[{"abstract":[{"text":"Motivated by a problem posed in [10], we investigate the closure operators of the category SLatt of join semilattices and its subcategory SLattO of join semilattices with bottom element. In particular, we show that there are only finitely many closure operators of both categories, and provide a complete classification. We use this result to deduce the known fact that epimorphisms of SLatt and SLattO are surjective. We complement the paper with two different proofs of this result using either generators or Isbell’s zigzag theorem.","lang":"eng"}],"issue":"S1","type":"journal_article","oa_version":"None","_id":"14557","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","title":"Epimorphisms and closure operators of categories of semilattices","intvolume":" 46","day":"01","article_processing_charge":"No","scopus_import":"1","date_published":"2023-11-01T00:00:00Z","publication":"Quaestiones Mathematicae","citation":{"short":"D. Dikranjan, A. Giordano Bruno, N. Zava, Quaestiones Mathematicae 46 (2023) 191–221.","mla":"Dikranjan, D., et al. “Epimorphisms and Closure Operators of Categories of Semilattices.” Quaestiones Mathematicae, vol. 46, no. S1, Taylor & Francis, 2023, pp. 191–221, doi:10.2989/16073606.2023.2247731.","chicago":"Dikranjan, D., A. Giordano Bruno, and Nicolò Zava. “Epimorphisms and Closure Operators of Categories of Semilattices.” Quaestiones Mathematicae. Taylor & Francis, 2023. https://doi.org/10.2989/16073606.2023.2247731.","ama":"Dikranjan D, Giordano Bruno A, Zava N. Epimorphisms and closure operators of categories of semilattices. Quaestiones Mathematicae. 2023;46(S1):191-221. doi:10.2989/16073606.2023.2247731","ieee":"D. Dikranjan, A. Giordano Bruno, and N. Zava, “Epimorphisms and closure operators of categories of semilattices,” Quaestiones Mathematicae, vol. 46, no. S1. Taylor & Francis, pp. 191–221, 2023.","apa":"Dikranjan, D., Giordano Bruno, A., & Zava, N. (2023). Epimorphisms and closure operators of categories of semilattices. Quaestiones Mathematicae. Taylor & Francis. https://doi.org/10.2989/16073606.2023.2247731","ista":"Dikranjan D, Giordano Bruno A, Zava N. 2023. Epimorphisms and closure operators of categories of semilattices. Quaestiones Mathematicae. 46(S1), 191–221."},"article_type":"original","page":"191-221","author":[{"first_name":"D.","last_name":"Dikranjan","full_name":"Dikranjan, D."},{"first_name":"A.","last_name":"Giordano Bruno","full_name":"Giordano Bruno, A."},{"full_name":"Zava, Nicolò","first_name":"Nicolò","last_name":"Zava","id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad","orcid":"0000-0001-8686-1888"}],"date_created":"2023-11-19T23:00:55Z","date_updated":"2023-11-20T09:24:48Z","volume":46,"year":"2023","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","publication_status":"published","publisher":"Taylor & Francis","department":[{"_id":"HeEd"}],"month":"11","publication_identifier":{"eissn":["1727-933X"],"issn":["1607-3606"]},"doi":"10.2989/16073606.2023.2247731","language":[{"iso":"eng"}],"quality_controlled":"1","project":[{"grant_number":"I04245","_id":"26AD5D90-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Algebraic Footprints of Geometric Features in Homology"}]},{"author":[{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Garber, Alexey","last_name":"Garber","first_name":"Alexey"},{"full_name":"Ghafari, Mohadese","first_name":"Mohadese","last_name":"Ghafari"},{"first_name":"Teresa","last_name":"Heiss","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1780-2689","full_name":"Heiss, Teresa"},{"full_name":"Saghafian, Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","last_name":"Saghafian","first_name":"Morteza"}],"date_created":"2023-09-17T22:01:10Z","date_updated":"2023-12-13T12:25:06Z","acknowledgement":"Work by all authors but A. Garber is supported by the European Research Council (ERC), Grant No. 788183, by the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), Grant No. I 02979-N35. Work by A. Garber is partially supported by the Alexander von Humboldt Foundation.","year":"2023","publication_status":"epub_ahead","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"ec_funded":1,"doi":"10.1007/s00454-023-00566-1","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s00454-023-00566-1"}],"external_id":{"arxiv":["2204.01076"],"isi":["001060727600004"]},"oa":1,"quality_controlled":"1","isi":1,"project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020"},{"call_identifier":"FWF","name":"The Wittgenstein Prize","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"}],"month":"09","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"14345","status":"public","title":"On angles in higher order Brillouin tessellations and related tilings in the plane","abstract":[{"lang":"eng","text":"For a locally finite set in R2, the order-k Brillouin tessellations form an infinite sequence of convex face-to-face tilings of the plane. If the set is coarsely dense and generic, then the corresponding infinite sequences of minimum and maximum angles are both monotonic in k. As an example, a stationary Poisson point process in R2 is locally finite, coarsely dense, and generic with probability one. For such a set, the distributions of angles in the Voronoi tessellations, Delaunay mosaics, and Brillouin tessellations are independent of the order and can be derived from the formula for angles in order-1 Delaunay mosaics given by Miles (Math. Biosci. 6, 85–127 (1970))."}],"type":"journal_article","date_published":"2023-09-07T00:00:00Z","publication":"Discrete and Computational Geometry","citation":{"ieee":"H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, and M. Saghafian, “On angles in higher order Brillouin tessellations and related tilings in the plane,” Discrete and Computational Geometry. Springer Nature, 2023.","apa":"Edelsbrunner, H., Garber, A., Ghafari, M., Heiss, T., & Saghafian, M. (2023). On angles in higher order Brillouin tessellations and related tilings in the plane. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-023-00566-1","ista":"Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. 2023. On angles in higher order Brillouin tessellations and related tilings in the plane. Discrete and Computational Geometry.","ama":"Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. On angles in higher order Brillouin tessellations and related tilings in the plane. Discrete and Computational Geometry. 2023. doi:10.1007/s00454-023-00566-1","chicago":"Edelsbrunner, Herbert, Alexey Garber, Mohadese Ghafari, Teresa Heiss, and Morteza Saghafian. “On Angles in Higher Order Brillouin Tessellations and Related Tilings in the Plane.” Discrete and Computational Geometry. Springer Nature, 2023. https://doi.org/10.1007/s00454-023-00566-1.","short":"H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, Discrete and Computational Geometry (2023).","mla":"Edelsbrunner, Herbert, et al. “On Angles in Higher Order Brillouin Tessellations and Related Tilings in the Plane.” Discrete and Computational Geometry, Springer Nature, 2023, doi:10.1007/s00454-023-00566-1."},"article_type":"original","day":"07","article_processing_charge":"Yes (via OA deal)","scopus_import":"1"},{"date_published":"2023-10-05T00:00:00Z","citation":{"chicago":"Ambrus, Áron, Mónika Csikós, Gergely Kiss, János Pach, and Gábor Somlai. “Optimal Embedded and Enclosing Isosceles Triangles.” International Journal of Foundations of Computer Science. World Scientific Publishing, 2023. https://doi.org/10.1142/S012905412342008X.","short":"Á. Ambrus, M. Csikós, G. Kiss, J. Pach, G. Somlai, International Journal of Foundations of Computer Science 34 (2023) 737–760.","mla":"Ambrus, Áron, et al. “Optimal Embedded and Enclosing Isosceles Triangles.” International Journal of Foundations of Computer Science, vol. 34, no. 7, World Scientific Publishing, 2023, pp. 737–60, doi:10.1142/S012905412342008X.","apa":"Ambrus, Á., Csikós, M., Kiss, G., Pach, J., & Somlai, G. (2023). Optimal embedded and enclosing isosceles triangles. International Journal of Foundations of Computer Science. World Scientific Publishing. https://doi.org/10.1142/S012905412342008X","ieee":"Á. Ambrus, M. Csikós, G. Kiss, J. Pach, and G. Somlai, “Optimal embedded and enclosing isosceles triangles,” International Journal of Foundations of Computer Science, vol. 34, no. 7. World Scientific Publishing, pp. 737–760, 2023.","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.","ama":"Ambrus Á, Csikós M, Kiss G, Pach J, Somlai G. Optimal embedded and enclosing isosceles triangles. International Journal of Foundations of Computer Science. 