[{"_id":"6287","file_date_updated":"2020-07-14T12:47:26Z","doi":"10.15479/AT:ISTA:th_873","citation":{"apa":"Nikitenko, A. (2017). <i>Discrete Morse theory for random complexes </i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT:ISTA:th_873\">https://doi.org/10.15479/AT:ISTA:th_873</a>","ama":"Nikitenko A. Discrete Morse theory for random complexes . 2017. doi:<a href=\"https://doi.org/10.15479/AT:ISTA:th_873\">10.15479/AT:ISTA:th_873</a>","ieee":"A. Nikitenko, “Discrete Morse theory for random complexes ,” Institute of Science and Technology Austria, 2017.","short":"A. Nikitenko, Discrete Morse Theory for Random Complexes , Institute of Science and Technology Austria, 2017.","ista":"Nikitenko A. 2017. Discrete Morse theory for random complexes . Institute of Science and Technology Austria.","chicago":"Nikitenko, Anton. “Discrete Morse Theory for Random Complexes .” Institute of Science and Technology Austria, 2017. <a href=\"https://doi.org/10.15479/AT:ISTA:th_873\">https://doi.org/10.15479/AT:ISTA:th_873</a>.","mla":"Nikitenko, Anton. <i>Discrete Morse Theory for Random Complexes </i>. Institute of Science and Technology Austria, 2017, doi:<a href=\"https://doi.org/10.15479/AT:ISTA:th_873\">10.15479/AT:ISTA:th_873</a>."},"date_created":"2019-04-09T15:04:32Z","year":"2017","related_material":{"record":[{"id":"718","relation":"part_of_dissertation","status":"public"},{"status":"public","id":"5678","relation":"part_of_dissertation"},{"id":"87","relation":"part_of_dissertation","status":"public"}]},"degree_awarded":"PhD","department":[{"_id":"HeEd"}],"page":"86","date_published":"2017-10-27T00:00:00Z","supervisor":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"}],"publisher":"Institute of Science and Technology Austria","publication_status":"published","abstract":[{"lang":"eng","text":"The main objects considered in the present work are simplicial and CW-complexes with vertices forming a random point cloud. In particular, we consider a Poisson point process in R^n and study Delaunay and Voronoi complexes of the first and higher orders and weighted Delaunay complexes obtained as sections of Delaunay complexes, as well as the Čech complex. Further, we examine theDelaunay complex of a Poisson point process on the sphere S^n, as well as of a uniform point cloud, which is equivalent to the convex hull, providing a connection to the theory of random polytopes. Each of the complexes in question can be endowed with a radius function, which maps its cells to the radii of appropriately chosen circumspheres, called the radius of the cell. Applying and developing discrete Morse theory for these functions, joining it together with probabilistic and sometimes analytic machinery, and developing several integral geometric tools, we aim at getting the distributions of circumradii of typical cells. For all considered complexes, we are able to generalize and obtain up to constants the distribution of radii of typical intervals of all types. In low dimensions the constants can be computed explicitly, thus providing the explicit expressions for the expected numbers of cells. In particular, it allows to find the expected density of simplices of every dimension for a Poisson point process in R^4, whereas the result for R^3 was known already in 1970's."}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"ddc":["514","516","519"],"language":[{"iso":"eng"}],"title":"Discrete Morse theory for random complexes ","article_processing_charge":"No","date_updated":"2023-09-15T12:10:34Z","oa":1,"pubrep_id":"873","has_accepted_license":"1","type":"dissertation","status":"public","alternative_title":["ISTA Thesis"],"author":[{"last_name":"Nikitenko","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0659-3201","first_name":"Anton","full_name":"Nikitenko, Anton"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","file":[{"creator":"dernst","content_type":"application/pdf","access_level":"open_access","file_size":2324870,"relation":"main_file","file_id":"6289","checksum":"ece7e598a2f060b263c2febf7f3fe7f9","file_name":"2017_Thesis_Nikitenko.pdf","date_updated":"2020-07-14T12:47:26Z","date_created":"2019-04-09T14:54:51Z"},{"creator":"dernst","relation":"source_file","file_size":2863219,"content_type":"application/zip","access_level":"closed","file_id":"6290","file_name":"2017_Thesis_Nikitenko_source.zip","checksum":"99b7ad76e317efd447af60f91e29b49b","date_created":"2019-04-09T14:54:51Z","date_updated":"2020-07-14T12:47:26Z"}],"day":"27","oa_version":"Published Version","publication_identifier":{"issn":["2663-337X"]},"month":"10"},{"citation":{"chicago":"Edelsbrunner, Herbert, and Hubert Wagner. “Topological Data Analysis with Bregman Divergences,” 77:391–3916. