[{"department":[{"_id":"HeEd"}],"has_accepted_license":"1","doi":"10.1007/s00453-022-01027-6","language":[{"iso":"eng"}],"ec_funded":1,"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.","article_processing_charge":"Yes (via OA deal)","user_id":"2EBD1598-F248-11E8-B48F-1D18A9856A87","day":"01","oa_version":"Published Version","type":"journal_article","date_updated":"2023-06-27T12:53:43Z","scopus_import":"1","publication_identifier":{"issn":["0178-4617"],"eissn":["1432-0541"]},"page":"277-295","file":[{"file_size":911017,"creator":"dernst","content_type":"application/pdf","date_created":"2023-01-20T10:02:48Z","relation":"main_file","access_level":"open_access","file_name":"2023_Algorithmica_Edelsbrunner.pdf","checksum":"71685ca5121f4c837f40c3f8eb50c915","file_id":"12322","date_updated":"2023-01-20T10:02:48Z","success":1}],"external_id":{"isi":["000846967100001"]},"date_published":"2023-01-01T00:00:00Z","_id":"12086","ddc":["510"],"oa":1,"publication":"Algorithmica","title":"A simple algorithm for higher-order Delaunay mosaics and alpha shapes","abstract":[{"lang":"eng","text":"We present a simple algorithm for computing higher-order Delaunay mosaics that works in Euclidean spaces of any finite dimensions. The algorithm selects the vertices of the order-k mosaic from incrementally constructed lower-order mosaics and uses an algorithm for weighted first-order Delaunay mosaics as a black-box to construct the order-k mosaic from its vertices. Beyond this black-box, the algorithm uses only combinatorial operations, thus facilitating easy implementation. We extend this algorithm to compute higher-order α-shapes and provide open-source implementations. We present experimental results for properties of higher-order Delaunay mosaics of random point sets."}],"publication_status":"published","project":[{"name":"Alpha Shape Theory Extended","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"The Wittgenstein Prize","grant_number":"Z00342"},{"call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes"}],"quality_controlled":"1","author":[{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"full_name":"Osang, Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","last_name":"Osang","first_name":"Georg F"}],"citation":{"apa":"Edelsbrunner, H., &#38; Osang, G. F. (2023). A simple algorithm for higher-order Delaunay mosaics and alpha shapes. <i>Algorithmica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00453-022-01027-6\">https://doi.org/10.1007/s00453-022-01027-6</a>","mla":"Edelsbrunner, Herbert, and Georg F. Osang. “A Simple Algorithm for Higher-Order Delaunay Mosaics and Alpha Shapes.” <i>Algorithmica</i>, vol. 85, Springer Nature, 2023, pp. 277–95, doi:<a href=\"https://doi.org/10.1007/s00453-022-01027-6\">10.1007/s00453-022-01027-6</a>.","ieee":"H. Edelsbrunner and G. F. Osang, “A simple algorithm for higher-order Delaunay mosaics and alpha shapes,” <i>Algorithmica</i>, vol. 85. Springer Nature, pp. 277–295, 2023.","ama":"Edelsbrunner H, Osang GF. A simple algorithm for higher-order Delaunay mosaics and alpha shapes. <i>Algorithmica</i>. 2023;85:277-295. doi:<a href=\"https://doi.org/10.1007/s00453-022-01027-6\">10.1007/s00453-022-01027-6</a>","ista":"Edelsbrunner H, Osang GF. 2023. A simple algorithm for higher-order Delaunay mosaics and alpha shapes. Algorithmica. 85, 277–295.","short":"H. Edelsbrunner, G.F. Osang, Algorithmica 85 (2023) 277–295.","chicago":"Edelsbrunner, Herbert, and Georg F Osang. “A Simple Algorithm for Higher-Order Delaunay Mosaics and Alpha Shapes.” <i>Algorithmica</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00453-022-01027-6\">https://doi.org/10.1007/s00453-022-01027-6</a>."},"year":"2023","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"isi":1,"intvolume":"        85","status":"public","month":"01","date_created":"2022-09-11T22:01:57Z","volume":85,"publisher":"Springer Nature","article_type":"original","file_date_updated":"2023-01-20T10:02:48Z"},{"abstract":[{"lang":"eng","text":"Point-set topology is among the most abstract branches of mathematics in that it lacks tangible notions of distance, length, magnitude, order, and size. There is no shape, no geometry, no algebra, and no direction. Everything we are used to visualizing is gone. In the teaching and learning of mathematics, this can present a conundrum. Yet, this very property makes point set topology perfect for teaching and learning abstract mathematical concepts. It clears our minds of preconceived intuitions and expectations and forces us to think in new and creative ways. In this paper, we present guided investigations into topology through questions and thinking strategies that open up fascinating problems. They are intended for faculty who already teach or are thinking about teaching a class in topology or abstract mathematical reasoning for undergraduates. They can be used to build simple to challenging projects in topology, proofs, honors programs, and research experiences."}],"publication_status":"published","_id":"12307","title":"Tangible topology through the lens of limits","publication":"PRIMUS","year":"2022","quality_controlled":"1","author":[{"first_name":"Barbara A.","last_name":"Shipman","full_name":"Shipman, Barbara A."},{"last_name":"Stephenson","first_name":"Elizabeth R","id":"2D04F932-F248-11E8-B48F-1D18A9856A87","full_name":"Stephenson, Elizabeth R","orcid":"0000-0002-6862-208X"}],"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.","chicago":"Shipman, Barbara A., and Elizabeth R Stephenson. “Tangible Topology through the Lens of Limits.” <i>PRIMUS</i>. Taylor &#38; Francis, 2022. <a href=\"https://doi.org/10.1080/10511970.2021.1872750\">https://doi.org/10.1080/10511970.2021.1872750</a>.","short":"B.A. Shipman, E.R. Stephenson, PRIMUS 32 (2022) 593–609.","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>","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>."},"status":"public","month":"05","date_created":"2023-01-16T10:07:21Z","intvolume":"        32","publisher":"Taylor & Francis","article_type":"original","issue":"5","volume":32,"department":[{"_id":"HeEd"},{"_id":"GradSch"}],"doi":"10.1080/10511970.2021.1872750","language":[{"iso":"eng"}],"day":"28","oa_version":"None","type":"journal_article","date_updated":"2023-01-30T13:02:30Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","scopus_import":"1","publication_identifier":{"issn":["1051-1970"],"eissn":["1935-4053"]},"page":"593-609","keyword":["Education","General Mathematics"],"date_published":"2022-05-28T00:00:00Z"},{"intvolume":"         8","date_created":"2020-05-03T22:00:48Z","month":"12","status":"public","volume":8,"issue":"4","file_date_updated":"2020-07-14T12:48:03Z","article_type":"original","publisher":"Springer Nature","title":"When different norms lead to same billiard trajectories?","publication":"European Journal of Mathematics","oa":1,"ddc":["510"],"_id":"7791","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"publication_status":"published","abstract":[{"text":"Extending a result of Milena Radnovic and Serge Tabachnikov, we establish conditionsfor two different non-symmetric norms to define the same billiard reflection law.","lang":"eng"}],"citation":{"apa":"Akopyan, A., &#38; Karasev, R. (2022). When different norms lead to same billiard trajectories? <i>European Journal of Mathematics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s40879-020-00405-0\">https://doi.org/10.1007/s40879-020-00405-0</a>","mla":"Akopyan, Arseniy, and Roman Karasev. “When Different Norms Lead to Same Billiard Trajectories?” <i>European Journal of Mathematics</i>, vol. 8, no. 4, Springer Nature, 2022, pp. 1309–12, doi:<a href=\"https://doi.org/10.1007/s40879-020-00405-0\">10.1007/s40879-020-00405-0</a>.","ista":"Akopyan A, Karasev R. 2022. When different norms lead to same billiard trajectories? European Journal of Mathematics. 8(4), 1309–1312.","short":"A. Akopyan, R. Karasev, European Journal of Mathematics 8 (2022) 1309–1312.","chicago":"Akopyan, Arseniy, and Roman Karasev. “When Different Norms Lead to Same Billiard Trajectories?” <i>European Journal of Mathematics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s40879-020-00405-0\">https://doi.org/10.1007/s40879-020-00405-0</a>.","ama":"Akopyan A, Karasev R. When different norms lead to same billiard trajectories? <i>European Journal of Mathematics</i>. 