10.2989/16073606.2023.2247731</a>","ieee":"D. Dikranjan, A. Giordano Bruno, and N. Zava, “Epimorphisms and closure operators of categories of semilattices,” <i>Quaestiones Mathematicae</i>, vol. 46, no. S1. Taylor &#38; Francis, pp. 191–221, 2023.","mla":"Dikranjan, D., et al. “Epimorphisms and Closure Operators of Categories of Semilattices.” <i>Quaestiones Mathematicae</i>, vol. 46, no. S1, Taylor &#38; Francis, 2023, pp. 191–221, doi:<a href=\"https://doi.org/10.2989/16073606.2023.2247731\">10.2989/16073606.2023.2247731</a>.","short":"D. Dikranjan, A. Giordano Bruno, N. Zava, Quaestiones Mathematicae 46 (2023) 191–221.","ista":"Dikranjan D, Giordano Bruno A, Zava N. 2023. Epimorphisms and closure operators of categories of semilattices. Quaestiones Mathematicae. 46(S1), 191–221.","apa":"Dikranjan, D., Giordano Bruno, A., &#38; Zava, N. (2023). Epimorphisms and closure operators of categories of semilattices. <i>Quaestiones Mathematicae</i>. Taylor &#38; Francis. <a href=\"https://doi.org/10.2989/16073606.2023.2247731\">https://doi.org/10.2989/16073606.2023.2247731</a>","chicago":"Dikranjan, D., A. Giordano Bruno, and Nicolò Zava. “Epimorphisms and Closure Operators of Categories of Semilattices.” <i>Quaestiones Mathematicae</i>. Taylor &#38; Francis, 2023. <a href=\"https://doi.org/10.2989/16073606.2023.2247731\">https://doi.org/10.2989/16073606.2023.2247731</a>."},"publication_identifier":{"issn":["1607-3606"],"eissn":["1727-933X"]},"type":"journal_article","status":"public","title":"Epimorphisms and closure operators of categories of semilattices","isi":1,"acknowledgement":"The first and second named authors are members of GNSAGA – INdAM.\r\nThe third named author was supported by the FWF Grant, Project number I4245–N35","article_processing_charge":"No","date_published":"2023-11-01T00:00:00Z","volume":46,"month":"11","external_id":{"isi":["001098712000006"]},"quality_controlled":"1","date_updated":"2025-09-09T13:23:12Z"},{"type":"journal_article","publication_identifier":{"eissn":["1939-3539"],"issn":["0162-8828"]},"status":"public","publisher":"IEEE","scopus_import":"1","keyword":["Applied Mathematics","Artificial Intelligence","Computational Theory and Mathematics","Computer Vision and Pattern Recognition","Software"],"citation":{"ieee":"D. Ali, A. Asaad, M.-J. Jimenez, V. Nanda, E. Paluzo-Hidalgo, and M. Soriano Trigueros, “A survey of vectorization methods in topological data analysis,” <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>, vol. 45, no. 12. IEEE, pp. 14069–14080, 2023.","ama":"Ali D, Asaad A, Jimenez M-J, Nanda V, Paluzo-Hidalgo E, Soriano Trigueros M. A survey of vectorization methods in topological data analysis. <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>. 2023;45(12):14069-14080. doi:<a href=\"https://doi.org/10.1109/tpami.2023.3308391\">10.1109/tpami.2023.3308391</a>","chicago":"Ali, Dashti, Aras Asaad, Maria-Jose Jimenez, Vidit Nanda, Eduardo Paluzo-Hidalgo, and Manuel Soriano Trigueros. “A Survey of Vectorization Methods in Topological Data Analysis.” <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>. IEEE, 2023. <a href=\"https://doi.org/10.1109/tpami.2023.3308391\">https://doi.org/10.1109/tpami.2023.3308391</a>.","apa":"Ali, D., Asaad, A., Jimenez, M.-J., Nanda, V., Paluzo-Hidalgo, E., &#38; Soriano Trigueros, M. (2023). A survey of vectorization methods in topological data analysis. <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>. IEEE. <a href=\"https://doi.org/10.1109/tpami.2023.3308391\">https://doi.org/10.1109/tpami.2023.3308391</a>","short":"D. Ali, A. Asaad, M.-J. Jimenez, V. Nanda, E. Paluzo-Hidalgo, M. Soriano Trigueros, IEEE Transactions on Pattern Analysis and Machine Intelligence 45 (2023) 14069–14080.","ista":"Ali D, Asaad A, Jimenez M-J, Nanda V, Paluzo-Hidalgo E, Soriano Trigueros M. 2023. A survey of vectorization methods in topological data analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence. 45(12), 14069–14080.","mla":"Ali, Dashti, et al. “A Survey of Vectorization Methods in Topological Data Analysis.” <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>, vol. 45, no. 12, IEEE, 2023, pp. 14069–80, doi:<a href=\"https://doi.org/10.1109/tpami.2023.3308391\">10.1109/tpami.2023.3308391</a>."},"abstract":[{"text":"Attempts to incorporate topological information in supervised learning tasks have resulted in the creation of several techniques for vectorizing persistent homology barcodes. In this paper, we study thirteen such methods. Besides describing an organizational framework for these methods, we comprehensively benchmark them against three well-known classification tasks. Surprisingly, we discover that the best-performing method is a simple vectorization, which consists only of a few elementary summary statistics. Finally, we provide a convenient web application which has been designed to facilitate exploration and experimentation with various vectorization methods.","lang":"eng"}],"oa_version":"Published Version","month":"12","external_id":{"isi":["001104973300002"]},"quality_controlled":"1","date_updated":"2025-09-09T14:08:56Z","title":"A survey of vectorization methods in topological data analysis","article_processing_charge":"Yes (in subscription journal)","date_published":"2023-12-01T00:00:00Z","acknowledgement":"The work of Maria-Jose Jimenez, Eduardo Paluzo-Hidalgo and Manuel Soriano-Trigueros was supported in part by the Spanish grant Ministerio de Ciencia e Innovacion under Grants TED2021-129438B-I00 and PID2019-107339GB-I00, and in part by REXASI-PRO H-EU project, call HORIZON-CL4-2021-HUMAN-01-01 under Grant 101070028. The work of\r\nMaria-Jose Jimenez was supported by a grant of Convocatoria de la Universidad de Sevilla para la recualificacion del sistema universitario español, 2021-23, funded by the European Union, NextGenerationEU. The work of Vidit Nanda was supported in part by EPSRC under Grant EP/R018472/1 and in part by US AFOSR under Grant FA9550-22-1-0462. \r\nWe are grateful to the team of GUDHI and TEASPOON developers, for their work and their support. We are also grateful to Streamlit for providing extra resources to deploy the web app\r\nonline on Streamlit community cloud. We thank the anonymous referees for their helpful suggestions.","isi":1,"volume":45,"publication":"IEEE Transactions on Pattern Analysis and Machine