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2017.39\">https://doi.org/10.4230/LIPIcs.SoCG.2017.39</a>.","mla":"Edelsbrunner, Herbert, and Hubert Wagner. <i>Topological Data Analysis with Bregman Divergences</i>. Vol. 77, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017, pp. 391–3916, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2017.39\">10.4230/LIPIcs.SoCG.2017.39</a>.","ista":"Edelsbrunner H, Wagner H. 2017. Topological data analysis with Bregman divergences. Symposium on Computational Geometry, SoCG, LIPIcs, vol. 77, 391–3916.","ama":"Edelsbrunner H, Wagner H. Topological data analysis with Bregman divergences. In: Vol 77. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2017:391-3916. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2017.39\">10.4230/LIPIcs.SoCG.2017.39</a>","ieee":"H. Edelsbrunner and H. Wagner, “Topological data analysis with Bregman divergences,” presented at the Symposium on Computational Geometry, SoCG, Brisbane, Australia, 2017, vol. 77, pp. 391–3916.","short":"H. Edelsbrunner, H. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017, pp. 391–3916.","apa":"Edelsbrunner, H., &#38; Wagner, H. (2017). Topological data analysis with Bregman divergences (Vol. 77, pp. 391–3916). Presented at the Symposium on Computational Geometry, SoCG, Brisbane, Australia: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2017.39\">https://doi.org/10.4230/LIPIcs.SoCG.2017.39</a>"},"publist_id":"7021","date_created":"2018-12-11T11:47:56Z","year":"2017","_id":"688","file_date_updated":"2020-07-14T12:47:42Z","doi":"10.4230/LIPIcs.SoCG.2017.39","publication_status":"published","abstract":[{"text":"We show that the framework of topological data analysis can be extended from metrics to general Bregman divergences, widening the scope of possible applications. Examples are the Kullback - Leibler divergence, which is commonly used for comparing text and images, and the Itakura - Saito divergence, popular for speech and sound. In particular, we prove that appropriately generalized čech and Delaunay (alpha) complexes capture the correct homotopy type, namely that of the corresponding union of Bregman balls. Consequently, their filtrations give the correct persistence diagram, namely the one generated by the uniformly growing Bregman balls. Moreover, we show that unlike the metric setting, the filtration of Vietoris-Rips complexes may fail to approximate the persistence diagram. We propose algorithms to compute the thus generalized čech, Vietoris-Rips and Delaunay complexes and experimentally test their efficiency. Lastly, we explain their surprisingly good performance by making a connection with discrete Morse theory. ","lang":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"ddc":["514","516"],"volume":77,"quality_controlled":"1","department":[{"_id":"HeEd"},{"_id":"UlWa"}],"page":"391-3916","date_published":"2017-06-01T00:00:00Z","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","title":"Topological data analysis with Bregman divergences","date_updated":"2021-01-12T08:09:26Z","oa":1,"pubrep_id":"895","has_accepted_license":"1","scopus_import":1,"intvolume":"        77","language":[{"iso":"eng"}],"author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"full_name":"Wagner, Hubert","first_name":"Hubert","last_name":"Wagner","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87"}],"file":[{"date_created":"2018-12-12T10:11:03Z","date_updated":"2020-07-14T12:47:42Z","file_name":"IST-2017-895-v1+1_LIPIcs-SoCG-2017-39.pdf","file_id":"4856","checksum":"067ab0cb3f962bae6c3af6bf0094e0f3","file_size":990546,"access_level":"open_access","relation":"main_file","content_type":"application/pdf","creator":"system"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","day":"01","oa_version":"Published Version","month":"06","publication_identifier":{"issn":["18688969"]},"conference":{"start_date":"2017-07-04","name":"Symposium on Computational Geometry, SoCG","end_date":"2017-07-07","location":"Brisbane, Australia"},"type":"conference","status":"public","alternative_title":["LIPIcs"]},{"external_id":{"isi":["000395170200039"]},"abstract":[{"lang":"eng","text":"We