2023;34(7):737-760. doi:10.1142/S012905412342008X"},"publication":"International Journal of Foundations of Computer Science","page":"737-760","article_type":"original","article_processing_charge":"No","day":"05","scopus_import":"1","oa_version":"Preprint","_id":"14464","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 34","status":"public","title":"Optimal embedded and enclosing isosceles triangles","issue":"7","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"}],"type":"journal_article","doi":"10.1142/S012905412342008X","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2205.11637"}],"external_id":{"isi":["001080874400001"],"arxiv":["2205.11637"]},"oa":1,"isi":1,"quality_controlled":"1","publication_identifier":{"eissn":["1793-6373"],"issn":["0129-0541"]},"month":"10","author":[{"full_name":"Ambrus, Áron","last_name":"Ambrus","first_name":"Áron"},{"first_name":"Mónika","last_name":"Csikós","full_name":"Csikós, Mónika"},{"full_name":"Kiss, Gergely","first_name":"Gergely","last_name":"Kiss"},{"id":"E62E3130-B088-11EA-B919-BF823C25FEA4","first_name":"János","last_name":"Pach","full_name":"Pach, János"},{"last_name":"Somlai","first_name":"Gábor","full_name":"Somlai, Gábor"}],"volume":34,"date_updated":"2023-12-13T13:04:55Z","date_created":"2023-10-29T23:01:18Z","year":"2023","department":[{"_id":"HeEd"}],"publisher":"World Scientific Publishing","publication_status":"published"},{"file":[{"date_created":"2023-04-17T08:10:28Z","date_updated":"2023-04-17T08:10:28Z","success":1,"checksum":"439102ea4f6e2aeefd7107dfb9ccf532","file_id":"12844","relation":"main_file","creator":"dernst","content_type":"application/pdf","file_size":2072197,"file_name":"2022_DMTCS_Biniaz.pdf","access_level":"open_access"}],"oa_version":"Published Version","intvolume":" 24","status":"public","title":"Token swapping on trees","ddc":["000"],"_id":"12833","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","issue":"2","abstract":[{"text":"The input to the token swapping problem is a graph with vertices v1, v2, . . . , vn, and n tokens with labels 1,2, . . . , n, one on each vertex. The goal is to get token i to vertex vi for all i= 1, . . . , n using a minimum number of swaps, where a swap exchanges the tokens on the endpoints of an edge.Token swapping on a tree, also known as “sorting with a transposition tree,” is not known to be in P nor NP-complete. We present some partial results: 1. An optimum swap sequence may need to perform a swap on a leaf vertex that has the correct token (a “happy leaf”), disproving a conjecture of Vaughan. 2. Any algorithm that fixes happy leaves—as all known approximation algorithms for the problem do—has approximation factor at least 4/3. Furthermore, the two best-known 2-approximation algorithms have approximation factor exactly 2. 3. A generalized problem—weighted coloured token swapping—is NP-complete on trees, but solvable in polynomial time on paths and stars. In this version, tokens and vertices have colours, and colours have weights. The goal is to get every token to a vertex of the same colour, and the cost of a swap is the sum of the weights of the two tokens involved.","lang":"eng"}],"type":"journal_article","date_published":"2023-01-18T00:00:00Z","article_type":"original","citation":{"ama":"Biniaz A, Jain K, Lubiw A, et al. Token swapping on trees. Discrete Mathematics and Theoretical Computer Science. 2023;24(2). doi:10.46298/DMTCS.8383","ista":"Biniaz A, Jain K, Lubiw A, Masárová Z, Miltzow T, Mondal D, Naredla AM, Tkadlec J, Turcotte A. 2023. Token swapping on trees. Discrete Mathematics and Theoretical Computer Science. 24(2), 9.","ieee":"A. Biniaz et al., “Token swapping on trees,” Discrete Mathematics and Theoretical Computer Science, vol. 24, no. 2. EPI Sciences, 2023.","apa":"Biniaz, A., Jain, K., Lubiw, A., Masárová, Z., Miltzow, T., Mondal, D., … Turcotte, A. (2023). Token swapping on trees. Discrete Mathematics and Theoretical Computer Science. EPI Sciences. https://doi.org/10.46298/DMTCS.8383","mla":"Biniaz, Ahmad, et al. “Token Swapping on Trees.” Discrete Mathematics and Theoretical Computer Science, vol. 24, no. 2, 9, EPI Sciences, 2023, doi:10.46298/DMTCS.8383.","short":"A. Biniaz, K. Jain, A. Lubiw, Z. Masárová, T. Miltzow, D. Mondal, A.M. Naredla, J. Tkadlec, A. Turcotte, Discrete Mathematics and Theoretical Computer Science 24 (2023).","chicago":"Biniaz, Ahmad, Kshitij Jain, Anna Lubiw, Zuzana Masárová, Tillmann Miltzow, Debajyoti Mondal, Anurag Murty Naredla, Josef Tkadlec, and Alexi Turcotte. “Token Swapping on Trees.” Discrete Mathematics and Theoretical Computer Science. EPI Sciences, 2023. https://doi.org/10.46298/DMTCS.8383."},"publication":"Discrete Mathematics and Theoretical Computer Science","article_processing_charge":"No","has_accepted_license":"1","day":"18","scopus_import":"1","volume":24,"date_created":"2023-04-16T22:01:08Z","date_updated":"2024-01-04T12:42:09Z","related_material":{"record":[{"id":"7950","status":"public","relation":"earlier_version"}]},"author":[{"last_name":"Biniaz","first_name":"Ahmad","full_name":"Biniaz, Ahmad"},{"first_name":"Kshitij","last_name":"Jain","full_name":"Jain, Kshitij"},{"full_name":"Lubiw, Anna","last_name":"Lubiw","first_name":"Anna"},{"orcid":"0000-0002-6660-1322","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","last_name":"Masárová","first_name":"Zuzana","full_name":"Masárová, Zuzana"},{"first_name":"Tillmann","last_name":"Miltzow","full_name":"Miltzow, Tillmann"},{"last_name":"Mondal","first_name":"Debajyoti","full_name":"Mondal, Debajyoti"},{"last_name":"Naredla","first_name":"Anurag Murty","full_name":"Naredla, Anurag Murty"},{"id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1097-9684","first_name":"Josef","last_name":"Tkadlec","full_name":"Tkadlec, Josef"},{"first_name":"Alexi","last_name":"Turcotte","full_name":"Turcotte, Alexi"}],"department":[{"_id":"KrCh"},{"_id":"HeEd"},{"_id":"UlWa"}],"publisher":"EPI Sciences","publication_status":"published","acknowledgement":"This work was begun at the University of Waterloo and was partially supported by the Natural Sciences and Engineering Council of Canada (NSERC).\r\n","year":"2023","license":"https://creativecommons.org/licenses/by/4.0/","file_date_updated":"2023-04-17T08:10:28Z","article_number":"9","language":[{"iso":"eng"}],"doi":"10.46298/DMTCS.8383","quality_controlled":"1","external_id":{"arxiv":["1903.06981"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"publication_identifier":{"eissn":["1365-8050"],"issn":["1462-7264"]},"month":"01"},{"file":[{"creator":"dernst","content_type":"application/pdf","file_size":2370988,"access_level":"open_access","file_name":"2023_IEEEToP_Ali.pdf","success":1,"checksum":"465c28ef0b151b4b1fb47977ed5581ab","date_updated":"2024-01-08T10:09:14Z","date_created":"2024-01-08T10:09:14Z","file_id":"14740","relation":"main_file"}],"oa_version":"Published Version","_id":"14739","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 45","status":"public","title":"A survey of vectorization methods in topological data analysis","ddc":["000"],"issue":"12","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"}],"type":"journal_article","date_published":"2023-12-01T00:00:00Z","citation":{"chicago":"Ali, Dashti, Aras Asaad, Maria-Jose Jimenez, Vidit Nanda, Eduardo Paluzo-Hidalgo, and Manuel Soriano Trigueros. “A Survey of Vectorization Methods in Topological Data Analysis.” IEEE Transactions on Pattern Analysis and Machine Intelligence. IEEE, 2023. https://doi.org/10.1109/tpami.2023.3308391.","mla":"Ali, Dashti, et al. “A Survey of Vectorization Methods in Topological Data Analysis.” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 45, no. 12, IEEE, 2023, pp. 14069–80, doi:10.1109/tpami.2023.3308391.","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.","apa":"Ali, D., Asaad, A., Jimenez, M.-J., Nanda, V., Paluzo-Hidalgo, E., & Soriano Trigueros, M. (2023). A survey of vectorization methods in topological data analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence. IEEE. https://doi.org/10.1109/tpami.2023.3308391","ieee":"D. Ali, A. Asaad, M.-J. Jimenez, V. Nanda, E. Paluzo-Hidalgo, and M. Soriano Trigueros, “A survey of vectorization methods in topological data analysis,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 45, no. 12. IEEE, pp. 14069–14080, 2023.","ama":"Ali D, Asaad A, Jimenez M-J, Nanda V, Paluzo-Hidalgo E, Soriano Trigueros M. A survey of vectorization methods in topological data analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2023;45(12):14069-14080. doi:10.1109/tpami.2023.3308391"},"publication":"IEEE Transactions on Pattern Analysis and Machine Intelligence","page":"14069-14080","article_type":"original","article_processing_charge":"Yes (in subscription journal)","has_accepted_license":"1","day":"01","keyword":["Applied Mathematics","Artificial Intelligence","Computational Theory and Mathematics","Computer Vision and Pattern Recognition","Software"],"author":[{"full_name":"Ali, Dashti","last_name":"Ali","first_name":"Dashti"},{"full_name":"Asaad, Aras","first_name":"Aras","last_name":"Asaad"},{"first_name":"Maria-Jose","last_name":"Jimenez","full_name":"Jimenez, Maria-Jose"},{"full_name":"Nanda, Vidit","first_name":"Vidit","last_name":"Nanda"},{"full_name":"Paluzo-Hidalgo, Eduardo","last_name":"Paluzo-Hidalgo","first_name":"Eduardo"},{"full_name":"Soriano Trigueros, Manuel","id":"15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8","orcid":"0000-0003-2449-1433","first_name":"Manuel","last_name":"Soriano Trigueros"}],"volume":45,"date_updated":"2024-01-08T10:11:46Z","date_created":"2024-01-08T09:59:46Z","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.","year":"2023","publisher":"IEEE","department":[{"_id":"HeEd"}],"publication_status":"published","file_date_updated":"2024-01-08T10:09:14Z","doi":"10.1109/tpami.2023.3308391","language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"quality_controlled":"1","publication_identifier":{"eissn":["1939-3539"],"issn":["0162-8828"]},"month":"12"},{"publication_identifier":{"issn":["0097-3165"],"eissn":["1096-0899"]},"month":"10","tmp":{"name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","image":"/images/cc_by_nc_sa.png","short":"CC