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Schloss Dagstuhl - Leibniz-Zentrum für Informatik.","mla":"Biswas, Ranita, et al. “A Window to the Persistence of 1D Maps. I: Geometric Characterization of Critical Point Pairs.” LIPIcs, Schloss Dagstuhl - Leibniz-Zentrum für Informatik.","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.” LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, n.d.","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.","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. LIPIcs."},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"author":[{"id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita","last_name":"Biswas","full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890"},{"first_name":"Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","last_name":"Cultrera di Montesano","full_name":"Cultrera di Montesano, Sebastiano","orcid":"0000-0001-6249-0832"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner"},{"first_name":"Morteza","last_name":"Saghafian","full_name":"Saghafian, Morteza"}],"file_date_updated":"2022-07-27T09:30:30Z","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. ","publication":"LIPIcs","language":[{"iso":"eng"}],"has_accepted_license":"1","file":[{"date_created":"2022-07-27T09:30:30Z","file_name":"window 1.pdf","content_type":"application/pdf","file_id":"11661","date_updated":"2022-07-27T09:30:30Z","creator":"scultrer","checksum":"95903f9d1649e8e437a967b6f2f64730","file_size":564836,"access_level":"open_access","relation":"main_file"}],"abstract":[{"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. ","lang":"eng"}],"project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","call_identifier":"H2020","name":"Alpha Shape Theory Extended"},{"name":"The Wittgenstein Prize","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342"},{"name":"Persistence and stability of geometric complexes","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35"}],"article_processing_charge":"No","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"A window to the persistence of 1D maps. 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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.","publication_status":"submitted","type":"journal_article","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"citation":{"chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Depth in Arrangements: Dehn–Sommerville–Euler Relations with Applications.” Leibniz International Proceedings on Mathematics. Schloss Dagstuhl - Leibniz Zentrum für Informatik, n.d.","mla":"Biswas, Ranita, et al. “Depth in Arrangements: Dehn–Sommerville–Euler Relations with Applications.” Leibniz International Proceedings on Mathematics, 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.","ama":"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.).","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., & Saghafian, M. (n.d.). Depth in arrangements: Dehn–Sommerville–Euler relations with applications. Leibniz International Proceedings on Mathematics. Schloss Dagstuhl - Leibniz Zentrum für Informatik.","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Depth in arrangements: Dehn–Sommerville–Euler relations with applications,” Leibniz International Proceedings on Mathematics. Schloss Dagstuhl - Leibniz Zentrum für Informatik."},"date_published":"2022-07-27T00:00:00Z","month":"07","department":[{"_id":"GradSch"},{"_id":"HeEd"}],"_id":"11658","related_material":{"record":[{"status":"for_moderation","id":"15094","relation":"dissertation_contains"}]},"day":"27","date_updated":"2024-03-15T12:59:53Z","year":"2022","date_created":"2022-07-27T09:27:34Z","ec_funded":1,"ddc":["510"],"oa":1,"quality_controlled":"1","oa_version":"Submitted Version","title":"Depth in arrangements: Dehn–Sommerville–Euler relations with applications","publisher":"Schloss Dagstuhl - Leibniz Zentrum für Informatik","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","project":[{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"The Wittgenstein Prize","call_identifier":"FWF"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","call_identifier":"FWF","name":"Persistence and stability of geometric complexes"}],"has_accepted_license":"1","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"}],"file":[{"file_name":"D-S-E.pdf","date_created":"2022-07-27T09:25:53Z","content_type":"application/pdf","file_id":"11659","date_updated":"2022-07-27T09:25:53Z","creator":"scultrer","checksum":"b2f511e8b1cae5f1892b0cdec341acac","file_size":639266,"relation":"main_file","access_level":"open_access"}]},{"citation":{"mla":"Biswas, Ranita, et al. “On the Size of Chromatic Delaunay Mosaics.” ArXiv, 2212.03121.","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Ondrej