introduce a multiscale topological description of the Megaparsec web-like cosmic matter distribution. Betti numbers and topological persistence offer a powerful means of describing the rich connectivity structure of the cosmic web and of its multiscale arrangement of matter and galaxies. Emanating from algebraic topology and Morse theory, Betti numbers and persistence diagrams represent an extension and deepening of the cosmologically familiar topological genus measure and the related geometric Minkowski functionals. In addition to a description of the mathematical background, this study presents the computational procedure for computing Betti numbers and persistence diagrams for density field filtrations. The field may be computed starting from a discrete spatial distribution of galaxies or simulation particles. The main emphasis of this study concerns an extensive and systematic exploration of the imprint of different web-like morphologies and different levels of multiscale clustering in the corresponding computed Betti numbers and persistence diagrams. To this end, we use Voronoi clustering models as templates for a rich variety of web-like configurations and the fractal-like Soneira-Peebles models exemplify a range of multiscale configurations. We have identified the clear imprint of cluster nodes, filaments, walls, and voids in persistence diagrams, along with that of the nested hierarchy of structures in multiscale point distributions. We conclude by outlining the potential of persistent topology for understanding the connectivity structure of the cosmic web, in large simulations of cosmic structure formation and in the challenging context of the observed galaxy distribution in large galaxy surveys."}],"publication_status":"published","publisher":"Oxford University Press","date_published":"2017-01-01T00:00:00Z","page":"4281 - 4310","department":[{"_id":"HeEd"}],"volume":465,"quality_controlled":"1","acknowledgement":"Part of this work has been supported by the 7th Framework Programme for Research of the European Commission, under FETOpen grant number 255827 (CGL Computational Geometry Learning) and ERC advanced grant, URSAT (Understanding Random Systems via Algebraic Topology) number 320422.","year":"2017","date_created":"2018-12-11T11:49:44Z","citation":{"ama":"Pranav P, Edelsbrunner H, Van De Weygaert R, et al. The topology of the cosmic web in terms of persistent Betti numbers. <i>Monthly Notices of the Royal Astronomical Society</i>. 2017;465(4):4281-4310. doi:<a href=\"https://doi.org/10.1093/mnras/stw2862\">10.1093/mnras/stw2862</a>","ieee":"P. Pranav <i>et al.</i>, “The topology of the cosmic web in terms of persistent Betti numbers,” <i>Monthly Notices of the Royal Astronomical Society</i>, vol. 465, no. 4. Oxford University Press, pp. 4281–4310, 2017.","short":"P. Pranav, H. Edelsbrunner, R. Van De Weygaert, G. Vegter, M. Kerber, B. Jones, M. Wintraecken, Monthly Notices of the Royal Astronomical Society 465 (2017) 4281–4310.","ista":"Pranav P, Edelsbrunner H, Van De Weygaert R, Vegter G, Kerber M, Jones B, Wintraecken M. 2017. The topology of the cosmic web in terms of persistent Betti numbers. Monthly Notices of the Royal Astronomical Society. 465(4), 4281–4310.","mla":"Pranav, Pratyush, et al. “The Topology of the Cosmic Web in Terms of Persistent Betti Numbers.” <i>Monthly Notices of the Royal Astronomical Society</i>, vol. 465, no. 4, Oxford University Press, 2017, pp. 4281–310, doi:<a href=\"https://doi.org/10.1093/mnras/stw2862\">10.1093/mnras/stw2862</a>.","chicago":"Pranav, Pratyush, Herbert Edelsbrunner, Rien Van De Weygaert, Gert Vegter, Michael Kerber, Bernard Jones, and Mathijs Wintraecken. “The Topology of the Cosmic Web in Terms of Persistent Betti Numbers.” <i>Monthly Notices of the Royal Astronomical Society</i>. Oxford University Press, 2017. <a href=\"https://doi.org/10.1093/mnras/stw2862\">https://doi.org/10.1093/mnras/stw2862</a>.","apa":"Pranav, P., Edelsbrunner, H., Van De Weygaert, R., Vegter, G., Kerber, M., Jones, B., &#38; Wintraecken, M. (2017). The topology of the cosmic web in terms of persistent Betti numbers. <i>Monthly Notices of the Royal Astronomical