BY-NC-SA (4.0)"},"oa":1,"external_id":{"arxiv":["2206.13592"]},"quality_controlled":"1","doi":"10.1016/j.jcta.2023.105776","language":[{"iso":"eng"}],"article_number":"105776","file_date_updated":"2024-01-30T12:03:10Z","license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","year":"2023","department":[{"_id":"HeEd"}],"publisher":"Elsevier","publication_status":"published","author":[{"full_name":"Fang, Lixing","last_name":"Fang","first_name":"Lixing"},{"first_name":"Hao","last_name":"Huang","full_name":"Huang, Hao"},{"last_name":"Pach","first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4","full_name":"Pach, János"},{"full_name":"Tardos, Gábor","last_name":"Tardos","first_name":"Gábor"},{"last_name":"Zuo","first_name":"Junchi","full_name":"Zuo, Junchi"}],"volume":199,"date_created":"2023-06-25T22:00:45Z","date_updated":"2024-01-30T12:03:51Z","scopus_import":"1","article_processing_charge":"Yes (in subscription journal)","has_accepted_license":"1","day":"01","citation":{"chicago":"Fang, Lixing, Hao Huang, János Pach, Gábor Tardos, and Junchi Zuo. “Successive Vertex Orderings of Fully Regular Graphs.” Journal of Combinatorial Theory. Series A. Elsevier, 2023. https://doi.org/10.1016/j.jcta.2023.105776.","short":"L. Fang, H. Huang, J. Pach, G. Tardos, J. Zuo, Journal of Combinatorial Theory. Series A 199 (2023).","mla":"Fang, Lixing, et al. “Successive Vertex Orderings of Fully Regular Graphs.” Journal of Combinatorial Theory. Series A, vol. 199, no. 10, 105776, Elsevier, 2023, doi:10.1016/j.jcta.2023.105776.","ieee":"L. Fang, H. Huang, J. Pach, G. Tardos, and J. Zuo, “Successive vertex orderings of fully regular graphs,” Journal of Combinatorial Theory. Series A, vol. 199, no. 10. Elsevier, 2023.","apa":"Fang, L., Huang, H., Pach, J., Tardos, G., & Zuo, J. (2023). Successive vertex orderings of fully regular graphs. Journal of Combinatorial Theory. Series A. Elsevier. https://doi.org/10.1016/j.jcta.2023.105776","ista":"Fang L, Huang H, Pach J, Tardos G, Zuo J. 2023. Successive vertex orderings of fully regular graphs. Journal of Combinatorial Theory. Series A. 199(10), 105776.","ama":"Fang L, Huang H, Pach J, Tardos G, Zuo J. Successive vertex orderings of fully regular graphs. Journal of Combinatorial Theory Series A. 2023;199(10). doi:10.1016/j.jcta.2023.105776"},"publication":"Journal of Combinatorial Theory. Series A","article_type":"original","date_published":"2023-10-01T00:00:00Z","type":"journal_article","issue":"10","abstract":[{"lang":"eng","text":"A graph G=(V, E) is called fully regular if for every independent set I c V, the number of vertices in V\\I that are not connected to any element of I depends only on the size of I. A linear ordering of the vertices of G is called successive if for every i, the first i vertices induce a connected subgraph of G. We give an explicit formula for the number of successive vertex orderings of a fully regular graph.\r\nAs an application of our results, we give alternative proofs of two theorems of Stanley and Gao & Peng, determining the number of linear edge orderings of complete graphs and complete bipartite graphs, respectively, with the property that the first i edges induce a connected subgraph.\r\nAs another application, we give a simple product formula for the number of linear orderings of the hyperedges of a complete 3-partite 3-uniform hypergraph such that, for every i, the first i hyperedges induce a connected subgraph. We found similar formulas for complete (non-partite) 3-uniform hypergraphs and in another closely related case, but we managed to verify them only when the number of vertices is small."}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"13165","intvolume":" 199","ddc":["510"],"status":"public","title":"Successive vertex orderings of fully regular graphs","file":[{"success":1,"checksum":"9eebc213b4182a66063a99083ff5bd04","date_created":"2024-01-30T12:03:10Z","date_updated":"2024-01-30T12:03:10Z","file_id":"14902","relation":"main_file","creator":"dernst","file_size":352555,"content_type":"application/pdf","access_level":"open_access","file_name":"2023_JourCombinatiorialTheory_Fang.pdf"}],"oa_version":"Published Version"},{"date_published":"2023-10-25T00:00:00Z","citation":{"mla":"Castellano, Ilaria, et al. “Weakly Weighted Generalised Quasi-Metric Spaces and Semilattices.” Theoretical Computer Science, vol. 977, 114129, Elsevier, 2023, doi:10.1016/j.tcs.2023.114129.","short":"I. Castellano, A. Giordano Bruno, N. Zava, Theoretical Computer Science 977 (2023).","chicago":"Castellano, Ilaria, Anna Giordano Bruno, and Nicolò Zava. “Weakly Weighted Generalised Quasi-Metric Spaces and Semilattices.” Theoretical Computer Science. Elsevier, 2023. https://doi.org/10.1016/j.tcs.2023.114129.","ama":"Castellano I, Giordano Bruno A, Zava N. Weakly weighted generalised quasi-metric spaces and semilattices. Theoretical Computer Science. 2023;977. doi:10.1016/j.tcs.2023.114129","ista":"Castellano I, Giordano Bruno A, Zava N. 2023. Weakly weighted generalised quasi-metric spaces and semilattices. Theoretical Computer Science. 977, 114129.","ieee":"I. Castellano, A. Giordano Bruno, and N. Zava, “Weakly weighted generalised quasi-metric spaces and semilattices,” Theoretical Computer Science, vol. 977. Elsevier, 2023.","apa":"Castellano, I., Giordano Bruno, A., & Zava, N. (2023). Weakly weighted generalised quasi-metric spaces and semilattices. Theoretical Computer Science. Elsevier. https://doi.org/10.1016/j.tcs.2023.114129"},"publication":"Theoretical Computer Science","article_type":"original","article_processing_charge":"No","day":"25","scopus_import":"1","oa_version":"Preprint","_id":"14362","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 977","status":"public","title":"Weakly weighted generalised quasi-metric spaces and semilattices","abstract":[{"text":"Motivated by recent applications to entropy theory in dynamical systems, we generalise notions introduced by Matthews and define weakly weighted and componentwise weakly weighted (generalised) quasi-metrics. We then systematise and extend to full generality the correspondences between these objects and other structures arising in theoretical computer science and dynamics. In particular, we study the correspondences with weak partial metrics and, if the underlying space is a semilattice, with invariant (generalised) quasi-metrics satisfying the descending path condition, and with strictly monotone semi(-co-)valuations.\r\nWe conclude discussing, for endomorphisms of generalised quasi-metric semilattices, a generalisation of both the known intrinsic semilattice entropy and the semigroup entropy.","lang":"eng"}],"type":"journal_article","doi":"10.1016/j.tcs.2023.114129","language":[{"iso":"eng"}],"external_id":{"arxiv":["2212.08424"],"isi":["001076934000001"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2212.08424 "}],"quality_controlled":"1","isi":1,"publication_identifier":{"issn":["0304-3975"]},"month":"10","author":[{"first_name":"Ilaria","last_name":"Castellano","full_name":"Castellano, Ilaria"},{"full_name":"Giordano Bruno, Anna","last_name":"Giordano Bruno","first_name":"Anna"},{"full_name":"Zava, Nicolò","first_name":"Nicolò","last_name":"Zava","id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad","orcid":"0000-0001-8686-1888"}],"volume":977,"date_created":"2023-09-24T22:01:11Z","date_updated":"2024-01-30T13:22:04Z","year":"2023","department":[{"_id":"HeEd"}],"publisher":"Elsevier","publication_status":"published","article_number":"114129"},{"date_published":"2023-06-17T00:00:00Z","citation":{"ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Geometric characterization of the persistence of 1D maps. Journal of Applied and Computational Topology. 2023. doi:10.1007/s41468-023-00126-9","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian, M. (2023). Geometric characterization of the persistence of 1D maps. Journal of Applied and Computational Topology. Springer Nature. https://doi.org/10.1007/s41468-023-00126-9","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Geometric characterization of the persistence of 1D maps,” Journal of Applied and Computational Topology. Springer Nature, 2023.","ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2023. Geometric characterization of the persistence of 1D maps. Journal of Applied and Computational Topology.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology (2023).","mla":"Biswas, Ranita, et al. “Geometric Characterization of the Persistence of 1D Maps.” Journal of Applied and Computational Topology, Springer Nature, 2023, doi:10.1007/s41468-023-00126-9.","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Geometric Characterization of the Persistence of 1D Maps.” Journal of Applied and Computational Topology. Springer Nature, 2023. https://doi.org/10.1007/s41468-023-00126-9."