Intelligence","day":"01","page":"14069-14080","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","_id":"14739","issue":"12","department":[{"_id":"HeEd"}],"oa":1,"publication_status":"published","file":[{"content_type":"application/pdf","date_updated":"2024-01-08T10:09:14Z","relation":"main_file","file_size":2370988,"file_name":"2023_IEEEToP_Ali.pdf","access_level":"open_access","checksum":"465c28ef0b151b4b1fb47977ed5581ab","creator":"dernst","success":1,"file_id":"14740","date_created":"2024-01-08T10:09:14Z"}],"doi":"10.1109/tpami.2023.3308391","intvolume":"        45","file_date_updated":"2024-01-08T10:09:14Z","ddc":["000"],"language":[{"iso":"eng"}],"author":[{"full_name":"Ali, Dashti","last_name":"Ali","first_name":"Dashti"},{"full_name":"Asaad, Aras","last_name":"Asaad","first_name":"Aras"},{"full_name":"Jimenez, Maria-Jose","first_name":"Maria-Jose","last_name":"Jimenez"},{"full_name":"Nanda, Vidit","first_name":"Vidit","last_name":"Nanda"},{"full_name":"Paluzo-Hidalgo, Eduardo","first_name":"Eduardo","last_name":"Paluzo-Hidalgo"},{"full_name":"Soriano Trigueros, Manuel","id":"15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8","orcid":"0000-0003-2449-1433","last_name":"Soriano Trigueros","first_name":"Manuel"}],"date_created":"2024-01-08T09:59:46Z","article_type":"original","year":"2023"},{"year":"2023","date_created":"2023-05-14T22:01:00Z","article_type":"original","author":[{"first_name":"Jean Daniel","last_name":"Boissonnat","full_name":"Boissonnat, Jean Daniel"},{"full_name":"Kachanovich, Siargey","last_name":"Kachanovich","first_name":"Siargey"},{"orcid":"0000-0002-7472-2220","first_name":"Mathijs","last_name":"Wintraecken","full_name":"Wintraecken, Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"language":[{"iso":"eng"}],"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"}],"doi":"10.1137/21M1412918","oa":1,"publication_status":"published","intvolume":"        52","department":[{"_id":"HeEd"}],"ec_funded":1,"issue":"2","_id":"12960","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"452-486","day":"30","corr_author":"1","publication":"SIAM Journal on Computing","volume":52,"title":"Tracing isomanifolds in Rd in time polynomial in d using Coxeter–Freudenthal–Kuhn triangulations","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.","isi":1,"date_published":"2023-04-30T00:00:00Z","article_processing_charge":"No","external_id":{"isi":["001013183000012"]},"quality_controlled":"1","date_updated":"2026-07-07T13:43:40Z","month":"04","oa_version":"Submitted Version","citation":{"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>","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.","short":"J.D. Boissonnat, S. Kachanovich, M. Wintraecken, SIAM Journal on Computing 52 (2023) 452–486.","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>.","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>.","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>"},"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. "}],"scopus_import":"1","publisher":"Society for Industrial and Applied Mathematics","main_file_link":[{"open_access":"1","url":"https://hal-emse.ccsd.cnrs.fr/3IA-COTEDAZUR/hal-04083489v1"}],"related_material":{"record":[{"status":"public","id":"9441","relation":"earlier_version"}]},"publication_identifier":{"eissn":["1095-7111"],"issn":["0097-5397"]},"type":"journal_article","status":"public"},{"publisher":"Institute of Science and Technology Austria","oa_version":"Published Version","abstract":[{"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.","lang":"eng"}],"citation":{"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>","ieee":"E. R. Stephenson, “Generalizing medial axes with homology switches,” Institute of Science and Technology Austria, 2023.","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>.","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.","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>","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>."},"status":"public","publication_identifier":{"issn":["2791-4585"]},"type":"dissertation","date_published":"2023-08-24T00:00:00Z","article_processing_charge":"No","title":"Generalizing medial axes with homology switches","month":"08","date_updated":"2026-04-07T14:02:30Z","supervisor":[{"first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"}],"has_accepted_license":"1","page":"43","department":[{"_id":"GradSch"},{"_id":"HeEd"}],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","_id":"14226","corr_author":"1","OA_place":"publisher","day":"24","alternative_title":["ISTA Master's Thesis"],"date_created":"2023-08-24T13:01:18Z","year":"2023","doi":"10.15479/at:ista:14226","file":[{"file_size":15501411,"date_updated":"2024-02-26T23:30:03Z","content_type":"application/x-zip-compressed","relation":"source_file","checksum":"453caf851d75c3478c10ed09bd242a91","creator":"cchlebak","embargo_to":"open_access","file_name":"documents-export-2023-08-24.zip","access_level":"closed","date_created":"2023-08-24T13:02:49Z","file_id":"14227"},{"embargo":"2024-02-25","file_size":6854783,"content_type":"application/pdf","relation":"main_file","date_updated":"2024-02-26T23:30:03Z","checksum":"7349d29963d6695e555e171748648d9a","creator":"cchlebak","file_name":"thesis_pdf_a.pdf","access_level":"open_access","date_created":"2023-08-24T13:03:42Z","file_id":"14228"}],"publication_status":"published","oa":1,"author":[{"first_name":"Elizabeth R","last_name":"Stephenson","orcid":"0000-0002-6862-208X","id":"2D04F932-F248-11E8-B48F-1D18A9856A87","full_name":"Stephenson, Elizabeth R"}],"ddc":["500"],"language":[{"iso":"eng"}],"degree_awarded":"MS","file_date_updated":"2024-02-26T23:30:03Z"},{"related_material":{"record":[{"id":"18667","relation":"dissertation_contains","status":"public"}]},"status":"public","publication_identifier":{"isbn":["9781665439022"]},"type":"conference","oa_version":"Preprint","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"}],"citation":{"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.","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>","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>","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>.","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>.","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.","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."