Society</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/mnras/stw2862\">https://doi.org/10.1093/mnras/stw2862</a>"},"publist_id":"6373","doi":"10.1093/mnras/stw2862","_id":"1022","month":"01","publication_identifier":{"issn":["00358711"]},"day":"01","oa_version":"Submitted Version","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1608.04519"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","author":[{"last_name":"Pranav","first_name":"Pratyush","full_name":"Pranav, Pratyush"},{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Van De Weygaert, Rien","first_name":"Rien","last_name":"Van De Weygaert"},{"full_name":"Vegter, Gert","first_name":"Gert","last_name":"Vegter"},{"first_name":"Michael","full_name":"Kerber, Michael","last_name":"Kerber"},{"first_name":"Bernard","full_name":"Jones, Bernard","last_name":"Jones"},{"first_name":"Mathijs","full_name":"Wintraecken, Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","last_name":"Wintraecken","orcid":"0000-0002-7472-2220"}],"status":"public","type":"journal_article","isi":1,"scopus_import":"1","intvolume":"       465","date_updated":"2023-09-22T09:40:55Z","oa":1,"article_processing_charge":"No","issue":"4","title":"The topology of the cosmic web in terms of persistent Betti numbers","publication":"Monthly Notices of the Royal Astronomical Society","language":[{"iso":"eng"}]},{"scopus_import":"1","has_accepted_license":"1","intvolume":"       122","isi":1,"title":"Pushdown reachability with constant treewidth","article_processing_charge":"No","pubrep_id":"991","date_updated":"2023-09-20T12:08:18Z","oa":1,"publication":"Information Processing Letters","language":[{"iso":"eng"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","file":[{"relation":"main_file","file_size":247657,"content_type":"application/pdf","access_level":"open_access","creator":"system","date_updated":"2019-10-15T07:44:51Z","date_created":"2018-12-12T10:13:17Z","file_name":"IST-2018-991-v1+2_2018_Chatterjee_Pushdown_PREPRINT.pdf","file_id":"4998"}],"day":"01","oa_version":"Submitted Version","publication_identifier":{"issn":["00200190"]},"month":"06","author":[{"first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4561-241X"},{"orcid":"0000-0002-8882-5116","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","last_name":"Osang","first_name":"Georg F","full_name":"Osang, Georg F"}],"type":"journal_article","status":"public","ec_funded":1,"date_created":"2018-12-11T11:49:57Z","publist_id":"6323","citation":{"ama":"Chatterjee K, Osang GF. Pushdown reachability with constant treewidth. <i>Information Processing Letters</i>. 2017;122:25-29. doi:<a href=\"https://doi.org/10.1016/j.ipl.2017.02.003\">10.1016/j.ipl.2017.02.003</a>","ieee":"K. Chatterjee and G. F. Osang, “Pushdown reachability with constant treewidth,” <i>Information Processing Letters</i>, vol. 122. Elsevier, pp. 25–29, 2017.","short":"K. Chatterjee, G.F. Osang, Information Processing Letters 122 (2017) 25–29.","mla":"Chatterjee, Krishnendu, and Georg F. Osang. “Pushdown Reachability with Constant Treewidth.” <i>Information Processing Letters</i>, vol. 122, Elsevier, 2017, pp. 25–29, doi:<a href=\"https://doi.org/10.1016/j.ipl.2017.02.003\">10.1016/j.ipl.2017.02.003</a>.","ista":"Chatterjee K, Osang GF. 2017. Pushdown reachability with constant treewidth. Information Processing Letters. 122, 25–29.","chicago":"Chatterjee, Krishnendu, and Georg F Osang. “Pushdown Reachability with Constant Treewidth.” <i>Information Processing Letters</i>. Elsevier, 2017. <a href=\"https://doi.org/10.1016/j.ipl.2017.02.003\">https://doi.org/10.1016/j.ipl.2017.02.003</a>.","apa":"Chatterjee, K., &#38; Osang, G. F. (2017). Pushdown reachability with constant treewidth. <i>Information Processing Letters</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.ipl.2017.02.003\">https://doi.org/10.1016/j.ipl.2017.02.003</a>"},"year":"2017","doi":"10.1016/j.ipl.2017.02.003","_id":"1065","file_date_updated":"2019-10-15T07:44:51Z","abstract":[{"lang":"eng","text":"We consider the problem of reachability in pushdown graphs. We study the problem for pushdown graphs with constant treewidth. Even for pushdown graphs with treewidth 1, for the reachability problem we establish the following: (i) the problem is PTIME-complete, and (ii) any subcubic algorithm for the problem would contradict the k-clique conjecture and imply faster combinatorial algorithms for cliques in graphs."