2022;8(4):1309-1312. doi:<a href=\"https://doi.org/10.1007/s40879-020-00405-0\">10.1007/s40879-020-00405-0</a>","ieee":"A. Akopyan and R. Karasev, “When different norms lead to same billiard trajectories?,” <i>European Journal of Mathematics</i>, vol. 8, no. 4. Springer Nature, pp. 1309–1312, 2022."},"quality_controlled":"1","author":[{"full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","first_name":"Arseniy"},{"last_name":"Karasev","first_name":"Roman","full_name":"Karasev, Roman"}],"tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"year":"2022","publication_identifier":{"issn":["2199-675X"],"eissn":["2199-6768"]},"scopus_import":"1","arxiv":1,"date_published":"2022-12-01T00:00:00Z","external_id":{"arxiv":["1912.12685"]},"file":[{"file_size":263926,"creator":"dernst","content_type":"application/pdf","relation":"main_file","date_created":"2020-05-04T10:33:42Z","checksum":"f53e71fd03744075adcd0b8fc1b8423d","file_name":"2020_EuropMathematics_Akopyan.pdf","access_level":"open_access","file_id":"7796","date_updated":"2020-07-14T12:48:03Z"}],"page":"1309 - 1312","ec_funded":1,"language":[{"iso":"eng"}],"doi":"10.1007/s40879-020-00405-0","has_accepted_license":"1","department":[{"_id":"HeEd"}],"acknowledgement":"AA was supported by European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 78818 Alpha). RK was supported by the Federal professorship program Grant 1.456.2016/1.4 and the Russian Foundation for Basic Research Grants 18-01-00036 and 19-01-00169. Open access funding provided by Institute of Science and Technology (IST Austria). The authors thank Alexey Balitskiy, Milena Radnović, and Serge Tabachnikov for useful discussions.","article_processing_charge":"Yes (via OA deal)","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","date_updated":"2024-02-22T15:58:42Z","type":"journal_article","oa_version":"Published Version","day":"01"},{"status":"public","month":"05","date_created":"2021-11-02T09:28:55Z","isi":1,"intvolume":"        13","publisher":"Springer Nature","article_type":"original","file_date_updated":"2022-12-20T23:30:08Z","volume":13,"abstract":[{"text":"It is practical to collect a huge amount of movement data and environmental context information along with the health signals of individuals because there is the emergence of new generations of positioning and tracking technologies and rapid advancements of health sensors. The study of the relations between these datasets and their sequence similarity analysis is of interest to many applications such as health monitoring and recommender systems. However, entering all movement parameters and health signals can lead to the complexity of the problem and an increase in its computational load. In this situation, dimension reduction techniques can be used to avoid consideration of simultaneous dependent parameters in the process of similarity measurement of the trajectories. The present study provides a framework, named CaDRAW, to use spatial–temporal data and movement parameters along with independent context information in the process of measuring the similarity of trajectories. In this regard, the omission of dependent movement characteristic signals is conducted by using an unsupervised feature selection dimension reduction technique. To evaluate the effectiveness of the proposed framework, it was applied to a real contextualized movement and related health signal datasets of individuals. The results indicated the capability of the proposed framework in measuring the similarity and in decreasing the characteristic signals in such a way that the similarity results -before and after reduction of dependent characteristic signals- have small differences. The mean differences between the obtained results before and after reducing the dimension were 0.029 and 0.023 for the round path, respectively.","lang":"eng"}],"publication_status":"published","project":[{"_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"Z00342","name":"The Wittgenstein Prize"}],"_id":"10208","ddc":["000"],"oa":1,"publication":"Journal of Ambient Intelligence and Humanized Computing","title":"A context-aware dimension reduction framework for trajectory and health signal analyses","year":"2022","quality_controlled":"1","author":[{"full_name":"Goudarzi, Samira","first_name":"Samira","last_name":"Goudarzi"},{"full_name":"Sharif, Mohammad","last_name":"Sharif","first_name":"Mohammad"},{"orcid":"0000-0001-6746-4174","full_name":"Karimipour, Farid","id":"2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425","first_name":"Farid","last_name":"Karimipour"}],"citation":{"ieee":"S. Goudarzi, M. Sharif, and F. Karimipour, “A context-aware dimension reduction framework for trajectory and health signal analyses,” <i>Journal of Ambient Intelligence and Humanized Computing</i>, vol. 13. Springer Nature, pp. 2621–2635, 2022.","ama":"Goudarzi S, Sharif M, Karimipour F. A context-aware dimension reduction framework for trajectory and health signal analyses. <i>Journal of Ambient Intelligence and Humanized Computing</i>. 2022;13:2621–2635. doi:<a href=\"https://doi.org/10.1007/s12652-021-03569-z\">10.1007/s12652-021-03569-z</a>","ista":"Goudarzi S, Sharif M, Karimipour F. 2022. A context-aware dimension reduction framework for trajectory and health signal analyses. Journal of Ambient Intelligence and Humanized Computing. 13, 2621–2635.","chicago":"Goudarzi, Samira, Mohammad Sharif, and Farid Karimipour. “A Context-Aware Dimension Reduction Framework for Trajectory and Health Signal Analyses.” <i>Journal of Ambient Intelligence and Humanized Computing</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s12652-021-03569-z\">https://doi.org/10.1007/s12652-021-03569-z</a>.","short":"S. Goudarzi, M. Sharif, F. Karimipour, Journal of Ambient Intelligence and Humanized Computing 13 (2022) 2621–2635.","mla":"Goudarzi, Samira, et al. “A Context-Aware Dimension Reduction Framework for Trajectory and Health Signal Analyses.” <i>Journal of Ambient Intelligence and Humanized Computing</i>, vol. 13, Springer Nature, 2022, pp. 2621–2635, doi:<a href=\"https://doi.org/10.1007/s12652-021-03569-z\">10.1007/s12652-021-03569-z</a>.","apa":"Goudarzi, S., Sharif, M., &#38; Karimipour, F. (2022). A context-aware dimension reduction framework for trajectory and health signal analyses. <i>Journal of Ambient Intelligence and Humanized Computing</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s12652-021-03569-z\">https://doi.org/10.1007/s12652-021-03569-z</a>"},"scopus_import":"1","publication_identifier":{"issn":["1868-5137"],"eissn":["1868-5145"]},"page":"2621–2635","file":[{"content_type":"application/pdf","creator":"fkarimip","file_size":1634958,"embargo":"2022-11-12","relation":"main_file","date_created":"2021-11-12T19:38:05Z","checksum":"0a8961416a9bb2be5a1cebda65468bcf","file_name":"A Context‑aware Dimension Reduction Framework - Journal of Ambient Intelligence 2021 (Preprint version).pdf","access_level":"open_access","file_id":"10279","date_updated":"2022-12-20T23:30:08Z"}],"keyword":["general computer science"],"external_id":{"isi":["000712198000001"]},"date_published":"2022-05-01T00:00:00Z","acknowledgement":"The third author acknowledges the funding received from the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31.","department":[{"_id":"HeEd"}],"has_accepted_license":"1","language":[{"iso":"eng"}],"doi":"10.1007/s12652-021-03569-z","day":"01","oa_version":"Submitted Version","date_updated":"2023-08-02T13:31:48Z","type":"journal_article","article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"},{"scopus_import":"1","publication_identifier":{"issn":["0166-8641"]},"external_id":{"isi":["000791838800012"]},"date_published":"2022-03-15T00:00:00Z","department":[{"_id":"HeEd"}],"doi":"10.1016/j.topol.2021.107916","language":[{"iso":"eng"}],"acknowledgement":"Dedicated to the memory of Hans-Peter Künzi.","article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","day":"15","oa_version":"None","type":"journal_article","date_updated":"2023-08-02T13:33:24Z","isi":1,"intvolume":"       309","status":"public","article_number":"107916","month":"03","date_created":"2021-12-05T23:01:44Z","volume":309,"article_type":"original","publisher":"Elsevier","_id":"10413","title":"Generalized quasi-metric semilattices","publication":"Topology and its Applications","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"}],"publication_status":"published","quality_controlled":"1","author":[{"first_name":"Dikran","last_name":"Dikranjan","full_name":"Dikranjan, Dikran"},{"full_name":"Giordano Bruno, Anna","last_name":"Giordano Bruno","first_name":"Anna"},{"last_name":"Künzi","first_name":"Hans Peter","full_name":"Künzi, Hans Peter"},{"full_name":"Zava, Nicolò","orcid":"0000-0001-8686-1888","id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad","first_name":"Nicolò","last_name":"Zava"},{"full_name":"Toller, Daniele","first_name":"Daniele","last_name":"Toller"}],"citation":{"ista":"Dikranjan D, Giordano Bruno A, Künzi HP, Zava N, Toller D. 2022. Generalized quasi-metric semilattices. Topology and its Applications. 