},"scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/2111.05663","open_access":"1"}],"publisher":"IEEE","quality_controlled":"1","date_updated":"2026-04-07T12:54:09Z","external_id":{"isi":["000800559503126"],"arxiv":["2111.05663"]},"month":"01","isi":1,"date_published":"2022-01-13T00:00:00Z","arxiv":1,"article_processing_charge":"No","title":"The impact of changes in resolution on the persistent homology of images","day":"13","publication":"2021 IEEE International Conference on Big Data","conference":{"start_date":"2021-12-15","name":"Big Data: International Conference on Big Data","end_date":"2021-12-18","location":"Orlando, FL, United States; Virtuell"},"department":[{"_id":"HeEd"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"10828","page":"3824-3834","author":[{"full_name":"Heiss, Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1780-2689","first_name":"Teresa","last_name":"Heiss"},{"first_name":"Sarah","last_name":"Tymochko","full_name":"Tymochko, Sarah"},{"full_name":"Story, Brittany","last_name":"Story","first_name":"Brittany"},{"full_name":"Garin, Adélie","first_name":"Adélie","last_name":"Garin"},{"full_name":"Bui, Hoa","last_name":"Bui","first_name":"Hoa"},{"full_name":"Bleile, Bea","last_name":"Bleile","first_name":"Bea"},{"last_name":"Robins","first_name":"Vanessa","full_name":"Robins, Vanessa"}],"language":[{"iso":"eng"}],"doi":"10.1109/BigData52589.2021.9671483","oa":1,"publication_status":"published","year":"2022","date_created":"2022-03-06T23:01:53Z"},{"quality_controlled":"1","date_updated":"2025-04-14T07:43:57Z","month":"06","volume":224,"title":"A cautionary tale: Burning the medial axis is unstable","editor":[{"full_name":"Goaoc, Xavier","first_name":"Xavier","last_name":"Goaoc"},{"first_name":"Michael","last_name":"Kerber","full_name":"Kerber, Michael"}],"article_processing_charge":"No","date_published":"2022-06-01T00:00:00Z","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.","type":"conference","publication_identifier":{"issn":["1868-8969"],"isbn":["978-3-95977-227-3"]},"status":"public","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>.","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.","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.","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>","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>.","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>","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."},"abstract":[{"text":"The medial axis of a set consists of the points in the ambient space without a unique closest point on the original set. Since its introduction, the medial axis has been used extensively in many applications as a method of computing a topologically equivalent skeleton. Unfortunately, one limiting factor in the use of the medial axis of a smooth manifold is that it is not necessarily topologically stable under small perturbations of the manifold. To counter these instabilities various prunings of the medial axis have been proposed. Here, we examine one type of pruning, called burning. Because of the good experimental results, it was hoped that the burning method of simplifying the medial axis would be stable. In this work we show a simple example that dashes such hopes based on Bing’s house with two rooms, demonstrating an isotopy of a shape where the medial axis goes from collapsible to non-collapsible.","lang":"eng"}],"scopus_import":"1","oa_version":"Published Version","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","file_date_updated":"2022-06-07T07:58:30Z","language":[{"iso":"eng"}],"ddc":["510"],"author":[{"full_name":"Chambers, Erin","last_name":"Chambers","first_name":"Erin"},{"first_name":"Christopher D","last_name":"Fillmore","full_name":"Fillmore, Christopher D","id":"35638A5C-AAC7-11E9-B0BF-5503E6697425"},{"id":"2D04F932-F248-11E8-B48F-1D18A9856A87","full_name":"Stephenson, Elizabeth R","first_name":"Elizabeth R","last_name":"Stephenson","orcid":"0000-0002-6862-208X"},{"id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","full_name":"Wintraecken, Mathijs","first_name":"Mathijs","last_name":"Wintraecken","orcid":"0000-0002-7472-2220"}],"series_title":"LIPIcs","oa":1,"publication_status":"published","file":[{"checksum":"b25ce40fade4ebc0bcaae176db4f5f1f","creator":"dernst","file_name":"2022_LIPICs_Chambers.pdf","access_level":"open_access","date_created":"2022-06-07T07:58:30Z","success":1,"file_id":"11437","file_size":17580705,"relation":"main_file","content_type":"application/pdf","date_updated":"2022-06-07T07:58:30Z"}],"project":[{"_id":"fc390959-9c52-11eb-aca3-afa58bd282b2","grant_number":"M03073","name":"Learning and triangulating manifolds via collapses"},{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships"}],"doi":"10.4230/LIPIcs.SoCG.2022.66","intvolume":"       224","year":"2022","date_created":"2022-06-01T14:18:04Z","day":"01","corr_author":"1","publication":"38th International Symposium on Computational Geometry","_id":"11428","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","conference":{"start_date":"2022-06-07","end_date":"2022-06-10","name":"SoCG: Symposium on Computational Geometry","location":"Berlin, Germany"},"ec_funded":1,"department":[{"_id":"HeEd"}],"page":"66:1-66:9","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1"},{"date_updated":"2024-10-09T21:02:30Z","quality_controlled":"1","language":[{"iso":"eng"}],"edition":"1","intvolume":"     13238","month":"05","doi":"10.1007/978-3-031-06245-2","publication_status":"published","year":"2022","volume":13238,"place":"Cham","date_published":"2022-05-01T00:00:00Z","article_processing_charge":"No","alternative_title":["LNCS"],"date_created":"2022-06-02T05:40:53Z","title":"Web and Wireless Geographical Information Systems","editor":[{"orcid":"0000-0001-6746-4174","first_name":"Farid","last_name":"Karimipour","full_name":"Karimipour, Farid","id":"2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425"},{"full_name":"Storandt, Sabine","last_name":"Storandt","first_name":"Sabine"}],"day":"01","status":"public","publication_identifier":{"eissn":["1611-3349"],"eisbn":["9783031062452"],"issn":["0302-9743"],"isbn":["9783031062445"]},"corr_author":"1","type":"book_editor","oa_version":"None","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"}],"citation":{"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>","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.","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>.","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>.","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>"},"department":[{"_id":"HeEd"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"11429","page":"153","publisher":"Springer Nature"},{"publisher":"Springer Nature","main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2102.11397","open_access":"1"}],"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."