},"publication":"Journal of Applied and Computational Topology","article_type":"original","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","day":"17","scopus_import":"1","file":[{"checksum":"697249d5d1c61dea4410b9f021b70fce","success":1,"date_created":"2023-07-03T09:41:05Z","date_updated":"2023-07-03T09:41:05Z","relation":"main_file","file_id":"13185","file_size":487355,"content_type":"application/pdf","creator":"alisjak","access_level":"open_access","file_name":"2023_Journal of Applied and Computational Topology_Biswas.pdf"}],"oa_version":"Published Version","_id":"13182","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","title":"Geometric characterization of the persistence of 1D maps","ddc":["000"],"abstract":[{"lang":"eng","text":"We characterize critical points of 1-dimensional maps paired in persistent homology\r\ngeometrically and this way get elementary proofs of theorems about the symmetry\r\nof persistence diagrams and the variation of such maps. In particular, we identify\r\nbranching points and endpoints of networks as the sole source of asymmetry and\r\nrelate the cycle basis in persistent homology with a version of the stable marriage\r\nproblem. Our analysis provides the foundations of fast algorithms for maintaining a\r\ncollection of sorted lists together with its persistence diagram."}],"type":"journal_article","doi":"10.1007/s41468-023-00126-9","language":[{"iso":"eng"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"project":[{"call_identifier":"H2020","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"},{"name":"Discretization in Geometry and Dynamics","grant_number":"I4887","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316"},{"grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"The Wittgenstein Prize"}],"quality_controlled":"1","publication_identifier":{"issn":["2367-1726"],"eissn":["2367-1734"]},"month":"06","related_material":{"record":[{"id":"15094","status":"public","relation":"dissertation_contains"}]},"author":[{"first_name":"Ranita","last_name":"Biswas","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5372-7890","full_name":"Biswas, Ranita"},{"first_name":"Sebastiano","last_name":"Cultrera Di Montesano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-6249-0832","full_name":"Cultrera Di Montesano, Sebastiano"},{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Saghafian, Morteza","last_name":"Saghafian","first_name":"Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824"}],"date_updated":"2024-03-20T09:36:56Z","date_created":"2023-07-02T22:00:44Z","acknowledgement":"Open access funding provided by Austrian Science Fund (FWF). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), Grant No. I 02979-N35. The authors of this paper thank anonymous reviewers for their constructive criticism and Monika Henzinger for detailed comments on an earlier version of this paper.","year":"2023","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"publication_status":"epub_ahead","ec_funded":1,"file_date_updated":"2023-07-03T09:41:05Z"},{"_id":"14226","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","status":"public","title":"Generalizing medial axes with homology switches","ddc":["500"],"file":[{"content_type":"application/x-zip-compressed","file_size":15501411,"creator":"cchlebak","access_level":"closed","embargo_to":"open_access","file_name":"documents-export-2023-08-24.zip","checksum":"453caf851d75c3478c10ed09bd242a91","date_updated":"2024-02-26T23:30:03Z","date_created":"2023-08-24T13:02:49Z","relation":"source_file","file_id":"14227"},{"file_size":6854783,"content_type":"application/pdf","creator":"cchlebak","file_name":"thesis_pdf_a.pdf","access_level":"open_access","date_created":"2023-08-24T13:03:42Z","date_updated":"2024-02-26T23:30:03Z","checksum":"7349d29963d6695e555e171748648d9a","relation":"main_file","embargo":"2024-02-25","file_id":"14228"}],"oa_version":"Published Version","type":"dissertation","alternative_title":["ISTA Master's Thesis"],"abstract":[{"lang":"eng","text":"We introduce the notion of a Faustian interchange in a 1-parameter family of smooth\r\nfunctions to generalize the medial axis to critical points of index larger than 0.\r\nWe construct and implement a general purpose algorithm for approximating such\r\ngeneralized medial axes."}],"citation":{"chicago":"Stephenson, Elizabeth R. “Generalizing Medial Axes with Homology Switches.” Institute of Science and Technology Austria, 2023. https://doi.org/10.15479/at:ista:14226.","mla":"Stephenson, Elizabeth R. Generalizing Medial Axes with Homology Switches. Institute of Science and Technology Austria, 2023, doi:10.15479/at:ista:14226.","short":"E.R. Stephenson, Generalizing Medial Axes with Homology Switches, Institute of Science and Technology Austria, 2023.","ista":"Stephenson ER. 2023. Generalizing medial axes with homology switches. Institute of Science and Technology Austria.","ieee":"E. R. Stephenson, “Generalizing medial axes with homology switches,” Institute of Science and Technology Austria, 2023.","apa":"Stephenson, E. R. (2023). Generalizing medial axes with homology switches. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:14226","ama":"Stephenson ER. Generalizing medial axes with homology switches. 2023. doi:10.15479/at:ista:14226"},"page":"43","date_published":"2023-08-24T00:00:00Z","day":"24","has_accepted_license":"1","article_processing_charge":"No","year":"2023","publication_status":"published","publisher":"Institute of Science and Technology Austria","department":[{"_id":"GradSch"},{"_id":"HeEd"}],"author":[{"id":"2D04F932-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6862-208X","first_name":"Elizabeth R","last_name":"Stephenson","full_name":"Stephenson, Elizabeth R"}],"date_created":"2023-08-24T13:01:18Z","date_updated":"2024-02-26T23:30:04Z","file_date_updated":"2024-02-26T23:30:03Z","oa":1,"doi":"10.15479/at:ista:14226","supervisor":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"}],"degree_awarded":"MS","language":[{"iso":"eng"}],"month":"08","publication_identifier":{"issn":["2791-4585"]}},{"day":"01","article_processing_charge":"No","has_accepted_license":"1","scopus_import":"1","series_title":"LIPIcs","date_published":"2022-06-01T00:00:00Z","publication":"38th International Symposium on Computational Geometry","citation":{"chicago":"Chambers, Erin, Christopher D Fillmore, Elizabeth R Stephenson, and Mathijs Wintraecken. “A Cautionary Tale: Burning the Medial Axis Is Unstable.” In 38th International Symposium on Computational Geometry, edited by Xavier Goaoc and Michael Kerber, 224:66:1-66:9. LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. https://doi.org/10.4230/LIPIcs.SoCG.2022.66.","mla":"Chambers, Erin, et al. “A Cautionary Tale: Burning the Medial Axis Is Unstable.” 38th International Symposium on Computational Geometry, edited by Xavier Goaoc and Michael Kerber, vol. 224, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022, p. 66:1-66:9, doi:10.4230/LIPIcs.SoCG.2022.66.","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.","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.","apa":"Chambers, E., Fillmore, C. D., Stephenson, E. R., & Wintraecken, M. (2022). A cautionary tale: Burning the medial axis is unstable. In X. Goaoc & M. Kerber (Eds.), 38th International Symposium on Computational Geometry (Vol. 224, p. 66:1-66:9). Berlin, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2022.66","ieee":"E. Chambers, C. D. Fillmore, E. R. Stephenson, and M. Wintraecken, “A cautionary tale: Burning the medial axis is unstable,” in 38th International Symposium on Computational Geometry, Berlin, Germany, 2022, vol. 224, p. 66:1-66:9.","ama":"Chambers E, Fillmore CD, Stephenson ER, Wintraecken M. A cautionary tale: Burning the medial axis is unstable. In: Goaoc X, Kerber M, eds. 38th International Symposium on Computational Geometry. Vol 224. LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2022:66:1-66:9. doi:10.4230/LIPIcs.SoCG.2022.66"},"page":"66:1-66:9","abstract":[{"lang":"eng","text":"The medial axis of a set consists of the points in the ambient space without a unique closest point on the original set. Since its introduction, the medial axis has been used extensively in many applications as a method of computing a topologically equivalent skeleton. Unfortunately, one limiting factor in the use of the medial axis of a smooth manifold is that it is not necessarily topologically stable under small perturbations of the manifold. To counter these instabilities various prunings of the medial axis have been proposed. Here, we examine one type of pruning, called burning. Because of the good experimental results, it was hoped that the burning method of simplifying the medial axis would be stable. In this work we show a simple example that dashes such hopes based on Bing’s house with two rooms, demonstrating an isotopy of a shape where the medial axis goes from collapsible to non-collapsible."