Draganov, Herbert Edelsbrunner, and Morteza Saghafian. “On the Size of Chromatic Delaunay Mosaics.” ArXiv, n.d.","ista":"Biswas R, Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. On the size of chromatic Delaunay mosaics. arXiv, 2212.03121.","ama":"Biswas R, Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. On the size of chromatic Delaunay mosaics. arXiv.","short":"R. Biswas, S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.).","apa":"Biswas, R., Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., & Saghafian, M. (n.d.). On the size of chromatic Delaunay mosaics. arXiv.","ieee":"R. Biswas, S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian, “On the size of chromatic Delaunay mosaics,” arXiv. ."},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"main_file_link":[{"url":"https://arxiv.org/abs/2212.03121","open_access":"1"}],"oa_version":"Preprint","publication_status":"submitted","title":"On the size of chromatic Delaunay mosaics","type":"preprint","status":"public","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","language":[{"iso":"eng"}],"oa":1,"publication":"arXiv","author":[{"full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890","first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","last_name":"Biswas"},{"last_name":"Cultrera di Montesano","first_name":"Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-6249-0832","full_name":"Cultrera di Montesano, Sebastiano"},{"last_name":"Draganov","id":"2B23F01E-F248-11E8-B48F-1D18A9856A87","first_name":"Ondrej","full_name":"Draganov, Ondrej"},{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Saghafian","id":"f86f7148-b140-11ec-9577-95435b8df824","first_name":"Morteza","full_name":"Saghafian, Morteza"}],"date_created":"2024-03-08T09:54:20Z","ec_funded":1,"date_updated":"2024-03-15T12:59:53Z","year":"2022","external_id":{"arxiv":["2212.03121"]},"related_material":{"record":[{"status":"for_moderation","relation":"dissertation_contains","id":"15094"}]},"day":"06","article_processing_charge":"No","department":[{"_id":"HeEd"}],"project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","call_identifier":"H2020"},{"name":"Discretization in Geometry and Dynamics","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","grant_number":"I4887"},{"grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"The Wittgenstein Prize","call_identifier":"FWF"}],"_id":"15090","abstract":[{"text":"Given a locally finite set A⊆Rd and a coloring χ:A→{0,1,…,s}, we introduce the chromatic Delaunay mosaic of χ, which is a Delaunay mosaic in Rs+d that represents how points of different colors mingle. Our main results are bounds on the size of the chromatic Delaunay mosaic, in which we assume that d and s are constants. For example, if A is finite with n=#A, and the coloring is random, then the chromatic Delaunay mosaic has O(n⌈d/2⌉) cells in expectation. In contrast, for Delone sets and Poisson point processes in Rd, the expected number of cells within a closed ball is only a constant times the number of points in this ball. Furthermore, in R2 all colorings of a dense set of n points have chromatic Delaunay mosaics of size O(n). This encourages the use of chromatic Delaunay mosaics in applications.","lang":"eng"}],"article_number":"2212.03121","date_published":"2022-12-06T00:00:00Z","month":"12"},{"title":"A context-aware dimension reduction framework for trajectory and health signal analyses","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"Springer Nature","quality_controlled":"1","oa_version":"Submitted Version","date_created":"2021-11-02T09:28:55Z","ddc":["000"],"article_type":"original","oa":1,"scopus_import":"1","external_id":{"isi":["000712198000001"]},"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"}],"file":[{"file_name":"A Context‑aware Dimension Reduction Framework - Journal of Ambient Intelligence 2021 (Preprint version).pdf","date_created":"2021-11-12T19:38:05Z","file_id":"10279","content_type":"application/pdf","embargo":"2022-11-12","relation":"main_file","access_level":"open_access","file_size":1634958,"checksum":"0a8961416a9bb2be5a1cebda65468bcf","creator":"fkarimip","date_updated":"2022-12-20T23:30:08Z"}],"page":"2621–2635","has_accepted_license":"1","article_processing_charge":"No","project":[{"name":"The Wittgenstein Prize","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342"}],"volume":13,"type":"journal_article","status":"public","publication_status":"published","citation":{"ieee":"S. Goudarzi, M. Sharif, and F. Karimipour, “A context-aware dimension reduction framework for trajectory and health signal analyses,” Journal of Ambient Intelligence and Humanized Computing, vol. 13. Springer Nature, pp. 2621–2635, 2022.","short":"S. Goudarzi, M. Sharif, F. Karimipour, Journal of Ambient Intelligence and Humanized Computing 13 (2022) 2621–2635.","apa":"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. Springer Nature. https://doi.org/10.1007/s12652-021-03569-z","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.","ama":"Goudarzi S, Sharif M, Karimipour F. A context-aware dimension reduction framework for trajectory and health signal analyses. Journal of Ambient Intelligence and Humanized Computing. 