}],"citation":{"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.","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>","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>.","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>","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.","ista":"Bleile B, Garin A, Heiss T, Maggs K, Robins V. 2022.The persistent homology of dual digital image constructions. In: Research in Computational Topology 2. Association for Women in Mathematics Series, vol. 30, 1–26.","mla":"Bleile, Bea, et al. “The Persistent Homology of Dual Digital Image Constructions.” <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>."},"oa_version":"Preprint","type":"book_chapter","publication_identifier":{"isbn":["9783030955182"],"eisbn":["9783030955199"]},"status":"public","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"18667"}]},"title":"The persistent homology of dual digital image constructions","editor":[{"full_name":"Gasparovic, Ellen","first_name":"Ellen","last_name":"Gasparovic"},{"first_name":"Vanessa","last_name":"Robins","full_name":"Robins, Vanessa"},{"full_name":"Turner, Katharine","first_name":"Katharine","last_name":"Turner"}],"arxiv":1,"article_processing_charge":"No","date_published":"2022-01-27T00:00:00Z","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,"month":"01","external_id":{"arxiv":["2102.11397"]},"quality_controlled":"1","date_updated":"2026-04-07T12:54:09Z","page":"1-26","_id":"11440","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ec_funded":1,"department":[{"_id":"HeEd"}],"publication":"Research in Computational Topology 2","day":"27","date_created":"2022-06-07T08:21:11Z","alternative_title":["Association for Women in Mathematics Series"],"place":"Cham","year":"2022","oa":1,"publication_status":"published","series_title":"AWMS","project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended"}],"doi":"10.1007/978-3-030-95519-9_1","intvolume":"        30","edition":"1","language":[{"iso":"eng"}],"author":[{"full_name":"Bleile, Bea","last_name":"Bleile","first_name":"Bea"},{"full_name":"Garin, Adélie","first_name":"Adélie","last_name":"Garin"},{"first_name":"Teresa","last_name":"Heiss","orcid":"0000-0002-1780-2689","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","full_name":"Heiss, Teresa"},{"first_name":"Kelly","last_name":"Maggs","full_name":"Maggs, Kelly"},{"full_name":"Robins, Vanessa","last_name":"Robins","first_name":"Vanessa"}]},{"day":"01","publication":"Journal of Algebra","corr_author":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"11545","department":[{"_id":"HeEd"}],"issue":"11","ec_funded":1,"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1","page":"145-179","ddc":["510"],"language":[{"iso":"eng"}],"author":[{"first_name":"Adam","last_name":"Brown","full_name":"Brown, Adam","id":"70B7FDF6-608D-11E9-9333-8535E6697425"},{"last_name":"Romanov","first_name":"Anna","full_name":"Romanov, Anna"}],"file_date_updated":"2023-02-02T07:32:48Z","intvolume":"       609","oa":1,"publication_status":"published","file":[{"success":1,"file_id":"12473","date_created":"2023-02-02T07:32:48Z","file_name":"2022_JournalAlgebra_Brown.pdf","access_level":"open_access","checksum":"82abaee3d7837f703e499a9ecbb25b7c","creator":"dernst","content_type":"application/pdf","date_updated":"2023-02-02T07:32:48Z","relation":"main_file","file_size":582962}],"doi":"10.1016/j.jalgebra.2022.06.017","project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"}],"year":"2022","article_type":"original","date_created":"2022-07-08T11:40:07Z","status":"public","type":"journal_article","publication_identifier":{"issn":["0021-8693"]},"keyword":["Algebra and Number Theory"],"citation":{"short":"A. Brown, A. Romanov, Journal of Algebra 609 (2022) 145–179.","ista":"Brown A, Romanov A. 2022. Contravariant pairings between standard Whittaker modules and Verma modules. Journal of Algebra. 609(11), 145–179.","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>.","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>.","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>","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."},"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 ."}],"scopus_import":"1","oa_version":"Published Version","publisher":"Elsevier","quality_controlled":"1","date_updated":"2025-04-14T07:43:58Z","external_id":{"isi":["000861841100004"]},"month":"11","volume":609,"article_processing_charge":"Yes (via OA deal)","date_published":"2022-11-01T00:00:00Z","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.","isi":1,"title":"Contravariant pairings between standard Whittaker modules and Verma modules"},{"month":"07","quality_controlled":"1","date_updated":"2026-04-07T12:58:48Z","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.","date_published":"2022-07-27T00:00:00Z","article_processing_charge":"No","title":"Depth in arrangements: Dehn–Sommerville–Euler relations with applications","status":"public","type":"journal_article","related_material":{"record":[{"status":"public","relation":"later_version","id":"15380"},{"id":"15094","relation":"dissertation_contains","status":"public"}]},"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","oa_version":"Submitted Version","abstract":[{"lang":"eng","text":"The depth of a cell in an arrangement of n (non-vertical) great-spheres in Sd is the number of great-spheres that pass above the cell. We prove Euler-type relations, which imply extensions of the classic Dehn–Sommerville relations for convex polytopes to sublevel sets of the depth function, and we use the relations to extend the expressions for the number of faces of neighborly polytopes to the number of cells of levels in neighborly arrangements."}],"citation":{"apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., &#38; Saghafian, M. (n.d.). Depth in arrangements: Dehn–Sommerville–Euler relations with applications. <i>Leibniz International Proceedings on Mathematics</i>. Schloss Dagstuhl - Leibniz-Zentrum für Informatik.","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Depth in Arrangements: Dehn–Sommerville–Euler Relations with Applications.” <i>Leibniz International Proceedings on Mathematics</i>. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, n.d.","mla":"Biswas, Ranita, et al. “Depth in Arrangements: Dehn–Sommerville–Euler Relations with Applications.” <i>Leibniz International Proceedings on Mathematics</i>, Schloss Dagstuhl - Leibniz-Zentrum für Informatik.