309, 107916.","short":"D. Dikranjan, A. Giordano Bruno, H.P. Künzi, N. Zava, D. Toller, Topology and Its Applications 309 (2022).","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>.","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>","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.","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>.","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>"},"year":"2022"},{"scopus_import":"1","publication_identifier":{"issn":["16616596"],"eissn":["14220067"]},"external_id":{"isi":["000754773500001"]},"file":[{"creator":"dernst","content_type":"application/pdf","file_size":24416183,"date_created":"2022-02-14T07:46:30Z","relation":"main_file","access_level":"open_access","file_name":"2022_IJMS_Chang.pdf","checksum":"8890ad20c54e90dc58ad5ea97c902998","file_id":"10756","date_updated":"2022-02-14T07:46:30Z","success":1}],"date_published":"2022-02-01T00:00:00Z","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.). ","has_accepted_license":"1","department":[{"_id":"HeEd"}],"doi":"10.3390/ijms23031763","language":[{"iso":"eng"}],"oa_version":"Published Version","date_updated":"2023-08-09T10:17:07Z","type":"journal_article","day":"01","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"Yes","month":"02","date_created":"2022-02-13T23:01:35Z","status":"public","article_number":"1763","intvolume":"        23","isi":1,"file_date_updated":"2022-02-14T07:46:30Z","publisher":"MDPI","article_type":"original","volume":23,"issue":"3","abstract":[{"lang":"eng","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."}],"publication_status":"published","title":"Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer","publication":"International Journal of Molecular Sciences","_id":"10754","ddc":["510","576"],"oa":1,"tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"year":"2022","citation":{"mla":"Chang, Yan, et al. “Developing a Mathematical Model of Intracellular Calcium Dynamics for Evaluating Combined Anticancer Effects of Afatinib and RP4010 in Esophageal Cancer.” <i>International Journal of Molecular Sciences</i>, vol. 23, no. 3, 1763, MDPI, 2022, doi:<a href=\"https://doi.org/10.3390/ijms23031763\">10.3390/ijms23031763</a>.","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).","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>.","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>"},"author":[{"full_name":"Chang, Yan","first_name":"Yan","last_name":"Chang"},{"full_name":"Funk, Marah","last_name":"Funk","first_name":"Marah"},{"full_name":"Roy, Souvik","last_name":"Roy","first_name":"Souvik"},{"last_name":"Stephenson","first_name":"Elizabeth R","id":"2D04F932-F248-11E8-B48F-1D18A9856A87","full_name":"Stephenson, Elizabeth R","orcid":"0000-0002-6862-208X"},{"full_name":"Choi, Sangyong","last_name":"Choi","first_name":"Sangyong"},{"first_name":"Hristo V.","last_name":"Kojouharov","full_name":"Kojouharov, Hristo V."},{"first_name":"Benito","last_name":"Chen","full_name":"Chen, Benito"},{"full_name":"Pan, Zui","first_name":"Zui","last_name":"Pan"}],"quality_controlled":"1"},{"publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"scopus_import":"1","date_published":"2022-04-01T00:00:00Z","file":[{"success":1,"file_id":"11718","date_updated":"2022-08-02T06:07:55Z","checksum":"9383d3b70561bacee905e335dc922680","file_name":"2022_DiscreteCompGeometry_Biswas.pdf","access_level":"open_access","relation":"main_file","date_created":"2022-08-02T06:07:55Z","creator":"dernst","content_type":"application/pdf","file_size":2518111}],"external_id":{"isi":["000752175300002"]},"page":"811-842","acknowledgement":"Open access funding provided by the Institute of Science and Technology (IST Austria).","doi":"10.1007/s00454-022-00371-2","language":[{"iso":"eng"}],"department":[{"_id":"HeEd"}],"has_accepted_license":"1","date_updated":"2023-08-02T14:31:25Z","type":"journal_article","oa_version":"Published Version","day":"01","article_processing_charge":"Yes (via OA deal)","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_created":"2022-02-20T23:01:34Z","month":"04","status":"public","intvolume":"        67","isi":1,"file_date_updated":"2022-08-02T06:07:55Z","article_type":"original","publisher":"Springer Nature","volume":67,"publication_status":"published","abstract":[{"lang":"eng","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."}],"publication":"Discrete and Computational Geometry","title":"Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics","ddc":["510"],"oa":1,"_id":"10773","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"year":"2022","citation":{"mla":"Biswas, Ranita, et al. “Continuous and Discrete Radius Functions on Voronoi Tessellations and Delaunay Mosaics.” <i>Discrete and Computational Geometry</i>, vol. 67, Springer Nature, 2022, pp. 811–42, doi:<a href=\"https://doi.org/10.1007/s00454-022-00371-2\">10.1007/s00454-022-00371-2</a>.","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., &#38; Saghafian, M. (2022). Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-022-00371-2\">https://doi.org/10.1007/s00454-022-00371-2</a>","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics. <i>Discrete and Computational Geometry</i>. 2022;67:811-842. doi:<a href=\"https://doi.org/10.1007/s00454-022-00371-2\">10.1007/s00454-022-00371-2</a>","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics,” <i>Discrete and Computational Geometry</i>, vol. 67. Springer Nature, pp. 811–842, 2022.","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.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Discrete and Computational Geometry 67 (2022) 811–842.","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Continuous and Discrete Radius Functions on Voronoi Tessellations and Delaunay Mosaics.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00454-022-00371-2\">https://doi.org/10.1007/s00454-022-00371-2</a>."},"quality_controlled":"1","author":[{"id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890","last_name":"Biswas","first_name":"Ranita"},{"id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","full_name":"Cultrera Di Montesano, Sebastiano","orcid":"0000-0001-6249-0832","first_name":"Sebastiano","last_name":"Cultrera Di Montesano"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert"},{"full_name":"Saghafian, Morteza","first_name":"Morteza","last_name":"Saghafian"}]},{"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.","ec_funded":1,"doi":"10.1007/s10208-021-09520-0","language":[{"iso":"eng"}],"has_accepted_license":"1","department":[{"_id":"HeEd"}],"type":"journal_article","date_updated":"2023-08-02T06:49:17Z","oa_version":"Published Version","day":"01","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"Yes (via OA deal)","publication_identifier":{"eissn":["1615-3383"]},"scopus_import":"1","date_published":"2022-01-01T00:00:00Z","external_id":{"isi":["000673039600001"]},"file":[{"access_level":"open_access","file_name":"Boissonnat-Wintraecken2021_Article_TheTopologicalCorrectnessOfPLA.pdf","checksum":"f1d372ec3c08ec22e84f8e93e1126b8c","date_updated":"2021-07-14T06:44:36Z","file_id":"9650","content_type":"application/pdf","creator":"mwintrae","file_size":1455699,"date_created":"2021-07-14T06:44:36Z","relation":"main_file"}],"page":"967-1012","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}],"publication_status":"published","abstract":[{"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.","lang":"eng"}],"title":"The topological correctness of PL approximations of isomanifolds","publication":"Foundations of Computational Mathematics ","related_material":{"record":[{"relation":"earlier_version","status":"public","id":"7952"}]},"ddc":["516"],"oa":1,"_id":"9649","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"year":"2022","citation":{"apa":"Boissonnat, J.