}],"external_id":{"isi":["000399506600005"]},"ddc":["000"],"publication_status":"published","volume":122,"quality_controlled":"1","page":"25 - 29","department":[{"_id":"KrCh"},{"_id":"HeEd"}],"date_published":"2017-06-01T00:00:00Z","publisher":"Elsevier","project":[{"call_identifier":"FWF","name":"Modern Graph Algorithmic Techniques in Formal Verification","grant_number":"P 23499-N23","_id":"2584A770-B435-11E9-9278-68D0E5697425"},{"_id":"25863FF4-B435-11E9-9278-68D0E5697425","grant_number":"S11407","name":"Game Theory","call_identifier":"FWF"},{"name":"Quantitative Graph Games: Theory and Applications","call_identifier":"FP7","_id":"2581B60A-B435-11E9-9278-68D0E5697425","grant_number":"279307"}]},{"type":"journal_article","status":"public","month":"05","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","day":"01","oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1312.1231"}],"arxiv":1,"author":[{"id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","last_name":"Bauer","orcid":"0000-0002-9683-0724","full_name":"Bauer, Ulrich","first_name":"Ulrich"},{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner"}],"publication":"Transactions of the American Mathematical Society","language":[{"iso":"eng"}],"isi":1,"intvolume":"       369","scopus_import":"1","issue":"5","article_processing_charge":"No","date_updated":"2023-09-20T12:05:56Z","oa":1,"title":"The Morse theory of Čech and delaunay complexes","date_published":"2017-05-01T00:00:00Z","publisher":"American Mathematical Society","quality_controlled":"1","volume":369,"page":"3741 - 3762","department":[{"_id":"HeEd"}],"project":[{"name":"Topological Complex Systems","call_identifier":"FP7","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"abstract":[{"text":"Given a finite set of points in Rn and a radius parameter, we study the Čech, Delaunay–Čech, Delaunay (or alpha), and Wrap complexes in the light of generalized discrete Morse theory. Establishing the Čech and Delaunay complexes as sublevel sets of generalized discrete Morse functions, we prove that the four complexes are simple-homotopy equivalent by a sequence of simplicial collapses, which are explicitly described by a single discrete gradient field.","lang":"eng"}],"external_id":{"isi":["000398030400024"],"arxiv":["1312.1231"]},"publication_status":"published","doi":"10.1090/tran/6991","_id":"1072","article_type":"original","ec_funded":1,"year":"2017","acknowledgement":"This research has been supported by the EU project Toposys(FP7-ICT-318493-STREP), by ESF under the ACAT Research Network Programme, by the Russian Government under mega project 11.G34.31.0053, and by the DFG Collaborative Research Center SFB/TRR 109 “Discretization in Geometry and Dynamics”.","citation":{"ista":"Bauer U, Edelsbrunner H. 2017. The Morse theory of Čech and delaunay complexes. Transactions of the American Mathematical Society. 369(5), 3741–3762.","mla":"Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay Complexes.” <i>Transactions of the American Mathematical Society</i>, vol. 369, no. 5, American Mathematical Society, 2017, pp. 3741–62, doi:<a href=\"https://doi.org/10.1090/tran/6991\">10.1090/tran/6991</a>.","chicago":"Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay Complexes.” <i>Transactions of the American Mathematical Society</i>. American Mathematical Society, 2017. <a href=\"https://doi.org/10.1090/tran/6991\">https://doi.org/10.1090/tran/6991</a>.","short":"U. Bauer, H. Edelsbrunner, Transactions of the American Mathematical Society 369 (2017) 3741–3762.","ieee":"U. Bauer and H. Edelsbrunner, “The Morse theory of Čech and delaunay complexes,” <i>Transactions of the American Mathematical Society</i>, vol. 369, no. 5. American Mathematical Society, pp. 3741–3762, 2017.","ama":"Bauer U, Edelsbrunner H. The Morse theory of Čech and delaunay complexes. <i>Transactions of the American Mathematical Society</i>. 2017;369(5):3741-3762. doi:<a href=\"https://doi.org/10.1090/tran/6991\">10.1090/tran/6991</a>","apa":"Bauer, U., &#38; Edelsbrunner, H. (2017). The Morse theory of Čech and delaunay complexes. <i>Transactions of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/tran/6991\">https://doi.org/10.1090/tran/6991</a>"},"date_created":"2018-12-11T11:49:59Z","publist_id":"6311"},{"acknowledgement":"This research is partially supported by the Russian Government under the Mega Project 11.G34.31.0053, by the Toposys project FP7-ICT-318493-STREP, by ESF under the ACAT Research Network Programme, by RFBR grant 11-01-00735, and by NSF grants DMS-1101688, DMS-1400876.","year":"2017","date_created":"2018-12-11T11:50:32Z","publist_id":"6182","citation":{"ama":"Edelsbrunner H, Glazyrin A, Musin O, Nikitenko A. The Voronoi functional is maximized by the Delaunay triangulation in the plane. <i>Combinatorica</i>. 