}],"type":"conference","oa_version":"Published Version","file":[{"content_type":"application/pdf","file_size":17580705,"creator":"dernst","access_level":"open_access","file_name":"2022_LIPICs_Chambers.pdf","checksum":"b25ce40fade4ebc0bcaae176db4f5f1f","success":1,"date_created":"2022-06-07T07:58:30Z","date_updated":"2022-06-07T07:58:30Z","relation":"main_file","file_id":"11437"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"11428","status":"public","title":"A cautionary tale: Burning the medial axis is unstable","ddc":["510"],"intvolume":" 224","month":"06","publication_identifier":{"issn":["1868-8969"],"isbn":["978-3-95977-227-3"]},"conference":{"name":"SoCG: Symposium on Computational Geometry","end_date":"2022-06-10","location":"Berlin, Germany","start_date":"2022-06-07"},"doi":"10.4230/LIPIcs.SoCG.2022.66","language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"quality_controlled":"1","project":[{"grant_number":"M03073","_id":"fc390959-9c52-11eb-aca3-afa58bd282b2","name":"Learning and triangulating manifolds via collapses"},{"call_identifier":"H2020","name":"Alpha Shape Theory Extended","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"}],"file_date_updated":"2022-06-07T07:58:30Z","ec_funded":1,"author":[{"full_name":"Chambers, Erin","first_name":"Erin","last_name":"Chambers"},{"first_name":"Christopher D","last_name":"Fillmore","id":"35638A5C-AAC7-11E9-B0BF-5503E6697425","full_name":"Fillmore, Christopher D"},{"full_name":"Stephenson, Elizabeth R","id":"2D04F932-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6862-208X","first_name":"Elizabeth R","last_name":"Stephenson"},{"orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","last_name":"Wintraecken","first_name":"Mathijs","full_name":"Wintraecken, Mathijs"}],"date_updated":"2023-02-21T09:50:52Z","date_created":"2022-06-01T14:18:04Z","volume":224,"year":"2022","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.","publication_status":"published","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"HeEd"}],"editor":[{"full_name":"Goaoc, Xavier","first_name":"Xavier","last_name":"Goaoc"},{"full_name":"Kerber, Michael","last_name":"Kerber","first_name":"Michael"}]},{"year":"2022","_id":"11429","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","title":"Web and Wireless Geographical Information Systems","status":"public","intvolume":" 13238","department":[{"_id":"HeEd"}],"publisher":"Springer Nature","editor":[{"last_name":"Karimipour","first_name":"Farid","orcid":"0000-0001-6746-4174","id":"2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425","full_name":"Karimipour, Farid"},{"full_name":"Storandt, Sabine","first_name":"Sabine","last_name":"Storandt"}],"edition":"1","date_updated":"2022-06-02T05:56:22Z","date_created":"2022-06-02T05:40:53Z","volume":13238,"oa_version":"None","type":"book_editor","alternative_title":["LNCS"],"place":"Cham","abstract":[{"lang":"eng","text":"This book constitutes the refereed proceedings of the 18th International Symposium on Web and Wireless Geographical Information Systems, W2GIS 2022, held in Konstanz, Germany, in April 2022.\r\nThe 7 full papers presented together with 6 short papers in the volume were carefully reviewed and selected from 16 submissions. The papers cover topics that range from mobile GIS and Location-Based Services to Spatial Information Retrieval and Wireless Sensor Networks."}],"citation":{"chicago":"Karimipour, Farid, and Sabine Storandt, eds. Web and Wireless Geographical Information Systems. 1st ed. Vol. 13238. Cham: Springer Nature, 2022. https://doi.org/10.1007/978-3-031-06245-2.","short":"F. Karimipour, S. Storandt, eds., Web and Wireless Geographical Information Systems, 1st ed., Springer Nature, Cham, 2022.","mla":"Karimipour, Farid, and Sabine Storandt, editors. Web and Wireless Geographical Information Systems. 1st ed., vol. 13238, Springer Nature, 2022, doi:10.1007/978-3-031-06245-2.","apa":"Karimipour, F., & Storandt, S. (Eds.). (2022). Web and Wireless Geographical Information Systems (1st ed., Vol. 13238). Cham: Springer Nature. https://doi.org/10.1007/978-3-031-06245-2","ieee":"F. Karimipour and S. Storandt, Eds., Web and Wireless Geographical Information Systems, 1st ed., vol. 13238. Cham: Springer Nature, 2022.","ista":"Karimipour F, Storandt S eds. 2022. Web and Wireless Geographical Information Systems 1st ed., Cham: Springer Nature, 153p.","ama":"Karimipour F, Storandt S, eds. Web and Wireless Geographical Information Systems. Vol 13238. 1st ed. Cham: Springer Nature; 2022. doi:10.1007/978-3-031-06245-2"},"quality_controlled":"1","page":"153","doi":"10.1007/978-3-031-06245-2","date_published":"2022-05-01T00:00:00Z","language":[{"iso":"eng"}],"day":"01","month":"05","article_processing_charge":"No","publication_identifier":{"issn":["0302-9743"],"eisbn":["9783031062452"],"eissn":["1611-3349"],"isbn":["9783031062445"]}},{"oa_version":"Preprint","intvolume":" 30","status":"public","title":"The persistent homology of dual digital image constructions","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"11440","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."}],"alternative_title":["Association for Women in Mathematics Series"],"type":"book_chapter","date_published":"2022-01-27T00:00:00Z","page":"1-26","citation":{"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.","mla":"Bleile, Bea, et al. “The Persistent Homology of Dual Digital Image Constructions.” Research in Computational Topology 2, edited by Ellen Gasparovic et al., 1st ed., vol. 30, Springer Nature, 2022, pp. 1–26, doi:10.1007/978-3-030-95519-9_1.","chicago":"Bleile, Bea, Adélie Garin, Teresa Heiss, Kelly Maggs, and Vanessa Robins. “The Persistent Homology of Dual Digital Image Constructions.” In Research in Computational Topology 2, edited by Ellen Gasparovic, Vanessa Robins, and Katharine Turner, 1st ed., 30:1–26. AWMS. Cham: Springer Nature, 2022. https://doi.org/10.1007/978-3-030-95519-9_1.","ama":"Bleile B, Garin A, Heiss T, Maggs K, Robins V. The persistent homology of dual digital image constructions. In: Gasparovic E, Robins V, Turner K, eds. Research in Computational Topology 2. Vol 30. 1st ed. AWMS. Cham: Springer Nature; 2022:1-26. doi:10.1007/978-3-030-95519-9_1","ieee":"B. Bleile, A. Garin, T. Heiss, K. Maggs, and V. Robins, “The persistent homology of dual digital image constructions,” in Research in Computational Topology 2, 1st ed., vol. 30, E. Gasparovic, V. Robins, and K. Turner, Eds. Cham: Springer Nature, 2022, pp. 1–26.","apa":"Bleile, B., Garin, A., Heiss, T., Maggs, K., & Robins, V. (2022). The persistent homology of dual digital image constructions. In E. Gasparovic, V. Robins, & K. Turner (Eds.), Research in Computational Topology 2 (1st ed., Vol. 30, pp. 1–26). Cham: Springer Nature. https://doi.org/10.1007/978-3-030-95519-9_1","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."},"publication":"Research in Computational Topology 2","article_processing_charge":"No","day":"27","series_title":"AWMS","scopus_import":"1","volume":30,"date_created":"2022-06-07T08:21:11Z","date_updated":"2022-06-07T08:32:42Z","edition":"1","author":[{"first_name":"Bea","last_name":"Bleile","full_name":"Bleile, Bea"},{"full_name":"Garin, Adélie","first_name":"Adélie","last_name":"Garin"},{"last_name":"Heiss","first_name":"Teresa","orcid":"0000-0002-1780-2689","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","full_name":"Heiss, Teresa"},{"full_name":"Maggs, Kelly","first_name":"Kelly","last_name":"Maggs"},{"last_name":"Robins","first_name":"Vanessa","full_name":"Robins, Vanessa"}],"department":[{"_id":"HeEd"}],"editor":[{"full_name":"Gasparovic, Ellen","last_name":"Gasparovic","first_name":"Ellen"},{"first_name":"Vanessa","last_name":"Robins","full_name":"Robins, Vanessa"},{"full_name":"Turner, Katharine","last_name":"Turner","first_name":"Katharine"}],"publisher":"Springer Nature","publication_status":"published","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.","year":"2022","ec_funded":1,"place":"Cham","language":[{"iso":"eng"}],"doi":"10.1007/978-3-030-95519-9_1","project":[{"call_identifier":"H2020","name":"Alpha Shape Theory Extended","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","oa":1,"main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2102.11397","open_access":"1"}],"external_id":{"arxiv":["2102.11397"]},"publication_identifier":{"isbn":["9783030955182"],"eisbn":["9783030955199"]},"month":"01"},{"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"}],"issue":"5","type":"journal_article","oa_version":"None","status":"public","title":"Tangible topology through the lens of limits","intvolume":" 32","_id":"12307","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"28","article_processing_charge":"No","keyword":["Education","General Mathematics"],"scopus_import":"1","date_published":"2022-05-28T00:00:00Z","article_type":"original","page":"593-609","publication":"PRIMUS","citation":{"ama":"Shipman BA, Stephenson ER. Tangible topology through the lens of limits. PRIMUS. 2022;32(5):593-609. doi:10.1080/10511970.2021.1872750","ieee":"B. A. Shipman and E. R. Stephenson, “Tangible topology through the lens of limits,” PRIMUS, vol. 32, no. 5. Taylor & Francis, pp. 593–609, 2022.","apa":"Shipman, B. A., & Stephenson, E. R. (2022). Tangible topology through the lens of limits. PRIMUS. Taylor & Francis. https://doi.org/10.1080/10511970.2021.1872750","ista":"Shipman BA, Stephenson ER. 2022. Tangible topology through the lens of limits. PRIMUS. 32(5), 593–609.","short":"B.A. Shipman, E.R. Stephenson, PRIMUS 32 (2022) 593–609.","mla":"Shipman, Barbara A., and Elizabeth R. Stephenson. “Tangible Topology through the Lens of Limits.” PRIMUS, vol. 32, no. 5, Taylor & Francis, 2022, pp. 593–609, doi:10.1080/10511970.2021.1872750.","chicago":"Shipman, Barbara A., and Elizabeth R Stephenson. “Tangible Topology through the Lens of Limits.” PRIMUS. Taylor & Francis, 2022. https://doi.org/10.1080/10511970.2021.1872750."