-D., &#38; Wintraecken, M. (2022). The topological correctness of PL approximations of isomanifolds. <i>Foundations of Computational Mathematics </i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10208-021-09520-0\">https://doi.org/10.1007/s10208-021-09520-0</a>","mla":"Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness of PL Approximations of Isomanifolds.” <i>Foundations of Computational Mathematics </i>, vol. 22, Springer Nature, 2022, pp. 967–1012, doi:<a href=\"https://doi.org/10.1007/s10208-021-09520-0\">10.1007/s10208-021-09520-0</a>.","ieee":"J.-D. Boissonnat and M. Wintraecken, “The topological correctness of PL approximations of isomanifolds,” <i>Foundations of Computational Mathematics </i>, vol. 22. Springer Nature, pp. 967–1012, 2022.","ama":"Boissonnat J-D, Wintraecken M. The topological correctness of PL approximations of isomanifolds. <i>Foundations of Computational Mathematics </i>. 2022;22:967-1012. doi:<a href=\"https://doi.org/10.1007/s10208-021-09520-0\">10.1007/s10208-021-09520-0</a>","chicago":"Boissonnat, Jean-Daniel, and Mathijs Wintraecken. “The Topological Correctness of PL Approximations of Isomanifolds.” <i>Foundations of Computational Mathematics </i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s10208-021-09520-0\">https://doi.org/10.1007/s10208-021-09520-0</a>.","short":"J.-D. Boissonnat, M. Wintraecken, Foundations of Computational Mathematics  22 (2022) 967–1012.","ista":"Boissonnat J-D, Wintraecken M. 2022. The topological correctness of PL approximations of isomanifolds. Foundations of Computational Mathematics . 22, 967–1012."},"author":[{"first_name":"Jean-Daniel","last_name":"Boissonnat","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"}],"quality_controlled":"1","date_created":"2021-07-14T06:44:53Z","month":"0","status":"public","intvolume":"        22","isi":1,"file_date_updated":"2021-07-14T06:44:36Z","publisher":"Springer Nature","article_type":"original","volume":22},{"external_id":{"arxiv":["2111.05663"],"isi":["000800559503126"]},"date_published":"2022-01-13T00:00:00Z","page":"3824-3834","arxiv":1,"scopus_import":"1","publication_identifier":{"isbn":["9781665439022"]},"oa_version":"Preprint","date_updated":"2023-08-02T14:44:21Z","type":"conference","day":"13","article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"HeEd"}],"doi":"10.1109/BigData52589.2021.9671483","language":[{"iso":"eng"}],"publisher":"IEEE","conference":{"name":"Big Data: International Conference on Big Data","end_date":"2021-12-18","start_date":"2021-12-15","location":"Orlando, FL, United States; Virtuell"},"month":"01","date_created":"2022-03-06T23:01:53Z","status":"public","isi":1,"year":"2022","main_file_link":[{"url":"https://arxiv.org/abs/2111.05663","open_access":"1"}],"citation":{"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>.","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>.","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.","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>","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."},"author":[{"first_name":"Teresa","last_name":"Heiss","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1780-2689","full_name":"Heiss, Teresa"},{"first_name":"Sarah","last_name":"Tymochko","full_name":"Tymochko, Sarah"},{"full_name":"Story, Brittany","last_name":"Story","first_name":"Brittany"},{"first_name":"Adélie","last_name":"Garin","full_name":"Garin, Adélie"},{"full_name":"Bui, Hoa","first_name":"Hoa","last_name":"Bui"},{"full_name":"Bleile, Bea","last_name":"Bleile","first_name":"Bea"},{"full_name":"Robins, Vanessa","last_name":"Robins","first_name":"Vanessa"}],"quality_controlled":"1","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."}],"publication_status":"published","title":"The impact of changes in resolution on the persistent homology of images","publication":"2021 IEEE International Conference on Big Data","_id":"10828","oa":1},{"publication_identifier":{"issn":["1868-8969"],"isbn":["978-3-95977-227-3"]},"scopus_import":"1","page":"66:1-66:9","date_published":"2022-06-01T00:00:00Z","file":[{"relation":"main_file","date_created":"2022-06-07T07:58:30Z","file_size":17580705,"creator":"dernst","content_type":"application/pdf","success":1,"date_updated":"2022-06-07T07:58:30Z","file_id":"11437","file_name":"2022_LIPICs_Chambers.pdf","checksum":"b25ce40fade4ebc0bcaae176db4f5f1f","access_level":"open_access"}],"language":[{"iso":"eng"}],"doi":"10.4230/LIPIcs.SoCG.2022.66","department":[{"_id":"HeEd"}],"has_accepted_license":"1","ec_funded":1,"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.","article_processing_charge":"No","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","day":"01","type":"conference","date_updated":"2023-02-21T09:50:52Z","series_title":"LIPIcs","oa_version":"Published Version","intvolume":"       224","status":"public","date_created":"2022-06-01T14:18:04Z","conference":{"name":"SoCG: Symposium on Computational Geometry","end_date":"2022-06-10","start_date":"2022-06-07","location":"Berlin, Germany"},"month":"06","volume":224,"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","editor":[{"last_name":"Goaoc","first_name":"Xavier","full_name":"Goaoc, Xavier"},{"full_name":"Kerber, Michael","first_name":"Michael","last_name":"Kerber"}],"file_date_updated":"2022-06-07T07:58:30Z","ddc":["510"],"oa":1,"_id":"11428","title":"A cautionary tale: Burning the medial axis is unstable","publication":"38th International Symposium on Computational Geometry","publication_status":"published","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."}],"project":[{"_id":"fc390959-9c52-11eb-aca3-afa58bd282b2","name":"Learning and triangulating manifolds via collapses","grant_number":"M03073"},{"grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"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"},{"last_name":"Stephenson","first_name":"Elizabeth R","orcid":"0000-0002-6862-208X","full_name":"Stephenson, Elizabeth R","id":"2D04F932-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Wintraecken","first_name":"Mathijs","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"quality_controlled":"1","citation":{"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>","mla":"Chambers, Erin, et al. “A Cautionary Tale: Burning the Medial Axis Is Unstable.” <i>38th International Symposium on Computational Geometry</i>, edited by Xavier Goaoc and Michael Kerber, vol. 224, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022, p. 66:1-66:9, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2022.66\">10.4230/LIPIcs.SoCG.2022.66</a>.","short":"E. Chambers, C.D. Fillmore, E.R. Stephenson, M. Wintraecken, in:, X. Goaoc, M. Kerber (Eds.), 38th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022, p. 66:1-66:9.","chicago":"Chambers, Erin, Christopher D Fillmore, Elizabeth R Stephenson, and Mathijs Wintraecken. “A Cautionary Tale: Burning the Medial Axis Is Unstable.” In <i>38th International Symposium on Computational Geometry</i>, edited by Xavier Goaoc and Michael Kerber, 224:66:1-66:9. LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2022.66\">https://doi.org/10.4230/LIPIcs.SoCG.2022.66</a>.","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.","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.","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>"},"year":"2022","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"}},{"publisher":"Springer Nature","editor":[{"full_name":"Karimipour, Farid","orcid":"0000-0001-6746-4174","id":"2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425","last_name":"Karimipour","first_name":"Farid"},{"full_name":"Storandt, Sabine","first_name":"Sabine","last_name":"Storandt"}],"date_published":"2022-05-01T00:00:00Z","volume":13238,"page":"153","date_created":"2022-06-02T05:40:53Z","month":"05","status":"public","intvolume":"     13238","alternative_title":["LNCS"],"publication_identifier":{"issn":["0302-9743"],"eisbn":["9783031062452"],"isbn":["9783031062445"],"eissn":["1611-3349"]},"place":"Cham","type":"book_editor","date_updated":"2022-06-02T05:56:22Z","oa_version":"None","day":"01","year":"2022","citation":{"ista":"Karimipour F, Storandt S eds. 2022. Web and Wireless Geographical Information Systems 1st ed., Cham: Springer Nature, 153p.","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>.","short":"F. Karimipour, S. Storandt, eds., Web and Wireless Geographical Information Systems, 1st ed., Springer Nature, Cham, 2022.","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.","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>.","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>"},"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","publication_status":"published","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."