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Leibniz International Proceedings on Mathematics (n.d.).","ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Depth in arrangements: Dehn–Sommerville–Euler relations with applications. Leibniz International Proceedings on Mathematics.","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Depth in arrangements: Dehn–Sommerville–Euler relations with applications,” <i>Leibniz International Proceedings on Mathematics</i>. Schloss Dagstuhl - Leibniz-Zentrum für Informatik.","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Depth in arrangements: Dehn–Sommerville–Euler relations with applications. <i>Leibniz International Proceedings on Mathematics</i>."},"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","grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"name":"Persistence and stability of geometric complexes","call_identifier":"FWF","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"file":[{"file_size":639266,"content_type":"application/pdf","relation":"main_file","date_updated":"2022-07-27T09:25:53Z","creator":"scultrer","checksum":"b2f511e8b1cae5f1892b0cdec341acac","access_level":"open_access","file_name":"D-S-E.pdf","date_created":"2022-07-27T09:25:53Z","file_id":"11659"}],"publication_status":"draft","oa":1,"author":[{"first_name":"Ranita","last_name":"Biswas","orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","full_name":"Biswas, Ranita"},{"orcid":"0000-0001-6249-0832","last_name":"Cultrera di Montesano","first_name":"Sebastiano","full_name":"Cultrera di Montesano, Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert"},{"id":"f86f7148-b140-11ec-9577-95435b8df824","full_name":"Saghafian, Morteza","last_name":"Saghafian","first_name":"Morteza"}],"language":[{"iso":"eng"}],"ddc":["510"],"file_date_updated":"2022-07-27T09:25:53Z","date_created":"2022-07-27T09:27:34Z","year":"2022","publication":"Leibniz International Proceedings on Mathematics","corr_author":"1","day":"27","has_accepted_license":"1","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"ec_funded":1,"department":[{"_id":"GradSch"},{"_id":"HeEd"}],"_id":"11658","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"type":"journal_article","status":"public","related_material":{"record":[{"relation":"dissertation_contains","id":"15094","status":"public"}]},"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","oa_version":"Submitted Version","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. "}],"citation":{"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.","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>.","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.","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.","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.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, LIPIcs (n.d.).","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."},"month":"07","date_updated":"2026-04-07T12:58:47Z","quality_controlled":"1","title":"A window to the persistence of 1D maps. I: Geometric characterization of critical point pairs","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. ","date_published":"2022-07-25T00:00:00Z","article_processing_charge":"No","corr_author":"1","publication":"LIPIcs","day":"25","has_accepted_license":"1","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"department":[{"_id":"GradSch"},{"_id":"HeEd"}],"ec_funded":1,"_id":"11660","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"date_updated":"2022-07-27T09:30:30Z","relation":"main_file","content_type":"application/pdf","file_size":564836,"file_id":"11661","date_created":"2022-07-27T09:30:30Z","access_level":"open_access","file_name":"window 1.pdf","creator":"scultrer","checksum":"95903f9d1649e8e437a967b6f2f64730"}],"project":[{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","name":"Mathematics, Computer Science","grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"oa":1,"publication_status":"submitted","file_date_updated":"2022-07-27T09:30:30Z","author":[{"full_name":"Biswas, Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5372-7890","last_name":"Biswas","first_name":"Ranita"},{"orcid":"0000-0001-6249-0832","first_name":"Sebastiano","last_name":"Cultrera di Montesano","full_name":"Cultrera di Montesano, Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833"},{"first_name":"Morteza","last_name":"Saghafian","full_name":"Saghafian, Morteza"}],"language":[{"iso":"eng"}],"ddc":["510"],"date_created":"2022-07-27T09:31:15Z","alternative_title":["LIPIcs"],"year":"2022"},{"corr_author":"1","publication":"Journal of Graph Algorithms and Applications","day":"01","page":"225-240","has_accepted_license":"1","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"KrCh"}],"ec_funded":1,"issue":"2","_id":"11938","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342"},{"call_identifier":"FP7","name":"Quantitative Graph Games: Theory and Applications","grant_number":"279307","_id":"2581B60A-B435-11E9-9278-68D0E5697425"},{"name":"Modern Graph Algorithmic Techniques in Formal Verification","call_identifier":"FWF","_id":"2584A770-B435-11E9-9278-68D0E5697425","grant_number":"P 23499-N23"},{"grant_number":"S11407","_id":"25863FF4-B435-11E9-9278-68D0E5697425","name":"Game Theory","call_identifier":"FWF"}],"file":[{"file_size":694538,"content_type":"application/pdf","date_updated":"2022-08-22T06:42:42Z","relation":"main_file","date_created":"2022-08-22T06:42:42Z","success":1,"file_id":"11940","creator":"dernst","checksum":"dc6e255e3558faff924fd9e370886c11","file_name":"2022_JourGraphAlgorithmsApplic_Aichholzer.pdf","access_level":"open_access"}],"doi":"10.7155/jgaa.00591","oa":1,"publication_status":"published","intvolume":"        26","file_date_updated":"2022-08-22T06:42:42Z","author":[{"full_name":"Aichholzer, Oswin","first_name":"Oswin","last_name":"Aichholzer"},{"orcid":"0000-0003-2401-8670","last_name":"Arroyo Guevara","first_name":"Alan M","full_name":"Arroyo Guevara, Alan M","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87"},{"id":"45CFE238-F248-11E8-B48F-1D18A9856A87","full_name":"Masárová, Zuzana","last_name":"Masárová","first_name":"Zuzana","orcid":"0000-0002-6660-1322"},{"last_name":"Parada","first_name":"Irene","full_name":"Parada, Irene"},{"last_name":"Perz","first_name":"Daniel","full_name":"Perz, Daniel"},{"first_name":"Alexander","last_name":"Pilz","full_name":"Pilz, Alexander"},{"first_name":"Josef","last_name":"Tkadlec","orcid":"0000-0002-1097-9684","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","full_name":"Tkadlec, Josef"},{"first_name":"Birgit","last_name":"Vogtenhuber","full_name":"Vogtenhuber, Birgit"}],"language":[{"iso":"eng"}],"ddc":["000"],"date_created":"2022-08-21T22:01:56Z","article_type":"original","year":"2022","publication_identifier":{"issn":["1526-1719"]},"type":"journal_article","status":"public","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"9296"}]},"publisher":"Brown University","oa_version":"Published Version","citation":{"ieee":"O. Aichholzer <i>et al.