2017;37(5):887-910. doi:<a href=\"https://doi.org/10.1007/s00493-016-3308-y\">10.1007/s00493-016-3308-y</a>","ieee":"H. Edelsbrunner, A. Glazyrin, O. Musin, and A. Nikitenko, “The Voronoi functional is maximized by the Delaunay triangulation in the plane,” <i>Combinatorica</i>, vol. 37, no. 5. Springer, pp. 887–910, 2017.","short":"H. Edelsbrunner, A. Glazyrin, O. Musin, A. Nikitenko, Combinatorica 37 (2017) 887–910.","ista":"Edelsbrunner H, Glazyrin A, Musin O, Nikitenko A. 2017. The Voronoi functional is maximized by the Delaunay triangulation in the plane. Combinatorica. 37(5), 887–910.","mla":"Edelsbrunner, Herbert, et al. “The Voronoi Functional Is Maximized by the Delaunay Triangulation in the Plane.” <i>Combinatorica</i>, vol. 37, no. 5, Springer, 2017, pp. 887–910, doi:<a href=\"https://doi.org/10.1007/s00493-016-3308-y\">10.1007/s00493-016-3308-y</a>.","chicago":"Edelsbrunner, Herbert, Alexey Glazyrin, Oleg Musin, and Anton Nikitenko. “The Voronoi Functional Is Maximized by the Delaunay Triangulation in the Plane.” <i>Combinatorica</i>. Springer, 2017. <a href=\"https://doi.org/10.1007/s00493-016-3308-y\">https://doi.org/10.1007/s00493-016-3308-y</a>.","apa":"Edelsbrunner, H., Glazyrin, A., Musin, O., &#38; Nikitenko, A. (2017). The Voronoi functional is maximized by the Delaunay triangulation in the plane. <i>Combinatorica</i>. Springer. <a href=\"https://doi.org/10.1007/s00493-016-3308-y\">https://doi.org/10.1007/s00493-016-3308-y</a>"},"ec_funded":1,"_id":"1173","doi":"10.1007/s00493-016-3308-y","publication_status":"published","external_id":{"isi":["000418056000005"]},"abstract":[{"text":"We introduce the Voronoi functional of a triangulation of a finite set of points in the Euclidean plane and prove that among all geometric triangulations of the point set, the Delaunay triangulation maximizes the functional. This result neither extends to topological triangulations in the plane nor to geometric triangulations in three and higher dimensions.","lang":"eng"}],"project":[{"call_identifier":"FP7","name":"Topological Complex Systems","_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493"}],"publisher":"Springer","date_published":"2017-10-01T00:00:00Z","department":[{"_id":"HeEd"}],"page":"887 - 910","quality_controlled":"1","volume":37,"date_updated":"2023-09-20T11:23:53Z","oa":1,"issue":"5","article_processing_charge":"No","title":"The Voronoi functional is maximized by the Delaunay triangulation in the plane","isi":1,"intvolume":"        37","scopus_import":"1","language":[{"iso":"eng"}],"publication":"Combinatorica","author":[{"orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","first_name":"Herbert"},{"last_name":"Glazyrin","first_name":"Alexey","full_name":"Glazyrin, Alexey"},{"last_name":"Musin","full_name":"Musin, Oleg","first_name":"Oleg"},{"orcid":"0000-0002-0659-3201","last_name":"Nikitenko","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","full_name":"Nikitenko, Anton","first_name":"Anton"}],"month":"10","publication_identifier":{"issn":["02099683"]},"day":"01","oa_version":"Submitted Version","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1411.6337"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","type":"journal_article","status":"public"},{"project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"}],"publisher":"Academic Press","date_published":"2017-02-21T00:00:00Z","department":[{"_id":"HeEd"}],"page":"627 - 644","volume":308,"quality_controlled":"1","publication_status":"published","external_id":{"isi":["000409292900015"]},"abstract":[{"lang":"eng","text":"In this article we define an algebraic vertex of a generalized polyhedron and show that the set of algebraic vertices is the smallest set of points needed to define the polyhedron. We prove that the indicator function of a generalized polytope P is a linear combination of indicator functions of simplices whose vertices are algebraic vertices of P. We also show that the indicator function of any generalized polyhedron is a linear combination, with integer coefficients, of indicator functions of cones with apices at algebraic vertices and line-cones. The concept of an algebraic vertex is closely related to the Fourier–Laplace transform. We show that a point v is an algebraic vertex of a generalized polyhedron P if and only if the tangent cone of P, at v, has non-zero Fourier–Laplace transform."