}],"title":"Web and Wireless Geographical Information Systems","edition":"1","doi":"10.1007/978-3-031-06245-2","language":[{"iso":"eng"}],"department":[{"_id":"HeEd"}],"_id":"11429"},{"scopus_import":"1","publication_identifier":{"eisbn":["9783030955199"],"isbn":["9783030955182"]},"alternative_title":["Association for Women in Mathematics Series"],"arxiv":1,"page":"1-26","external_id":{"arxiv":["2102.11397"]},"date_published":"2022-01-27T00:00:00Z","department":[{"_id":"HeEd"}],"language":[{"iso":"eng"}],"doi":"10.1007/978-3-030-95519-9_1","edition":"1","ec_funded":1,"acknowledgement":"This project started during the Women in Computational Topology workshop held in Canberra in July of 2019. All authors are very grateful for its organisation and the financial support for the workshop from the Mathematical Sciences Institute at ANU, the US National Science Foundation through the award CCF-1841455, the Australian Mathematical Sciences Institute and the Association for Women in Mathematics. AG is supported by the Swiss National Science Foundation grant CRSII5_177237. TH is supported by the European Research Council (ERC) Horizon 2020 project “Alpha Shape Theory Extended” No. 788183. KM is supported by the ERC Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 859860. VR was supported by Australian Research Council Future Fellowship FT140100604 during the early stages of this project.","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","day":"27","oa_version":"Preprint","series_title":"AWMS","date_updated":"2022-06-07T08:32:42Z","type":"book_chapter","place":"Cham","intvolume":"        30","status":"public","month":"01","date_created":"2022-06-07T08:21:11Z","volume":30,"editor":[{"last_name":"Gasparovic","first_name":"Ellen","full_name":"Gasparovic, Ellen"},{"full_name":"Robins, Vanessa","last_name":"Robins","first_name":"Vanessa"},{"first_name":"Katharine","last_name":"Turner","full_name":"Turner, Katharine"}],"publisher":"Springer Nature","_id":"11440","oa":1,"publication":"Research in Computational Topology 2","title":"The persistent homology of dual digital image constructions","abstract":[{"lang":"eng","text":"To compute the persistent homology of a grayscale digital image one needs to build a simplicial or cubical complex from it. For cubical complexes, the two commonly used constructions (corresponding to direct and indirect digital adjacencies) can give different results for the same image. The two constructions are almost dual to each other, and we use this relationship to extend and modify the cubical complexes to become dual filtered cell complexes. We derive a general relationship between the persistent homology of two dual filtered cell complexes, and also establish how various modifications to a filtered complex change the persistence diagram. Applying these results to images, we derive a method to transform the persistence diagram computed using one type of cubical complex into a persistence diagram for the other construction. This means software for computing persistent homology from images can now be easily adapted to produce results for either of the two cubical complex constructions without additional low-level code implementation."}],"publication_status":"published","project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended"}],"author":[{"full_name":"Bleile, Bea","last_name":"Bleile","first_name":"Bea"},{"full_name":"Garin, Adélie","last_name":"Garin","first_name":"Adélie"},{"id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1780-2689","full_name":"Heiss, Teresa","last_name":"Heiss","first_name":"Teresa"},{"full_name":"Maggs, Kelly","first_name":"Kelly","last_name":"Maggs"},{"full_name":"Robins, Vanessa","last_name":"Robins","first_name":"Vanessa"}],"quality_controlled":"1","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>","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.","short":"B. Bleile, A. Garin, T. Heiss, K. Maggs, V. Robins, in:, E. Gasparovic, V. Robins, K. Turner (Eds.), Research in Computational Topology 2, 1st ed., Springer Nature, Cham, 2022, pp. 1–26.","chicago":"Bleile, Bea, Adélie Garin, Teresa Heiss, Kelly Maggs, and Vanessa Robins. “The Persistent Homology of Dual Digital Image Constructions.” In <i>Research in Computational Topology 2</i>, edited by Ellen Gasparovic, Vanessa Robins, and Katharine Turner, 1st ed., 30:1–26. AWMS. Cham: Springer Nature, 2022. <a href=\"https://doi.org/10.1007/978-3-030-95519-9_1\">https://doi.org/10.1007/978-3-030-95519-9_1</a>.","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>","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>."},"main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2102.11397","open_access":"1"}],"year":"2022"},{"department":[{"_id":"HeEd"}],"has_accepted_license":"1","language":[{"iso":"eng"}],"doi":"10.1016/j.jalgebra.2022.06.017","ec_funded":1,"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.","article_processing_charge":"Yes (via OA deal)","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","day":"01","oa_version":"Published Version","date_updated":"2023-08-03T11:56:30Z","type":"journal_article","scopus_import":"1","publication_identifier":{"issn":["0021-8693"]},"page":"145-179","keyword":["Algebra and Number Theory"],"file":[{"creator":"dernst","content_type":"application/pdf","file_size":582962,"date_created":"2023-02-02T07:32:48Z","relation":"main_file","access_level":"open_access","checksum":"82abaee3d7837f703e499a9ecbb25b7c","file_name":"2022_JournalAlgebra_Brown.pdf","file_id":"12473","date_updated":"2023-02-02T07:32:48Z","success":1}],"external_id":{"isi":["000861841100004"]},"date_published":"2022-11-01T00:00:00Z","_id":"11545","oa":1,"ddc":["510"],"publication":"Journal of Algebra","title":"Contravariant pairings between standard Whittaker modules and Verma modules","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"}],"publication_status":"published","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"author":[{"last_name":"Brown","first_name":"Adam","full_name":"Brown, Adam","id":"70B7FDF6-608D-11E9-9333-8535E6697425"},{"full_name":"Romanov, Anna","first_name":"Anna","last_name":"Romanov"}],"quality_controlled":"1","citation":{"short":"A. Brown, A. Romanov, Journal of Algebra 609 (2022) 145–179.","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>.","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,” <i>Journal of Algebra</i>, vol. 609, no. 11. Elsevier, pp. 145–179, 2022.","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>","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>.","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>"},"year":"2022","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"isi":1,"intvolume":"       609","status":"public","month":"11","date_created":"2022-07-08T11:40:07Z","volume":609,"issue":"11","publisher":"Elsevier","article_type":"original","file_date_updated":"2023-02-02T07:32:48Z"},{"language":[{"iso":"eng"}],"department":[{"_id":"GradSch"},{"_id":"HeEd"}],"has_accepted_license":"1","ec_funded":1,"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.","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"27","date_updated":"2022-07-28T07:57:48Z","type":"journal_article","oa_version":"Submitted