</i>, “On compatible matchings,” <i>Journal of Graph Algorithms and Applications</i>, vol. 26, no. 2. Brown University, pp. 225–240, 2022.","ama":"Aichholzer O, Arroyo Guevara AM, Masárová Z, et al. On compatible matchings. <i>Journal of Graph Algorithms and Applications</i>. 2022;26(2):225-240. doi:<a href=\"https://doi.org/10.7155/jgaa.00591\">10.7155/jgaa.00591</a>","apa":"Aichholzer, O., Arroyo Guevara, A. M., Masárová, Z., Parada, I., Perz, D., Pilz, A., … Vogtenhuber, B. (2022). On compatible matchings. <i>Journal of Graph Algorithms and Applications</i>. Brown University. <a href=\"https://doi.org/10.7155/jgaa.00591\">https://doi.org/10.7155/jgaa.00591</a>","chicago":"Aichholzer, Oswin, Alan M Arroyo Guevara, Zuzana Masárová, Irene Parada, Daniel Perz, Alexander Pilz, Josef Tkadlec, and Birgit Vogtenhuber. “On Compatible Matchings.” <i>Journal of Graph Algorithms and Applications</i>. Brown University, 2022. <a href=\"https://doi.org/10.7155/jgaa.00591\">https://doi.org/10.7155/jgaa.00591</a>.","mla":"Aichholzer, Oswin, et al. “On Compatible Matchings.” <i>Journal of Graph Algorithms and Applications</i>, vol. 26, no. 2, Brown University, 2022, pp. 225–40, doi:<a href=\"https://doi.org/10.7155/jgaa.00591\">10.7155/jgaa.00591</a>.","ista":"Aichholzer O, Arroyo Guevara AM, Masárová Z, Parada I, Perz D, Pilz A, Tkadlec J, Vogtenhuber B. 2022. On compatible matchings. Journal of Graph Algorithms and Applications. 26(2), 225–240.","short":"O. Aichholzer, A.M. Arroyo Guevara, Z. Masárová, I. Parada, D. Perz, A. Pilz, J. Tkadlec, B. Vogtenhuber, Journal of Graph Algorithms and Applications 26 (2022) 225–240."},"abstract":[{"lang":"eng","text":"A matching is compatible to two or more labeled point sets of size n with labels {1, . . . , n} if its straight-line drawing on each of these point sets is crossing-free. We study the maximum number of edges in a matching compatible to two or more labeled point sets in general position in the plane. We show that for any two labeled sets of n points in convex position there exists a compatible matching with ⌊√2n + 1 − 1⌋ edges. More generally, for any ℓ labeled point sets we construct compatible matchings of size Ω(n1/ℓ). As a corresponding upper bound, we use probabilistic arguments to show that for any ℓ given sets of n points there exists a labeling of each set such that the largest compatible matching has O(n2/(ℓ+1)) edges. Finally, we show that Θ(log n) copies of any set of n points are necessary and sufficient for the existence of labelings of these point sets such that any compatible matching consists only of a single edge."}],"scopus_import":"1","month":"06","external_id":{"arxiv":["2101.03928"]},"date_updated":"2026-04-16T09:18:20Z","quality_controlled":"1","title":"On compatible matchings","acknowledgement":"A.A. funded by the Marie Sklodowska-Curie grant agreement No 754411. Z.M. partially funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31. I.P., D.P., and B.V. partially supported by FWF within the collaborative DACH project Arrangements and Drawings as FWF project I 3340-N35. A.P. supported by a Schrödinger fellowship of the FWF: J-3847-N35. J.T. partially supported by ERC Start grant no. (279307: Graph Games), FWF grant no. P23499-N23 and S11407-N23 (RiSE).","article_processing_charge":"No","arxiv":1,"date_published":"2022-06-01T00:00:00Z","volume":26},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"12307","department":[{"_id":"HeEd"},{"_id":"GradSch"}],"issue":"5","page":"593-609","day":"28","corr_author":"1","publication":"PRIMUS","year":"2022","date_created":"2023-01-16T10:07:21Z","article_type":"original","language":[{"iso":"eng"}],"author":[{"last_name":"Shipman","first_name":"Barbara A.","full_name":"Shipman, Barbara A."},{"last_name":"Stephenson","first_name":"Elizabeth R","orcid":"0000-0002-6862-208X","id":"2D04F932-F248-11E8-B48F-1D18A9856A87","full_name":"Stephenson, Elizabeth R"}],"publication_status":"published","doi":"10.1080/10511970.2021.1872750","intvolume":"        32","scopus_import":"1","citation":{"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>","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.","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>.","short":"B.A. Shipman, E.R. Stephenson, PRIMUS 32 (2022) 593–609.","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>","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>."},"abstract":[{"text":"Point-set topology is among the most abstract branches of mathematics in that it lacks tangible notions of distance, length, magnitude, order, and size. There is no shape, no geometry, no algebra, and no direction. Everything we are used to visualizing is gone. In the teaching and learning of mathematics, this can present a conundrum. Yet, this very property makes point set topology perfect for teaching and learning abstract mathematical concepts. It clears our minds of preconceived intuitions and expectations and forces us to think in new and creative ways. In this paper, we present guided investigations into topology through questions and thinking strategies that open up fascinating problems. They are intended for faculty who already teach or are thinking about teaching a class in topology or abstract mathematical reasoning for undergraduates. They can be used to build simple to challenging projects in topology, proofs, honors programs, and research experiences.","lang":"eng"}],"keyword":["Education","General Mathematics"],"oa_version":"None","publisher":"Taylor & Francis","type":"journal_article","publication_identifier":{"eissn":["1935-4053"],"issn":["1051-1970"]},"status":"public","volume":32,"title":"Tangible topology through the lens of