2022;13:2621–2635. doi:10.1007/s12652-021-03569-z","chicago":"Goudarzi, Samira, Mohammad Sharif, and Farid Karimipour. “A Context-Aware Dimension Reduction Framework for Trajectory and Health Signal Analyses.” Journal of Ambient Intelligence and Humanized Computing. Springer Nature, 2022. https://doi.org/10.1007/s12652-021-03569-z.","mla":"Goudarzi, Samira, et al. “A Context-Aware Dimension Reduction Framework for Trajectory and Health Signal Analyses.” Journal of Ambient Intelligence and Humanized Computing, vol. 13, Springer Nature, 2022, pp. 2621–2635, doi:10.1007/s12652-021-03569-z."},"keyword":["general computer science"],"file_date_updated":"2022-12-20T23:30:08Z","author":[{"first_name":"Samira","last_name":"Goudarzi","full_name":"Goudarzi, Samira"},{"full_name":"Sharif, Mohammad","first_name":"Mohammad","last_name":"Sharif"},{"last_name":"Karimipour","first_name":"Farid","id":"2A2BCDC4-CF62-11E9-BE5E-3B1EE6697425","orcid":"0000-0001-6746-4174","full_name":"Karimipour, Farid"}],"publication":"Journal of Ambient Intelligence and Humanized Computing","acknowledgement":"The third author acknowledges the funding received from the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31.","doi":"10.1007/s12652-021-03569-z","intvolume":" 13","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1868-5145"],"issn":["1868-5137"]},"day":"01","year":"2022","date_updated":"2023-08-02T13:31:48Z","date_published":"2022-05-01T00:00:00Z","month":"05","department":[{"_id":"HeEd"}],"isi":1,"_id":"10208"},{"scopus_import":"1","page":"1511-1514","article_processing_charge":"No","publisher":"American Mathematical Society","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","title":"How to tutorial-a-thon","oa_version":"Published Version","quality_controlled":"1","main_file_link":[{"open_access":"1","url":"http://www.ams.org/notices/"}],"issue":"9","date_created":"2021-10-03T22:01:22Z","oa":1,"article_type":"letter_note","day":"01","year":"2021","date_updated":"2021-12-03T07:31:26Z","month":"10","date_published":"2021-10-01T00:00:00Z","alternative_title":["Early Career"],"_id":"10071","department":[{"_id":"HeEd"}],"status":"public","type":"journal_article","volume":68,"publication_status":"published","citation":{"short":"H. Adams, H. Kourimska, T. Heiss, S. Percival, L. Ziegelmeier, Notices of the American Mathematical Society 68 (2021) 1511–1514.","apa":"Adams, H., Kourimska, H., Heiss, T., Percival, S., & Ziegelmeier, L. (2021). How to tutorial-a-thon. Notices of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/noti2349","ieee":"H. Adams, H. Kourimska, T. Heiss, S. Percival, and L. Ziegelmeier, “How to tutorial-a-thon,” Notices of the American Mathematical Society, vol. 68, no. 9. American Mathematical Society, pp. 1511–1514, 2021.","chicago":"Adams, Henry, Hana Kourimska, Teresa Heiss, Sarah Percival, and Lori Ziegelmeier. “How to Tutorial-a-Thon.” Notices of the American Mathematical Society. American Mathematical Society, 2021. https://doi.org/10.1090/noti2349.","mla":"Adams, Henry, et al. “How to Tutorial-a-Thon.” Notices of the American Mathematical Society, vol. 68, no. 9, American Mathematical Society, 2021, pp. 1511–14, doi:10.1090/noti2349.","ista":"Adams H, Kourimska H, Heiss T, Percival S, Ziegelmeier L. 2021. How to tutorial-a-thon. Notices of the American Mathematical Society. 68(9), 1511–1514.","ama":"Adams H, Kourimska H, Heiss T, Percival S, Ziegelmeier L. How to tutorial-a-thon. Notices of the American Mathematical Society. 2021;68(9):1511-1514. doi:10.1090/noti2349"},"author":[{"first_name":"Henry","last_name":"Adams","full_name":"Adams, Henry"},{"full_name":"Kourimska, Hana","id":"D9B8E14C-3C26-11EA-98F5-1F833DDC885E","first_name":"Hana","last_name":"Kourimska"},{"orcid":"0000-0002-1780-2689","full_name":"Heiss, Teresa","last_name":"Heiss","first_name":"Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Percival","first_name":"Sarah","full_name":"Percival, Sarah"},{"first_name":"Lori","last_name":"Ziegelmeier","full_name":"Ziegelmeier, Lori"}],"doi":"10.1090/noti2349","publication":"Notices of the American Mathematical Society","publication_identifier":{"issn":["0002-9920"],"eissn":["1088-9477"]},"language":[{"iso":"eng"}],"intvolume":" 68"}]