}],"_id":"1180","doi":"10.1016/j.aim.2016.12.026","year":"2017","publist_id":"6173","citation":{"apa":"Akopyan, A., Bárány, I., &#38; Robins, S. (2017). Algebraic vertices of non-convex polyhedra. <i>Advances in Mathematics</i>. Academic Press. <a href=\"https://doi.org/10.1016/j.aim.2016.12.026\">https://doi.org/10.1016/j.aim.2016.12.026</a>","ista":"Akopyan A, Bárány I, Robins S. 2017. Algebraic vertices of non-convex polyhedra. Advances in Mathematics. 308, 627–644.","mla":"Akopyan, Arseniy, et al. “Algebraic Vertices of Non-Convex Polyhedra.” <i>Advances in Mathematics</i>, vol. 308, Academic Press, 2017, pp. 627–44, doi:<a href=\"https://doi.org/10.1016/j.aim.2016.12.026\">10.1016/j.aim.2016.12.026</a>.","chicago":"Akopyan, Arseniy, Imre Bárány, and Sinai Robins. “Algebraic Vertices of Non-Convex Polyhedra.” <i>Advances in Mathematics</i>. Academic Press, 2017. <a href=\"https://doi.org/10.1016/j.aim.2016.12.026\">https://doi.org/10.1016/j.aim.2016.12.026</a>.","ieee":"A. Akopyan, I. Bárány, and S. Robins, “Algebraic vertices of non-convex polyhedra,” <i>Advances in Mathematics</i>, vol. 308. Academic Press, pp. 627–644, 2017.","ama":"Akopyan A, Bárány I, Robins S. Algebraic vertices of non-convex polyhedra. <i>Advances in Mathematics</i>. 2017;308:627-644. doi:<a href=\"https://doi.org/10.1016/j.aim.2016.12.026\">10.1016/j.aim.2016.12.026</a>","short":"A. Akopyan, I. Bárány, S. Robins, Advances in Mathematics 308 (2017) 627–644."},"date_created":"2018-12-11T11:50:34Z","ec_funded":1,"status":"public","type":"journal_article","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","first_name":"Arseniy"},{"first_name":"Imre","full_name":"Bárány, Imre","last_name":"Bárány"},{"full_name":"Robins, Sinai","first_name":"Sinai","last_name":"Robins"}],"publication_identifier":{"issn":["00018708"]},"month":"02","oa_version":"Submitted Version","day":"21","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1508.07594"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","language":[{"iso":"eng"}],"publication":"Advances in Mathematics","oa":1,"date_updated":"2023-09-20T11:21:27Z","article_processing_charge":"No","title":"Algebraic vertices of non-convex polyhedra","isi":1,"scopus_import":"1","intvolume":"       308"},{"date_created":"2018-12-11T11:46:43Z","publist_id":"7338","citation":{"ista":"Biedl T, Huber S, Palfrader P. 2017. Planar matchings for weighted straight skeletons. International Journal of Computational Geometry and Applications. 26(3–4), 211–229.","mla":"Biedl, Therese, et al. “Planar Matchings for Weighted Straight Skeletons.” <i>International Journal of Computational Geometry and Applications</i>, vol. 26, no. 3–4, World Scientific Publishing, 2017, pp. 211–29, doi:<a href=\"https://doi.org/10.1142/S0218195916600050\">10.1142/S0218195916600050</a>.","chicago":"Biedl, Therese, Stefan Huber, and Peter Palfrader. “Planar Matchings for Weighted Straight Skeletons.” <i>International Journal of Computational Geometry and Applications</i>. World Scientific Publishing, 2017. <a href=\"https://doi.org/10.1142/S0218195916600050\">https://doi.org/10.1142/S0218195916600050</a>.","ama":"Biedl T, Huber S, Palfrader P. Planar matchings for weighted straight skeletons. <i>International Journal of Computational Geometry and Applications</i>. 2017;26(3-4):211-229. doi:<a href=\"https://doi.org/10.1142/S0218195916600050\">10.1142/S0218195916600050</a>","ieee":"T. Biedl, S. Huber, and P. Palfrader, “Planar matchings for weighted straight skeletons,” <i>International Journal of Computational Geometry and Applications</i>, vol. 26, no. 3–4. World Scientific Publishing, pp. 211–229, 2017.","short":"T. Biedl, S. Huber, P. Palfrader, International Journal of Computational Geometry and Applications 26 (2017) 211–229.","apa":"Biedl, T., Huber, S., &#38; Palfrader, P. (2017). Planar matchings for weighted straight skeletons. <i>International Journal of Computational Geometry and Applications</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S0218195916600050\">https://doi.org/10.1142/S0218195916600050</a>"},"acknowledgement":"Supported by NSERC and the Ross and Muriel