Version","date_published":"2022-07-27T00:00:00Z","file":[{"file_id":"11659","date_updated":"2022-07-27T09:25:53Z","checksum":"b2f511e8b1cae5f1892b0cdec341acac","file_name":"D-S-E.pdf","access_level":"open_access","relation":"main_file","date_created":"2022-07-27T09:25:53Z","content_type":"application/pdf","creator":"scultrer","file_size":639266}],"ddc":["510"],"oa":1,"_id":"11658","publication":"Leibniz International Proceedings on Mathematics","title":"Depth in arrangements: Dehn–Sommerville–Euler relations with applications","publication_status":"submitted","abstract":[{"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.","lang":"eng"}],"project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"Z00342","name":"The Wittgenstein Prize"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"author":[{"last_name":"Biswas","first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890"},{"id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-6249-0832","full_name":"Cultrera di Montesano, Sebastiano","first_name":"Sebastiano","last_name":"Cultrera di Montesano"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert"},{"last_name":"Saghafian","first_name":"Morteza","full_name":"Saghafian, Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824"}],"quality_controlled":"1","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.","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.","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>.","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.","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.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Leibniz International Proceedings on Mathematics (n.d.).","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."},"year":"2022","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"status":"public","date_created":"2022-07-27T09:27:34Z","month":"07","publisher":"Schloss Dagstuhl - Leibniz Zentrum für Informatik","file_date_updated":"2022-07-27T09:25:53Z"},{"day":"25","oa_version":"Submitted Version","type":"journal_article","date_updated":"2022-07-28T08:05:34Z","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","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. ","department":[{"_id":"GradSch"},{"_id":"HeEd"}],"has_accepted_license":"1","language":[{"iso":"eng"}],"ec_funded":1,"file":[{"date_created":"2022-07-27T09:30:30Z","relation":"main_file","content_type":"application/pdf","creator":"scultrer","file_size":564836,"date_updated":"2022-07-27T09:30:30Z","file_id":"11661","access_level":"open_access","file_name":"window 1.pdf","checksum":"95903f9d1649e8e437a967b6f2f64730"}],"date_published":"2022-07-25T00:00:00Z","alternative_title":["LIPIcs"],"year":"2022","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"author":[{"full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita","last_name":"Biswas"},{"first_name":"Sebastiano","last_name":"Cultrera di Montesano","orcid":"0000-0001-6249-0832","full_name":"Cultrera di Montesano, Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert"},{"full_name":"Saghafian, Morteza","last_name":"Saghafian","first_name":"Morteza"}],"quality_controlled":"1","citation":{"mla":"Biswas, Ranita, et al. “A Window to the Persistence of 1D Maps. I: Geometric Characterization of Critical Point Pairs.” <i>LIPIcs</i>, Schloss Dagstuhl - Leibniz-Zentrum für Informatik.","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., &#38; Saghafian, M. (n.d.). A window to the persistence of 1D maps. I: Geometric characterization of critical point pairs. <i>LIPIcs</i>. Schloss Dagstuhl - Leibniz-Zentrum für Informatik.","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.).","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.","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>."},"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. "}],"publication_status":"submitted","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183","name":"Alpha Shape Theory Extended"},{"call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342","name":"The Wittgenstein Prize"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"_id":"11660","oa":1,"ddc":["510"],"publication":"LIPIcs","title":"A window to the persistence of 1D maps. I: Geometric characterization of critical point pairs","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","file_date_updated":"2022-07-27T09:30:30Z","status":"public","month":"07","date_created":"2022-07-27T09:31:15Z"},{"ec_funded":1,"language":[{"iso":"eng"}],"doi":"10.7155/jgaa.00591","department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"KrCh"}],"has_accepted_license":"1","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).","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","type":"journal_article","date_updated":"2023-02-23T13:54:21Z","oa_version":"Published Version","day":"01","publication_identifier":{"issn":["1526-1719"]},"scopus_import":"1","arxiv":1,"date_published":"2022-06-01T00:00:00Z","file":[{"date_created":"2022-08-22T06:42:42Z","relation":"main_file","file_size":694538,"creator":"dernst","content_type":"application/pdf","file_id":"11940","date_updated":"2022-08-22T06:42:42Z","success":1,"access_level":"open_access","checksum":"dc6e255e3558faff924fd9e370886c11","file_name":"2022_JourGraphAlgorithmsApplic_Aichholzer.pdf"}],"external_id":{"arxiv":["2101.03928"]},"page":"225-240","publication":"Journal of Graph Algorithms and Applications","title":"On compatible matchings","ddc":["000"],"oa":1,"related_material":{"record":[{"status":"public","relation":"earlier_version","id":"9296"}]},"_id":"11938","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"},{"call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"The Wittgenstein Prize","grant_number":"Z00342"},{"call_identifier":"FP7","_id":"2581B60A-B435-11E9-9278-68D0E5697425","name":"Quantitative Graph Games: Theory and Applications","grant_number":"279307"},{"grant_number":"P 23499-N23","name":"Modern Graph Algorithmic Techniques in Formal Verification","_id":"2584A770-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"_id":"25863FF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"S11407","name":"Game Theory"}],"publication_status":"published","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"}],"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.","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>.","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.","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>","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>."},"quality_controlled":"1","author":[{"last_name":"Aichholzer","first_name":"Oswin","full_name":"Aichholzer, Oswin"},{"first_name":"Alan M","last_name":"Arroyo Guevara","orcid":"0000-0003-2401-8670","full_name":"Arroyo Guevara, Alan M","id":"3207FDC6-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Zuzana","last_name":"Masárová","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6660-1322","full_name":"Masárová, Zuzana"},{"full_name":"Parada, Irene","last_name":"Parada","first_name":"Irene"},{"first_name":"Daniel","last_name":"Perz","full_name":"Perz, Daniel"},{"first_name":"Alexander","last_name":"Pilz","full_name":"Pilz, Alexander"},{"last_name":"Tkadlec","first_name":"Josef","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","full_name":"Tkadlec, Josef","orcid":"0000-0002-1097-9684"},{"last_name":"Vogtenhuber","first_name":"Birgit","full_name":"Vogtenhuber, Birgit"}],"tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"year":"2022","intvolume":"        26","date_created":"2022-08-21T22:01:56Z","month":"06","status":"public","volume":26,"issue":"2","file_date_updated":"2022-08-22T06:42:42Z","publisher":"Brown University","article_type":"original"},{"page":"666-686","external_id":{"isi":["000558119300001"]},"date_published":"2021-09-01T00:00:00Z","scopus_import":"1","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"day":"01","oa_version":"Published Version","type":"journal_article","date_updated":"2024-03-07T14:54:59Z","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"Yes (via OA deal)","acknowledgement":"Open access funding provided by the Institute of Science and Technology (IST Austria). Arijit Ghosh is supported by the Ramanujan Fellowship (No. SB/S2/RJN-064/2015), India.