},"date_updated":"2023-01-30T13:02:30Z","date_created":"2023-01-16T10:07:21Z","volume":32,"author":[{"full_name":"Shipman, Barbara A.","first_name":"Barbara A.","last_name":"Shipman"},{"full_name":"Stephenson, Elizabeth R","id":"2D04F932-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6862-208X","first_name":"Elizabeth R","last_name":"Stephenson"}],"publication_status":"published","department":[{"_id":"HeEd"},{"_id":"GradSch"}],"publisher":"Taylor & Francis","year":"2022","month":"05","publication_identifier":{"issn":["1051-1970"],"eissn":["1935-4053"]},"language":[{"iso":"eng"}],"doi":"10.1080/10511970.2021.1872750","quality_controlled":"1"},{"month":"06","publication_identifier":{"issn":["1526-1719"]},"language":[{"iso":"eng"}],"doi":"10.7155/jgaa.00591","quality_controlled":"1","project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"},{"name":"The Wittgenstein Prize","call_identifier":"FWF","grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"grant_number":"279307","_id":"2581B60A-B435-11E9-9278-68D0E5697425","name":"Quantitative Graph Games: Theory and Applications","call_identifier":"FP7"},{"_id":"2584A770-B435-11E9-9278-68D0E5697425","grant_number":"P 23499-N23","name":"Modern Graph Algorithmic Techniques in Formal Verification","call_identifier":"FWF"},{"grant_number":"S11407","_id":"25863FF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Game Theory"}],"external_id":{"arxiv":["2101.03928"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"file_date_updated":"2022-08-22T06:42:42Z","ec_funded":1,"date_created":"2022-08-21T22:01:56Z","date_updated":"2023-02-23T13:54:21Z","volume":26,"author":[{"last_name":"Aichholzer","first_name":"Oswin","full_name":"Aichholzer, Oswin"},{"full_name":"Arroyo Guevara, Alan M","last_name":"Arroyo Guevara","first_name":"Alan M","orcid":"0000-0003-2401-8670","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Masárová","first_name":"Zuzana","orcid":"0000-0002-6660-1322","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","full_name":"Masárová, Zuzana"},{"full_name":"Parada, Irene","first_name":"Irene","last_name":"Parada"},{"first_name":"Daniel","last_name":"Perz","full_name":"Perz, Daniel"},{"last_name":"Pilz","first_name":"Alexander","full_name":"Pilz, Alexander"},{"orcid":"0000-0002-1097-9684","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","last_name":"Tkadlec","first_name":"Josef","full_name":"Tkadlec, Josef"},{"last_name":"Vogtenhuber","first_name":"Birgit","full_name":"Vogtenhuber, Birgit"}],"related_material":{"record":[{"id":"9296","relation":"earlier_version","status":"public"}]},"publication_status":"published","publisher":"Brown University","department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"KrCh"}],"year":"2022","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).","day":"01","has_accepted_license":"1","article_processing_charge":"No","scopus_import":"1","date_published":"2022-06-01T00:00:00Z","article_type":"original","page":"225-240","publication":"Journal of Graph Algorithms and Applications","citation":{"ista":"Aichholzer O, Arroyo Guevara AM, Masárová Z, Parada I, Perz D, Pilz A, Tkadlec J, Vogtenhuber B. 2022. On compatible matchings. Journal of Graph Algorithms and Applications. 26(2), 225–240.","apa":"Aichholzer, O., Arroyo Guevara, A. M., Masárová, Z., Parada, I., Perz, D., Pilz, A., … Vogtenhuber, B. (2022). On compatible matchings. Journal of Graph Algorithms and Applications. Brown University. https://doi.org/10.7155/jgaa.00591","ieee":"O. Aichholzer et al., “On compatible matchings,” Journal of Graph Algorithms and Applications, vol. 26, no. 2. Brown University, pp. 225–240, 2022.","ama":"Aichholzer O, Arroyo Guevara AM, Masárová Z, et al. On compatible matchings. Journal of Graph Algorithms and Applications. 2022;26(2):225-240. doi:10.7155/jgaa.00591","chicago":"Aichholzer, Oswin, Alan M Arroyo Guevara, Zuzana Masárová, Irene Parada, Daniel Perz, Alexander Pilz, Josef Tkadlec, and Birgit Vogtenhuber. “On Compatible Matchings.” Journal of Graph Algorithms and Applications. Brown University, 2022. https://doi.org/10.7155/jgaa.00591.","mla":"Aichholzer, Oswin, et al. “On Compatible Matchings.” Journal of Graph Algorithms and Applications, vol. 26, no. 2, Brown University, 2022, pp. 225–40, doi:10.7155/jgaa.00591.","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":[{"text":"A matching is compatible to two or more labeled point sets of size n with labels {1, . . . , n} if its straight-line drawing on each of these point sets is crossing-free. We study the maximum number of edges in a matching compatible to two or more labeled point sets in general position in the plane. We show that for any two labeled sets of n points in convex position there exists a compatible matching with ⌊√2n + 1 − 1⌋ edges. More generally, for any ℓ labeled point sets we construct compatible matchings of size Ω(n1/ℓ). As a corresponding upper bound, we use probabilistic arguments to show that for any ℓ given sets of n points there exists a labeling of each set such that the largest compatible matching has O(n2/(ℓ+1)) edges. Finally, we show that Θ(log n) copies of any set of n points are necessary and sufficient for the existence of labelings of these point sets such that any compatible matching consists only of a single edge.","lang":"eng"}],"issue":"2","type":"journal_article","file":[{"file_id":"11940","relation":"main_file","success":1,"checksum":"dc6e255e3558faff924fd9e370886c11","date_updated":"2022-08-22T06:42:42Z","date_created":"2022-08-22T06:42:42Z","access_level":"open_access","file_name":"2022_JourGraphAlgorithmsApplic_Aichholzer.pdf","creator":"dernst","content_type":"application/pdf","file_size":694538}],"oa_version":"Published Version","ddc":["000"],"status":"public","title":"On compatible matchings","intvolume":" 26","_id":"11938","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"date_published":"2022-01-01T00:00:00Z","article_type":"original","page":"967-1012","publication":"Foundations of Computational Mathematics ","citation":{"chicago":"Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness of PL Approximations of Isomanifolds.” Foundations of Computational Mathematics . Springer Nature, 2022. https://doi.org/10.1007/s10208-021-09520-0.","short":"J.-D. Boissonnat, M. Wintraecken, Foundations of Computational Mathematics 22 (2022) 967–1012.","mla":"Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness of PL Approximations of Isomanifolds.” Foundations of Computational Mathematics , vol. 22, Springer Nature, 2022, pp. 967–1012, doi:10.1007/s10208-021-09520-0.","apa":"Boissonnat, J.-D., & Wintraecken, M. (2022). The topological correctness of PL approximations of isomanifolds. Foundations of Computational Mathematics . Springer Nature. https://doi.org/10.1007/s10208-021-09520-0","ieee":"J.-D. Boissonnat and M. Wintraecken, “The topological correctness of PL approximations of isomanifolds,” Foundations of Computational Mathematics , vol. 22. Springer Nature, pp. 967–1012, 2022.","ista":"Boissonnat J-D, Wintraecken M. 2022. The topological correctness of PL approximations of isomanifolds. Foundations of Computational Mathematics . 22, 967–1012.","ama":"Boissonnat J-D, Wintraecken M. The topological correctness of PL approximations of isomanifolds. Foundations of Computational Mathematics . 2022;22:967-1012. doi:10.1007/s10208-021-09520-0"},"day":"01","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","scopus_import":"1","oa_version":"Published Version","file":[{"checksum":"f1d372ec3c08ec22e84f8e93e1126b8c","date_created":"2021-07-14T06:44:36Z","date_updated":"2021-07-14T06:44:36Z","relation":"main_file","file_id":"9650","file_size":1455699,"content_type":"application/pdf","creator":"mwintrae","access_level":"open_access","file_name":"Boissonnat-Wintraecken2021_Article_TheTopologicalCorrectnessOfPLA.pdf"}],"title":"The topological correctness of PL approximations of isomanifolds","status":"public","ddc":["516"],"intvolume":" 22","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"9649","abstract":[{"lang":"eng","text":"Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e. manifolds defined as the zero set of some multivariate vector-valued smooth function f : Rd → Rd−n. A natural (and efficient) way to approximate an isomanifold is to consider its Piecewise-Linear (PL) approximation based on a triangulation T of the ambient space Rd. In this paper, we give conditions under which the PL-approximation of an isomanifold is topologically equivalent to the isomanifold. The conditions are easy to satisfy in the sense that they can always be met by taking a sufficiently\r\nfine triangulation T . This contrasts with previous results on the triangulation of manifolds where, in arbitrary dimensions, delicate perturbations are needed to guarantee topological correctness, which leads to strong limitations in practice. We further give a bound on the Fréchet distance between the original isomanifold and its PL-approximation. Finally we show analogous results for the PL-approximation of an isomanifold with boundary."}],"type":"journal_article","language":[{"iso":"eng"}],"doi":"10.1007/s10208-021-09520-0","quality_controlled":"1","isi":1,"project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["000673039600001"]},"oa":1,"month":"0","publication_identifier":{"eissn":["1615-3383"]},"date_created":"2021-07-14T06:44:53Z","date_updated":"2023-08-02T06:49:17Z","volume":22,"author":[{"last_name":"Boissonnat","first_name":"Jean-Daniel","full_name":"Boissonnat, Jean-Daniel"},{"first_name":"Mathijs","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs"}],"related_material":{"record":[{"id":"7952","relation":"earlier_version","status":"public"}]},"publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Springer Nature","year":"2022","acknowledgement":"First and foremost, we acknowledge Siargey Kachanovich for discussions. We thank Herbert Edelsbrunner and all members of his group, all former and current members of the Datashape team (formerly known as Geometrica), and André Lieutier for encouragement. We further thank the reviewers of Foundations of Computational Mathematics and the reviewers and program committee of the Symposium on Computational Geometry for their feedback, which improved the exposition.