limits","date_published":"2022-05-28T00:00:00Z","article_processing_charge":"No","date_updated":"2024-10-09T21:03:58Z","quality_controlled":"1","month":"05"},{"related_material":{"record":[{"relation":"later_version","id":"20456","status":"public"},{"id":"15094","relation":"dissertation_contains","status":"public"}]},"type":"preprint","status":"public","oa_version":"Preprint","abstract":[{"text":"Given a locally finite set A⊆Rd and a coloring χ:A→{0,1,…,s}, we introduce the chromatic Delaunay mosaic of χ, which is a Delaunay mosaic in Rs+d that represents how points of different colors mingle. Our main results are bounds on the size of the chromatic Delaunay mosaic, in which we assume that d and s are constants. For example, if A is finite with n=#A, and the coloring is random, then the chromatic Delaunay mosaic has O(n⌈d/2⌉) cells in expectation. In contrast, for Delone sets and Poisson point processes in Rd, the expected number of cells within a closed ball is only a constant times the number of points in this ball. Furthermore, in R2 all colorings of a dense set of n points have chromatic Delaunay mosaics of size O(n). This encourages the use of chromatic Delaunay mosaics in applications.","lang":"eng"}],"citation":{"ieee":"R. Biswas, S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian, “On the size of chromatic Delaunay mosaics,” <i>arXiv</i>. .","ama":"Biswas R, Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. On the size of chromatic Delaunay mosaics. <i>arXiv</i>.","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Ondrej Draganov, Herbert Edelsbrunner, and Morteza Saghafian. “On the Size of Chromatic Delaunay Mosaics.” <i>ArXiv</i>, n.d.","apa":"Biswas, R., Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., &#38; Saghafian, M. (n.d.). On the size of chromatic Delaunay mosaics. <i>arXiv</i>.","short":"R. Biswas, S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.).","ista":"Biswas R, Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. On the size of chromatic Delaunay mosaics. arXiv, 2212.03121.","mla":"Biswas, Ranita, et al. “On the Size of Chromatic Delaunay Mosaics.” <i>ArXiv</i>, 2212.03121."},"article_number":"2212.03121","main_file_link":[{"url":"https://arxiv.org/abs/2212.03121","open_access":"1"}],"external_id":{"arxiv":["2212.03121"]},"date_updated":"2026-04-07T12:58:47Z","month":"12","title":"On the size of chromatic Delaunay mosaics","arxiv":1,"article_processing_charge":"No","date_published":"2022-12-06T00:00:00Z","day":"06","corr_author":"1","OA_place":"repository","publication":"arXiv","department":[{"_id":"HeEd"}],"ec_funded":1,"_id":"15090","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"author":[{"full_name":"Biswas, Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5372-7890","first_name":"Ranita","last_name":"Biswas"},{"first_name":"Sebastiano","last_name":"Cultrera di Montesano","orcid":"0000-0001-6249-0832","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","full_name":"Cultrera di Montesano, Sebastiano"},{"full_name":"Draganov, Ondrej","id":"2B23F01E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0464-3823","last_name":"Draganov","first_name":"Ondrej"},{"last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"first_name":"Morteza","last_name":"Saghafian","full_name":"Saghafian, Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824"}],"language":[{"iso":"eng"}],"project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended"},{"name":"Persistent Homology, Algorithms and Stochastic Geometry","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","grant_number":"I4887"},{"grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Mathematics, Computer Science"}],"oa":1,"publication_status":"draft","year":"2022","date_created":"2024-03-08T09:54:20Z"},{"volume":244,"article_processing_charge":"Yes","arxiv":1,"date_published":"2022-09-01T00:00:00Z","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.","title":"Hardness of token swapping on trees","date_updated":"2025-04-15T07:16:56Z","quality_controlled":"1","external_id":{"arxiv":["2103.06707"]},"month":"09","scopus_import":"1","article_number":"3","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."}],"citation":{"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>","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>.","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.","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.","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.","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>"},"oa_version":"Published Version","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","status":"public","type":"conference","year":"2022","alternative_title":["LIPIcs"],"date_created":"2024-05-29T06:27:16Z","ddc":["510"],"language":[{"iso":"eng"}],"author":[{"last_name":"Aichholzer","first_name":"Oswin","full_name":"Aichholzer, Oswin"},{"full_name":"Demaine, Erik D.","last_name":"Demaine","first_name":"Erik D."},{"last_name":"Korman","first_name":"Matias","full_name":"Korman, Matias"},{"first_name":"Anna","last_name":"Lubiw","full_name":"Lubiw, Anna"},{"full_name":"Lynch, Jayson","first_name":"Jayson","last_name":"Lynch"},{"full_name":"Masárová, Zuzana","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6660-1322","last_name":"Masárová","first_name":"Zuzana"},{"last_name":"Rudoy","first_name":"Mikhail","full_name":"Rudoy, Mikhail"},{"first_name":"Virginia","last_name":"Vassilevska Williams","full_name":"Vassilevska Williams, Virginia"},{"first_name":"Nicole","last_name":"Wein","full_name":"Wein, Nicole"}],"file_date_updated":"2024-08-12T08:51:44Z","intvolume":"       244","oa":1,"publication_status":"published","doi":"10.4230/LIPIcs.ESA.2022.3","project":[{"call_identifier":"FWF","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342"}],"file":[{"content_type":"application/pdf","date_updated":"2024-08-12T08:51:44Z","relation":"main_file","file_size":1406071,"success":1,"file_id":"17420","date_created":"2024-08-12T08:51:44Z","file_name":"2022_LIPIcS_Aichholzer.pdf","access_level":"open_access","checksum":"a1fbd3e7baad510fbcb998cf4a7d9f7f","creator":"dernst"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"17084","conference":{"location":"Berlin/Potsdam, Germany","start_date":"2022-09-05","end_date":"2022-09-09","name":"ESA: European Symposium on Algorithms"},"department":[{"_id":"HeEd"},{"_id":"UlWa"}],"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1","day":"01","publication":"30th Annual European Symposium on Algorithms","corr_author":"1"},{"date_updated":"2024-10-09T21:01:16Z","quality_controlled":"1","external_id":{"isi":["000791838800012"]},"month":"03","volume":309,"acknowledgement":"Dedicated