\r\nThis work has been 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). The third author is supported by Ramanujan Fellowship (No. SB/S2/RJN-064/2015), India. The fifth author also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411.","has_accepted_license":"1","department":[{"_id":"HeEd"}],"doi":"10.1007/s00454-020-00233-9","language":[{"iso":"eng"}],"ec_funded":1,"article_type":"original","publisher":"Springer Nature","volume":66,"status":"public","month":"09","date_created":"2020-08-11T07:11:51Z","isi":1,"intvolume":"        66","year":"2021","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"quality_controlled":"1","author":[{"full_name":"Boissonnat, Jean-Daniel","first_name":"Jean-Daniel","last_name":"Boissonnat"},{"full_name":"Dyer, Ramsay","first_name":"Ramsay","last_name":"Dyer"},{"last_name":"Ghosh","first_name":"Arijit","full_name":"Ghosh, Arijit"},{"full_name":"Lieutier, Andre","first_name":"Andre","last_name":"Lieutier"},{"last_name":"Wintraecken","first_name":"Mathijs","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"citation":{"ieee":"J.-D. Boissonnat, R. Dyer, A. Ghosh, A. Lieutier, and M. Wintraecken, “Local conditions for triangulating submanifolds of Euclidean space,” <i>Discrete and Computational Geometry</i>, vol. 66. Springer Nature, pp. 666–686, 2021.","ama":"Boissonnat J-D, Dyer R, Ghosh A, Lieutier A, Wintraecken M. Local conditions for triangulating submanifolds of Euclidean space. <i>Discrete and Computational Geometry</i>. 2021;66:666-686. doi:<a href=\"https://doi.org/10.1007/s00454-020-00233-9\">10.1007/s00454-020-00233-9</a>","short":"J.-D. Boissonnat, R. Dyer, A. Ghosh, A. Lieutier, M. Wintraecken, Discrete and Computational Geometry 66 (2021) 666–686.","chicago":"Boissonnat, Jean-Daniel, Ramsay Dyer, Arijit Ghosh, Andre Lieutier, and Mathijs Wintraecken. “Local Conditions for Triangulating Submanifolds of Euclidean Space.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00454-020-00233-9\">https://doi.org/10.1007/s00454-020-00233-9</a>.","ista":"Boissonnat J-D, Dyer R, Ghosh A, Lieutier A, Wintraecken M. 2021. Local conditions for triangulating submanifolds of Euclidean space. Discrete and Computational Geometry. 66, 666–686.","mla":"Boissonnat, Jean-Daniel, et al. “Local Conditions for Triangulating Submanifolds of Euclidean Space.” <i>Discrete and Computational Geometry</i>, vol. 66, Springer Nature, 2021, pp. 666–86, doi:<a href=\"https://doi.org/10.1007/s00454-020-00233-9\">10.1007/s00454-020-00233-9</a>.","apa":"Boissonnat, J.-D., Dyer, R., Ghosh, A., Lieutier, A., &#38; Wintraecken, M. (2021). Local conditions for triangulating submanifolds of Euclidean space. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-020-00233-9\">https://doi.org/10.1007/s00454-020-00233-9</a>"},"main_file_link":[{"url":"https://doi.org/10.1007/s00454-020-00233-9","open_access":"1"}],"abstract":[{"text":"We consider the following setting: suppose that we are given a manifold M in Rd with positive reach. Moreover assume that we have an embedded simplical complex A without boundary, whose vertex set lies on the manifold, is sufficiently dense and such that all simplices in A have sufficient quality. We prove that if, locally, interiors of the projection of the simplices onto the tangent space do not intersect, then A is a triangulation of the manifold, that is, they are homeomorphic.","lang":"eng"}],"publication_status":"published","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"_id":"8248","ddc":["510"],"oa":1,"title":"Local conditions for triangulating submanifolds of Euclidean space","publication":"Discrete and Computational Geometry"},{"date_created":"2020-08-30T22:01:09Z","month":"02","status":"public","article_number":"101700","intvolume":"        93","isi":1,"publisher":"Elsevier","article_type":"original","volume":93,"project":[{"_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"Z00342","name":"The Wittgenstein Prize"}],"publication_status":"published","abstract":[{"lang":"eng","text":"When can a polyomino piece of paper be folded into a unit cube? Prior work studied tree-like polyominoes, but polyominoes with holes remain an intriguing open problem. We present sufficient conditions for a polyomino with one or several holes to fold into a cube, and conditions under which cube folding is impossible. In particular, we show that all but five special “basic” holes guarantee foldability."}],"publication":"Computational Geometry: Theory and Applications","title":"Folding polyominoes with holes into a cube","oa":1,"related_material":{"record":[{"id":"6989","relation":"shorter_version","status":"public"}]},"_id":"8317","year":"2021","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1910.09917v3"}],"citation":{"apa":"Aichholzer, O., Akitaya, H. A., Cheung, K. C., Demaine, E. D., Demaine, M. L., Fekete, S. P., … Schmidt, C. (2021). Folding polyominoes with holes into a cube. <i>Computational Geometry: Theory and Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.comgeo.2020.101700\">https://doi.org/10.1016/j.comgeo.2020.101700</a>","mla":"Aichholzer, Oswin, et al. “Folding Polyominoes with Holes into a Cube.” <i>Computational Geometry: Theory and Applications</i>, vol. 93, 101700, Elsevier, 2021, doi:<a href=\"https://doi.org/10.1016/j.comgeo.2020.101700\">10.1016/j.comgeo.2020.101700</a>.","chicago":"Aichholzer, Oswin, Hugo A. Akitaya, Kenneth C. Cheung, Erik D. Demaine, Martin L. Demaine, Sándor P. Fekete, Linda Kleist, et al. “Folding Polyominoes with Holes into a Cube.” <i>Computational Geometry: Theory and Applications</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.comgeo.2020.101700\">https://doi.org/10.1016/j.comgeo.2020.101700</a>.","short":"O. Aichholzer, H.A. Akitaya, K.C. Cheung, E.D. Demaine, M.L. Demaine, S.P. Fekete, L. Kleist, I. Kostitsyna, M. Löffler, Z. Masárová, K. Mundilova, C. Schmidt, Computational Geometry: Theory and Applications 93 (2021).","ista":"Aichholzer O, Akitaya HA, Cheung KC, Demaine ED, Demaine ML, Fekete SP, Kleist L, Kostitsyna I, Löffler M, Masárová Z, Mundilova K, Schmidt C. 2021. Folding polyominoes with holes into a cube. Computational Geometry: Theory and Applications. 93, 101700.","ama":"Aichholzer O, Akitaya HA, Cheung KC, et al. Folding polyominoes with holes into a cube. <i>Computational Geometry: Theory and Applications</i>. 2021;93. doi:<a href=\"https://doi.org/10.1016/j.comgeo.2020.101700\">10.1016/j.comgeo.2020.101700</a>","ieee":"O. Aichholzer <i>et al.</i>, “Folding polyominoes with holes into a cube,” <i>Computational Geometry: Theory and Applications</i>, vol. 93. Elsevier, 2021."},"quality_controlled":"1","author":[{"full_name":"Aichholzer, Oswin","first_name":"Oswin","last_name":"Aichholzer"},{"last_name":"Akitaya","first_name":"Hugo A.","full_name":"Akitaya, Hugo A."},{"full_name":"Cheung, Kenneth C.","last_name":"Cheung","first_name":"Kenneth C."},{"full_name":"Demaine, Erik D.","last_name":"Demaine","first_name":"Erik D."},{"last_name":"Demaine","first_name":"Martin L.","full_name":"Demaine, Martin L."},{"full_name":"Fekete, Sándor P.","last_name":"Fekete","first_name":"Sándor P."