\r\nThis work was funded by the European Research Council under the European Union’s ERC Grant Agreement number 339025 GUDHI (Algorithmic Foundations of Geometric Understanding in Higher Dimensions). This work was also supported by the French government, through the 3IA Côte d’Azur Investments in the Future project managed by the National Research Agency (ANR) with the reference number ANR-19-P3IA-0002. Mathijs Wintraecken also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 754411.","file_date_updated":"2021-07-14T06:44:36Z","ec_funded":1},{"external_id":{"isi":["000791838800012"]},"isi":1,"quality_controlled":"1","doi":"10.1016/j.topol.2021.107916","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0166-8641"]},"month":"03","acknowledgement":"Dedicated to the memory of Hans-Peter Künzi.","year":"2022","publisher":"Elsevier","department":[{"_id":"HeEd"}],"publication_status":"published","author":[{"last_name":"Dikranjan","first_name":"Dikran","full_name":"Dikranjan, Dikran"},{"last_name":"Giordano Bruno","first_name":"Anna","full_name":"Giordano Bruno, Anna"},{"full_name":"Künzi, Hans Peter","first_name":"Hans Peter","last_name":"Künzi"},{"full_name":"Zava, Nicolò","last_name":"Zava","first_name":"Nicolò","orcid":"0000-0001-8686-1888","id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad"},{"full_name":"Toller, Daniele","first_name":"Daniele","last_name":"Toller"}],"volume":309,"date_created":"2021-12-05T23:01:44Z","date_updated":"2023-08-02T13:33:24Z","article_number":"107916","citation":{"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,” Topology and its Applications, vol. 309. Elsevier, 2022.","apa":"Dikranjan, D., Giordano Bruno, A., Künzi, H. P., Zava, N., & Toller, D. (2022). Generalized quasi-metric semilattices. Topology and Its Applications. Elsevier. https://doi.org/10.1016/j.topol.2021.107916","ama":"Dikranjan D, Giordano Bruno A, Künzi HP, Zava N, Toller D. Generalized quasi-metric semilattices. Topology and its Applications. 2022;309. doi:10.1016/j.topol.2021.107916","chicago":"Dikranjan, Dikran, Anna Giordano Bruno, Hans Peter Künzi, Nicolò Zava, and Daniele Toller. “Generalized Quasi-Metric Semilattices.” Topology and Its Applications. Elsevier, 2022. https://doi.org/10.1016/j.topol.2021.107916.","mla":"Dikranjan, Dikran, et al. “Generalized Quasi-Metric Semilattices.” Topology and Its Applications, vol. 309, 107916, Elsevier, 2022, doi:10.1016/j.topol.2021.107916.","short":"D. Dikranjan, A. Giordano Bruno, H.P. Künzi, N. Zava, D. Toller, Topology and Its Applications 309 (2022)."},"publication":"Topology and its Applications","article_type":"original","date_published":"2022-03-15T00:00:00Z","scopus_import":"1","article_processing_charge":"No","day":"15","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"10413","intvolume":" 309","status":"public","title":"Generalized quasi-metric semilattices","oa_version":"None","type":"journal_article","abstract":[{"lang":"eng","text":"Motivated by the recent introduction of the intrinsic semilattice entropy, we study generalized quasi-metric semilattices and their categories. We investigate the relationship between these objects and generalized semivaluations, extending Nakamura and Schellekens' approach. Finally, we use this correspondence to compare the intrinsic semilattice entropy and the semigroup entropy induced in particular situations, like sets, torsion abelian groups and vector spaces."}]},{"language":[{"iso":"eng"}],"doi":"10.1007/s00454-022-00371-2","quality_controlled":"1","isi":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["000752175300002"]},"oa":1,"publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"month":"04","volume":67,"date_updated":"2023-08-02T14:31:25Z","date_created":"2022-02-20T23:01:34Z","author":[{"full_name":"Biswas, Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5372-7890","first_name":"Ranita","last_name":"Biswas"},{"id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-6249-0832","first_name":"Sebastiano","last_name":"Cultrera Di Montesano","full_name":"Cultrera Di Montesano, Sebastiano"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"full_name":"Saghafian, Morteza","first_name":"Morteza","last_name":"Saghafian"}],"department":[{"_id":"HeEd"}],"publisher":"Springer Nature","publication_status":"published","acknowledgement":"Open access funding provided by the Institute of Science and Technology (IST Austria).","year":"2022","file_date_updated":"2022-08-02T06:07:55Z","date_published":"2022-04-01T00:00:00Z","page":"811-842","article_type":"original","citation":{"chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Continuous and Discrete Radius Functions on Voronoi Tessellations and Delaunay Mosaics.” Discrete and Computational Geometry. Springer Nature, 2022. https://doi.org/10.1007/s00454-022-00371-2.","mla":"Biswas, Ranita, et al. “Continuous and Discrete Radius Functions on Voronoi Tessellations and Delaunay Mosaics.” Discrete and Computational Geometry, vol. 67, Springer Nature, 2022, pp. 811–42, doi:10.1007/s00454-022-00371-2.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Discrete and Computational Geometry 67 (2022) 811–842.","ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2022. Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics. Discrete and Computational Geometry. 67, 811–842.","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian, M. (2022). Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-022-00371-2","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics,” Discrete and Computational Geometry, vol. 67. Springer Nature, pp. 811–842, 2022.","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics. Discrete and Computational Geometry. 2022;67:811-842. doi:10.1007/s00454-022-00371-2"},"publication":"Discrete and Computational Geometry","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","day":"01","scopus_import":"1","oa_version":"Published Version","file":[{"date_updated":"2022-08-02T06:07:55Z","date_created":"2022-08-02T06:07:55Z","checksum":"9383d3b70561bacee905e335dc922680","success":1,"relation":"main_file","file_id":"11718","content_type":"application/pdf","file_size":2518111,"creator":"dernst","file_name":"2022_DiscreteCompGeometry_Biswas.pdf","access_level":"open_access"}],"intvolume":" 67","status":"public","ddc":["510"],"title":"Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"10773","abstract":[{"text":"The Voronoi tessellation in Rd is defined by locally minimizing the power distance to given weighted points. Symmetrically, the Delaunay mosaic can be defined by locally maximizing the negative power distance to other such points. We prove that the average of the two piecewise quadratic functions is piecewise linear, and that all three functions have the same critical points and values. Discretizing the two piecewise quadratic functions, we get the alpha shapes as sublevel sets of the discrete function on the Delaunay mosaic, and analogous shapes as superlevel sets of the discrete function on the Voronoi tessellation. For the same non-critical value, the corresponding shapes are disjoint, separated by a narrow channel that contains no critical points but the entire level set of the piecewise linear function.","lang":"eng"}],"type":"journal_article"},{"article_processing_charge":"No","day":"13","scopus_import":"1","date_published":"2022-01-13T00:00:00Z","citation":{"chicago":"Heiss, Teresa, Sarah Tymochko, Brittany Story, Adélie Garin, Hoa Bui, Bea Bleile, and Vanessa Robins. “The Impact of Changes in Resolution on the Persistent Homology of Images.” In 2021 IEEE International Conference on Big Data, 3824–34. IEEE, 2022. https://doi.org/10.1109/BigData52589.2021.9671483.","mla":"Heiss, Teresa, et al. “The Impact of Changes in Resolution on the Persistent Homology of Images.” 2021 IEEE International Conference on Big Data, IEEE, 2022, pp. 3824–34, doi:10.1109/BigData52589.2021.9671483.","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.","apa":"Heiss, T., Tymochko, S., Story, B., Garin, A., Bui, H., Bleile, B., & Robins, V. (2022). The impact of changes in resolution on the persistent homology of images. In 2021 IEEE International Conference on Big Data (pp. 3824–3834). Orlando, FL, United States; Virtuell: IEEE. https://doi.org/10.1109/BigData52589.2021.9671483","ieee":"T. Heiss et al., “The impact of changes in resolution on the persistent homology of images,” in 2021 IEEE International Conference on Big Data, Orlando, FL, United States; Virtuell, 2022, pp. 3824–3834.","ama":"Heiss T, Tymochko S, Story B, et al. The impact of changes in resolution on the persistent homology of images. In: 2021 IEEE International Conference on Big Data. IEEE; 2022:3824-3834. doi:10.1109/BigData52589.2021.9671483"},"publication":"2021 IEEE International Conference on Big Data","page":"3824-3834","abstract":[{"lang":"eng","text":"Digital images enable quantitative analysis of material properties at micro and macro length scales, but choosing an appropriate resolution when acquiring the image is challenging. A high resolution means longer image acquisition and larger data requirements for a given sample, but if the resolution is too low, significant information may be lost. This paper studies the impact of changes in resolution on persistent homology, a tool from topological data analysis that provides a signature of structure in an image across all length scales. Given prior information about a function, the geometry of an object, or its density distribution at a given resolution, we provide methods to select the coarsest resolution yielding results within an acceptable tolerance. We present numerical case studies for an illustrative synthetic example and samples from porous materials where the theoretical bounds are unknown."