to the memory of Hans-Peter Künzi.","isi":1,"date_published":"2022-03-15T00:00:00Z","article_processing_charge":"No","title":"Generalized quasi-metric semilattices","status":"public","publication_identifier":{"issn":["0166-8641"]},"type":"journal_article","oa_version":"None","citation":{"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>.","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>.","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.","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.","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>"},"scopus_import":"1","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"}],"article_number":"107916","publisher":"Elsevier","author":[{"first_name":"Dikran","last_name":"Dikranjan","full_name":"Dikranjan, Dikran"},{"last_name":"Giordano Bruno","first_name":"Anna","full_name":"Giordano Bruno, Anna"},{"full_name":"Künzi, Hans Peter","last_name":"Künzi","first_name":"Hans Peter"},{"full_name":"Zava, Nicolò","id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad","orcid":"0000-0001-8686-1888","last_name":"Zava","first_name":"Nicolò"},{"full_name":"Toller, Daniele","first_name":"Daniele","last_name":"Toller"}],"language":[{"iso":"eng"}],"intvolume":"       309","doi":"10.1016/j.topol.2021.107916","publication_status":"published","year":"2022","article_type":"original","date_created":"2021-12-05T23:01:44Z","day":"15","publication":"Topology and its Applications","corr_author":"1","department":[{"_id":"HeEd"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"10413"},{"year":"2022","date_created":"2022-01-09T23:01:27Z","article_type":"original","file_date_updated":"2024-05-22T11:10:10Z","language":[{"iso":"eng"}],"ddc":["500"],"author":[{"full_name":"Weighill, Thomas","first_name":"Thomas","last_name":"Weighill"},{"full_name":"Yamauchi, Takamitsu","last_name":"Yamauchi","first_name":"Takamitsu"},{"id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad","full_name":"Zava, Nicolò","last_name":"Zava","first_name":"Nicolò","orcid":"0000-0001-8686-1888"}],"publication_status":"published","oa":1,"doi":"10.1007/s40879-021-00515-3","file":[{"file_size":371515,"relation":"main_file","content_type":"application/pdf","date_updated":"2024-05-22T11:10:10Z","date_created":"2024-05-22T11:10:10Z","success":1,"file_id":"17036","creator":"kschuh","checksum":"ce35cbb2d8c889dc7750719972634ed4","file_name":"2022_EuJournalMath_Weighill.pdf","access_level":"open_access"}],"intvolume":"         8","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"10608","issue":"1","department":[{"_id":"HeEd"}],"page":"335-355","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1","day":"01","publication":"European Journal of Mathematics","volume":8,"title":"Coarse infinite-dimensionality of hyperspaces of finite subsets","date_published":"2022-03-01T00:00:00Z","article_processing_charge":"Yes (via OA deal)","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).","quality_controlled":"1","date_updated":"2024-05-22T11:10:22Z","month":"03","scopus_import":"1","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."}],"citation":{"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>","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.","short":"T. Weighill, T. Yamauchi, N. Zava, European Journal of Mathematics 8 (2022) 335–355.","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>.","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>.","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>"},"oa_version":"Published Version","publisher":"Springer Nature","type":"journal_article","publication_identifier":{"issn":["2199-675X"],"eissn":["2199-6768"]},"status":"public"},{"file_date_updated":"2022-02-14T07:46:30Z","author":[{"full_name":"Chang, Yan","first_name":"Yan","last_name":"Chang"},{"first_name":"Marah","last_name":"Funk","full_name":"Funk, Marah"},{"last_name":"Roy","first_name":"Souvik","full_name":"Roy, Souvik"},{"id":"2D04F932-F248-11E8-B48F-1D18A9856A87","full_name":"Stephenson, Elizabeth R","last_name":"Stephenson","first_name":"Elizabeth R","orcid":"0000-0002-6862-208X"},{"full_name":"Choi, Sangyong","first_name":"Sangyong","last_name":"Choi"},{"last_name":"Kojouharov","first_name":"Hristo V.","full_name":"Kojouharov, Hristo V."},{"last_name":"Chen","first_name":"Benito","full_name":"Chen, Benito"},{"full_name":"Pan, Zui","first_name":"Zui","last_name":"Pan"}],"language":[{"iso":"eng"}],"ddc":["510","576"],"doi":"10.3390/ijms23031763","file":[{"access_level":"open_access","file_name":"2022_IJMS_Chang.pdf","checksum":"8890ad20c54e90dc58ad5ea97c902998","creator":"dernst","file_id":"10756","success":1,"date_created":"2022-02-14T07:46:30Z","date_updated":"2022-02-14T07:46:30Z","content_type":"application/pdf","relation":"main_file","file_size":24416183}],"publication_status":"published","oa":1,"intvolume":"        23","year":"2022","date_created":"2022-02-13T23:01:35Z","article_type":"original","day":"01","publication":"International Journal of Molecular Sciences","department":[{"_id":"HeEd"}],"issue":"3","_id":"10754","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","pmid":1,"has_accepted_license":"1","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"external_id":{"pmid":["35163685"],"isi":["000754773500001"]},"quality_controlled":"1","date_updated":"2025-06-11T13:46:46Z","month":"02","volume":23,"title":"Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer","isi":1,"acknowledgement":"This work was partially supported by grants from National Institutes of Health (NIH) (R01 CA185055, S10OD0252300) and The University of Texas System STARs Award (to Z.P.),\r\nThe University of Texas at Arlington Interdisciplinary Research Program (to B.C., H.V.K. and Z.P.). ","article_processing_charge":"Yes","date_published":"2022-02-01T00:00:00Z","publication_identifier":{"issn":["1661-6596"],"eissn":["1422-0067"]},"type":"journal_article","status":"public","oa_version":"Published Version","citation":{"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.","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>","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>.","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>","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.","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).","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>."},"article_number":"1763","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"}],"scopus_import":"1","publisher":"MDPI"}]