},{"full_name":"Kleist, Linda","first_name":"Linda","last_name":"Kleist"},{"last_name":"Kostitsyna","first_name":"Irina","full_name":"Kostitsyna, Irina"},{"first_name":"Maarten","last_name":"Löffler","full_name":"Löffler, Maarten"},{"id":"45CFE238-F248-11E8-B48F-1D18A9856A87","full_name":"Masárová, Zuzana","orcid":"0000-0002-6660-1322","last_name":"Masárová","first_name":"Zuzana"},{"first_name":"Klara","last_name":"Mundilova","full_name":"Mundilova, Klara"},{"first_name":"Christiane","last_name":"Schmidt","full_name":"Schmidt, Christiane"}],"arxiv":1,"publication_identifier":{"issn":["09257721"]},"scopus_import":"1","date_published":"2021-02-01T00:00:00Z","external_id":{"arxiv":["1910.09917"],"isi":["000579185100004"]},"acknowledgement":"This research was performed in part at the 33rd Bellairs Winter Workshop on Computational Geometry. We thank all other participants for a fruitful atmosphere. H. Akitaya was supported by NSF CCF-1422311 & 1423615. Z. Masárová was partially funded by Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31.","language":[{"iso":"eng"}],"doi":"10.1016/j.comgeo.2020.101700","department":[{"_id":"HeEd"}],"date_updated":"2023-08-04T10:57:42Z","type":"journal_article","oa_version":"Preprint","day":"01","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No"},{"isi":1,"intvolume":"        66","status":"public","month":"10","date_created":"2020-09-06T22:01:13Z","volume":66,"publisher":"Springer Nature","article_type":"original","_id":"8338","oa":1,"publication":"Discrete and Computational Geometry","title":"On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs","abstract":[{"text":"Canonical parametrisations of classical confocal coordinate systems are introduced and exploited to construct non-planar analogues of incircular (IC) nets on individual quadrics and systems of confocal quadrics. Intimate connections with classical deformations of quadrics that are isometric along asymptotic lines and circular cross-sections of quadrics are revealed. The existence of octahedral webs of surfaces of Blaschke type generated by asymptotic and characteristic lines that are diagonally related to lines of curvature is proved theoretically and established constructively. Appropriate samplings (grids) of these webs lead to three-dimensional extensions of non-planar IC nets. Three-dimensional octahedral grids composed of planes and spatially extending (checkerboard) IC-nets are shown to arise in connection with systems of confocal quadrics in Minkowski space. In this context, the Laguerre geometric notion of conical octahedral grids of planes is introduced. The latter generalise the octahedral grids derived from systems of confocal quadrics in Minkowski space. An explicit construction of conical octahedral grids is presented. The results are accompanied by various illustrations which are based on the explicit formulae provided by the theory.","lang":"eng"}],"publication_status":"published","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"788183","name":"Alpha Shape Theory Extended"}],"author":[{"orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","first_name":"Arseniy"},{"last_name":"Bobenko","first_name":"Alexander I.","full_name":"Bobenko, Alexander I."},{"full_name":"Schief, Wolfgang K.","first_name":"Wolfgang K.","last_name":"Schief"},{"full_name":"Techter, Jan","first_name":"Jan","last_name":"Techter"}],"quality_controlled":"1","citation":{"ama":"Akopyan A, Bobenko AI, Schief WK, Techter J. On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs. <i>Discrete and Computational Geometry</i>. 2021;66:938-976. doi:<a href=\"https://doi.org/10.1007/s00454-020-00240-w\">10.1007/s00454-020-00240-w</a>","ieee":"A. Akopyan, A. I. Bobenko, W. K. Schief, and J. Techter, “On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs,” <i>Discrete and Computational Geometry</i>, vol. 66. Springer Nature, pp. 938–976, 2021.","chicago":"Akopyan, Arseniy, Alexander I. Bobenko, Wolfgang K. Schief, and Jan Techter. “On Mutually Diagonal Nets on (Confocal) Quadrics and 3-Dimensional Webs.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00454-020-00240-w\">https://doi.org/10.1007/s00454-020-00240-w</a>.","short":"A. Akopyan, A.I. Bobenko, W.K. Schief, J. Techter, Discrete and Computational Geometry 66 (2021) 938–976.","ista":"Akopyan A, Bobenko AI, Schief WK, Techter J. 2021. On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs. Discrete and Computational Geometry. 66, 938–976.","apa":"Akopyan, A., Bobenko, A. I., Schief, W. K., &#38; Techter, J. (2021). On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-020-00240-w\">https://doi.org/10.1007/s00454-020-00240-w</a>","mla":"Akopyan, Arseniy, et al. “On Mutually Diagonal Nets on (Confocal) Quadrics and 3-Dimensional Webs.” <i>Discrete and Computational Geometry</i>, vol. 66, Springer Nature, 2021, pp. 938–76, doi:<a href=\"https://doi.org/10.1007/s00454-020-00240-w\">10.1007/s00454-020-00240-w</a>."},"main_file_link":[{"url":"https://arxiv.org/abs/1908.00856","open_access":"1"}],"year":"2021","scopus_import":"1","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"arxiv":1,"page":"938-976","external_id":{"arxiv":["1908.00856"],"isi":["000564488500002"]},"date_published":"2021-10-01T00:00:00Z","department":[{"_id":"HeEd"}],"language":[{"iso":"eng"}],"doi":"10.1007/s00454-020-00240-w","ec_funded":1,"acknowledgement":"This research was supported by the DFG Collaborative Research Center TRR 109 “Discretization in Geometry and Dynamics”. W.K.S. was also supported by the Australian Research Council (DP1401000851). A.V.A. was also supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 78818 Alpha).","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","day":"01","oa_version":"Preprint","date_updated":"2024-03-07T14:51:11Z","type":"journal_article"},{"page":"37-52","keyword":["Applied Mathematics","General Mathematics"],"external_id":{"isi":["000600416300004"],"arxiv":["1910.08286"]},"date_published":"2021-01-01T00:00:00Z","publication_identifier":{"issn":["0002-9939"],"eissn":["1088-6826"]},"arxiv":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","day":"01","oa_version":"Preprint","type":"journal_article","date_updated":"2023-08-04T11:11:47Z","department":[{"_id":"HeEd"}],"doi":"10.1090/proc/15205","language":[{"iso":"eng"}],"ec_funded":1,"acknowledgement":"We would like to thank Peter Trapa for useful discussions, and Dragan Milicic and Arun Ram for valuable feedback on the structure of the paper. The first author acknowledges the support of the European Unions Horizon 2020 research and innovation programme under the Marie Skodowska-Curie Grant Agreement No. 754411. The second author is\r\nsupported by the National Science Foundation Award No. 1803059.","volume":149,"issue":"1","publisher":"American Mathematical Society","article_type":"original","isi":1,"intvolume":"       149","status":"public","month":"01","date_created":"2020-11-19T10:17:40Z","author":[{"first_name":"Adam","last_name":"Brown","id":"70B7FDF6-608D-11E9-9333-8535E6697425","full_name":"Brown, Adam"},{"last_name":"Romanov","first_name":"Anna","full_name":"Romanov, Anna"}],"quality_controlled":"1","citation":{"apa":"Brown, A., &#38; Romanov, A. (2021). Contravariant forms on Whittaker modules. <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/proc/15205\">https://doi.org/10.1090/proc/15205</a>","mla":"Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.” <i>Proceedings of the American Mathematical Society</i>, vol. 149, no. 1, American Mathematical Society, 2021, pp. 37–52, doi:<a href=\"https://doi.org/10.1090/proc/15205\">10.1090/proc/15205</a>.","chicago":"Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.” <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society, 2021. <a href=\"https://doi.org/10.1090/proc/15205\">https://doi.org/10.1090/proc/15205</a>.","short":"A. Brown, A. Romanov, Proceedings of the American Mathematical Society 149 (2021) 37–52.","ista":"Brown A, Romanov A. 2021. Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. 149(1), 37–52.","ieee":"A. Brown and A. Romanov, “Contravariant forms on Whittaker modules,” <i>Proceedings of the American Mathematical Society</i>, vol. 149, no. 1. American Mathematical Society, pp. 37–52, 2021.","ama":"Brown A, Romanov A. Contravariant forms on Whittaker modules. <i>Proceedings of the American Mathematical Society</i>. 2021;149(1):37-52. doi:<a href=\"https://doi.org/10.1090/proc/15205\">10.1090/proc/15205</a>"},"main_file_link":[{"url":"https://arxiv.org/abs/1910.08286","open_access":"1"}],"year":"2021","_id":"8773","oa":1,"title":"Contravariant forms on Whittaker modules","publication":"Proceedings of the American Mathematical Society","abstract":[{"lang":"eng","text":"Let g be a complex semisimple Lie algebra. We give a classification of contravariant forms on the nondegenerate Whittaker g-modules Y(χ,η) introduced by Kostant. We prove that the set of all contravariant forms on Y(χ,η) forms a vector space whose dimension is given by the cardinality of the Weyl group of g. We also describe a procedure for parabolically inducing contravariant forms. As a corollary, we deduce the existence of the Shapovalov form on a Verma module, and provide a formula for the dimension of the space of contravariant forms on the degenerate Whittaker modules M(χ,η) introduced by McDowell."}],"publication_status":"published","project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}]}]