}],"type":"conference","oa_version":"Preprint","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"10828","title":"The impact of changes in resolution on the persistent homology of images","status":"public","publication_identifier":{"isbn":["9781665439022"]},"month":"01","doi":"10.1109/BigData52589.2021.9671483","conference":{"start_date":"2021-12-15","location":"Orlando, FL, United States; Virtuell","end_date":"2021-12-18","name":"Big Data: International Conference on Big Data"},"language":[{"iso":"eng"}],"external_id":{"isi":["000800559503126"],"arxiv":["2111.05663"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2111.05663"}],"isi":1,"quality_controlled":"1","author":[{"full_name":"Heiss, Teresa","last_name":"Heiss","first_name":"Teresa","orcid":"0000-0002-1780-2689","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Tymochko, Sarah","first_name":"Sarah","last_name":"Tymochko"},{"full_name":"Story, Brittany","last_name":"Story","first_name":"Brittany"},{"full_name":"Garin, Adélie","first_name":"Adélie","last_name":"Garin"},{"last_name":"Bui","first_name":"Hoa","full_name":"Bui, Hoa"},{"full_name":"Bleile, Bea","first_name":"Bea","last_name":"Bleile"},{"full_name":"Robins, Vanessa","first_name":"Vanessa","last_name":"Robins"}],"date_created":"2022-03-06T23:01:53Z","date_updated":"2023-08-02T14:44:21Z","year":"2022","department":[{"_id":"HeEd"}],"publisher":"IEEE","publication_status":"published"},{"file":[{"file_size":582962,"content_type":"application/pdf","creator":"dernst","access_level":"open_access","file_name":"2022_JournalAlgebra_Brown.pdf","checksum":"82abaee3d7837f703e499a9ecbb25b7c","success":1,"date_created":"2023-02-02T07:32:48Z","date_updated":"2023-02-02T07:32:48Z","relation":"main_file","file_id":"12473"}],"oa_version":"Published Version","status":"public","title":"Contravariant pairings between standard Whittaker modules and Verma modules","ddc":["510"],"intvolume":" 609","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"11545","abstract":[{"text":"We classify contravariant pairings between standard Whittaker modules and Verma modules over a complex semisimple Lie algebra. These contravariant pairings are useful in extending several classical techniques for category O to the Miličić–Soergel category N . We introduce a class of costandard modules which generalize dual Verma modules, and describe canonical maps from standard to costandard modules in terms of contravariant pairings.\r\nWe show that costandard modules have unique irreducible submodules and share the same composition factors as the corresponding standard Whittaker modules. We show that costandard modules give an algebraic characterization of the global sections of costandard twisted Harish-Chandra sheaves on the associated flag variety, which are defined using holonomic duality of D-modules. We prove that with these costandard modules, blocks of category\r\nN have the structure of highest weight categories and we establish a BGG reciprocity theorem for N .","lang":"eng"}],"issue":"11","type":"journal_article","date_published":"2022-11-01T00:00:00Z","article_type":"original","page":"145-179","publication":"Journal of Algebra","citation":{"ista":"Brown A, Romanov A. 2022. Contravariant pairings between standard Whittaker modules and Verma modules. Journal of Algebra. 609(11), 145–179.","ieee":"A. Brown and A. Romanov, “Contravariant pairings between standard Whittaker modules and Verma modules,” Journal of Algebra, vol. 609, no. 11. Elsevier, pp. 145–179, 2022.","apa":"Brown, A., & Romanov, A. (2022). Contravariant pairings between standard Whittaker modules and Verma modules. Journal of Algebra. Elsevier. https://doi.org/10.1016/j.jalgebra.2022.06.017","ama":"Brown A, Romanov A. Contravariant pairings between standard Whittaker modules and Verma modules. Journal of Algebra. 2022;609(11):145-179. doi:10.1016/j.jalgebra.2022.06.017","chicago":"Brown, Adam, and Anna Romanov. “Contravariant Pairings between Standard Whittaker Modules and Verma Modules.” Journal of Algebra. Elsevier, 2022. https://doi.org/10.1016/j.jalgebra.2022.06.017.","mla":"Brown, Adam, and Anna Romanov. “Contravariant Pairings between Standard Whittaker Modules and Verma Modules.” Journal of Algebra, vol. 609, no. 11, Elsevier, 2022, pp. 145–79, doi:10.1016/j.jalgebra.2022.06.017.","short":"A. Brown, A. Romanov, Journal of Algebra 609 (2022) 145–179."},"day":"01","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","keyword":["Algebra and Number Theory"],"scopus_import":"1","date_created":"2022-07-08T11:40:07Z","date_updated":"2023-08-03T11:56:30Z","volume":609,"author":[{"id":"70B7FDF6-608D-11E9-9333-8535E6697425","first_name":"Adam","last_name":"Brown","full_name":"Brown, Adam"},{"first_name":"Anna","last_name":"Romanov","full_name":"Romanov, Anna"}],"publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Elsevier","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.","year":"2022","file_date_updated":"2023-02-02T07:32:48Z","ec_funded":1,"language":[{"iso":"eng"}],"doi":"10.1016/j.jalgebra.2022.06.017","isi":1,"quality_controlled":"1","project":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["000861841100004"]},"month":"11","publication_identifier":{"issn":["0021-8693"]}},{"type":"journal_article","issue":"3","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"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"10754","intvolume":" 23","title":"Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer","status":"public","ddc":["510","576"],"file":[{"access_level":"open_access","file_name":"2022_IJMS_Chang.pdf","file_size":24416183,"content_type":"application/pdf","creator":"dernst","relation":"main_file","file_id":"10756","checksum":"8890ad20c54e90dc58ad5ea97c902998","success":1,"date_updated":"2022-02-14T07:46:30Z","date_created":"2022-02-14T07:46:30Z"}],"oa_version":"Published Version","scopus_import":"1","has_accepted_license":"1","article_processing_charge":"Yes","day":"01","citation":{"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.” International Journal of Molecular Sciences, vol. 23, no. 3, 1763, MDPI, 2022, doi:10.3390/ijms23031763.","chicago":"Chang, Yan, Marah Funk, Souvik Roy, Elizabeth R Stephenson, Sangyong Choi, Hristo V. Kojouharov, Benito Chen, and Zui Pan. “Developing a Mathematical Model of Intracellular Calcium Dynamics for Evaluating Combined Anticancer Effects of Afatinib and RP4010 in Esophageal Cancer.” International Journal of Molecular Sciences. MDPI, 2022. https://doi.org/10.3390/ijms23031763.","ama":"Chang Y, Funk M, Roy S, et al. Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer. International Journal of Molecular Sciences. 2022;23(3). doi:10.3390/ijms23031763","apa":"Chang, Y., Funk, M., Roy, S., Stephenson, E. R., Choi, S., Kojouharov, H. V., … Pan, Z. (2022). Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer. International Journal of Molecular Sciences. MDPI. https://doi.org/10.3390/ijms23031763","ieee":"Y. Chang et al., “Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer,” International Journal of Molecular Sciences, vol. 23, no. 3. MDPI, 2022.","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."},"publication":"International Journal of Molecular Sciences","article_type":"original","date_published":"2022-02-01T00:00:00Z","article_number":"1763","file_date_updated":"2022-02-14T07:46:30Z","year":"2022","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.). ","publisher":"MDPI","department":[{"_id":"HeEd"}],"publication_status":"published","author":[{"full_name":"Chang, Yan","last_name":"Chang","first_name":"Yan"},{"full_name":"Funk, Marah","first_name":"Marah","last_name":"Funk"},{"full_name":"Roy, Souvik","first_name":"Souvik","last_name":"Roy"},{"first_name":"Elizabeth R","last_name":"Stephenson","id":"2D04F932-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6862-208X","full_name":"Stephenson, Elizabeth R"},{"full_name":"Choi, Sangyong","first_name":"Sangyong","last_name":"Choi"},{"full_name":"Kojouharov, Hristo V.","first_name":"Hristo V.","last_name":"Kojouharov"},{"first_name":"Benito","last_name":"Chen","full_name":"Chen, Benito"},{"last_name":"Pan","first_name":"Zui","full_name":"Pan, Zui"}],"volume":23,"date_created":"2022-02-13T23:01:35Z","date_updated":"2023-08-09T10:17:07Z","publication_identifier":{"issn":["16616596"],"eissn":["14220067"]},"month":"02","external_id":{"isi":["000754773500001"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"isi":1,"quality_controlled":"1","doi":"10.3390/ijms23031763","language":[{"iso":"eng"}]}]