Cheriton Fellowship. Research supported by Austrian Science Fund (FWF): P25816-N15.","year":"2017","related_material":{"record":[{"relation":"earlier_version","id":"10892","status":"public"}]},"file_date_updated":"2020-07-14T12:46:35Z","_id":"481","doi":"10.1142/S0218195916600050","publication_status":"published","abstract":[{"lang":"eng","text":"We introduce planar matchings on directed pseudo-line arrangements, which yield a planar set of pseudo-line segments such that only matching-partners are adjacent. By translating the planar matching problem into a corresponding stable roommates problem we show that such matchings always exist. Using our new framework, we establish, for the first time, a complete, rigorous definition of weighted straight skeletons, which are based on a so-called wavefront propagation process. We present a generalized and unified approach to treat structural changes in the wavefront that focuses on the restoration of weak planarity by finding planar matchings."}],"ddc":["004","514","516"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"department":[{"_id":"HeEd"}],"page":"211 - 229","quality_controlled":"1","volume":26,"publisher":"World Scientific Publishing","date_published":"2017-04-13T00:00:00Z","title":"Planar matchings for weighted straight skeletons","pubrep_id":"949","oa":1,"date_updated":"2023-02-21T16:06:22Z","issue":"3-4","intvolume":"        26","has_accepted_license":"1","scopus_import":1,"language":[{"iso":"eng"}],"publication":"International Journal of Computational Geometry and Applications","author":[{"full_name":"Biedl, Therese","first_name":"Therese","last_name":"Biedl"},{"orcid":"0000-0002-8871-5814","id":"4700A070-F248-11E8-B48F-1D18A9856A87","last_name":"Huber","full_name":"Huber, Stefan","first_name":"Stefan"},{"first_name":"Peter","full_name":"Palfrader, Peter","last_name":"Palfrader"}],"day":"13","oa_version":"Published Version","file":[{"checksum":"f79e8558bfe4b368dfefeb8eec2e3a5e","file_id":"4758","file_name":"IST-2018-949-v1+1_2016_huber_PLanar_matchings.pdf","date_updated":"2020-07-14T12:46:35Z","date_created":"2018-12-12T10:09:34Z","creator":"system","file_size":769296,"access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","month":"04","status":"public","type":"journal_article"},{"type":"journal_article","status":"public","date_published":"2017-01-01T00:00:00Z","publisher":"Elsevier","quality_controlled":"1","volume":215,"department":[{"_id":"HeEd"}],"page":"45 - 57","publication_status":"published","author":[{"last_name":"Austin","first_name":"Kyle","full_name":"Austin, Kyle"},{"last_name":"Virk","id":"2E36B656-F248-11E8-B48F-1D18A9856A87","full_name":"Virk, Ziga","first_name":"Ziga"}],"month":"01","publication_identifier":{"issn":["01668641"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"lang":"eng","text":"Let X and Y be proper metric spaces. We show that a coarsely n-to-1 map f:X→Y induces an n-to-1 map of Higson coronas. This viewpoint turns out to be successful in showing that the classical dimension raising theorems hold in large scale; that is, if f:X→Y is a coarsely n-to-1 map between proper metric spaces X and Y then asdim(Y)≤asdim(X)+n−1. Furthermore we introduce coarsely open coarsely n-to-1 maps, which include the natural quotient maps via a finite group action, and prove that they preserve the asymptotic dimension."}],"day":"01","oa_version":"Submitted Version","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1608.03954v1"}],"language":[{"iso":"eng"}],"_id":"521","publication":"Topology and its Applications","doi":"10.1016/j.topol.2016.10.005","year":"2017","oa":1,"date_updated":"2021-01-12T08:01:21Z","date_created":"2018-12-11T11:46:56Z","citation":{"apa":"Austin, K., &#38; Virk, Z. (2017). Higson compactification and dimension raising. <i>Topology and Its Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.topol.2016.10.005\">https://doi.org/10.1016/j.topol.2016.10.005</a>","ieee":"K. Austin and Z. Virk, “Higson compactification and dimension raising,” <i>Topology and its Applications</i>, vol. 215. Elsevier, pp. 45–57, 2017.","ama":"Austin K, Virk Z. Higson compactification and dimension raising. <i>Topology and its Applications</i>. 2017;215:45-57. doi:<a href=\"https://doi.org/10.1016/j.topol.2016.10.005\">10.1016/j.topol.2016.10.005</a>","short":"K. Austin, Z. Virk, Topology and Its Applications 215 (2017) 45–57.","chicago":"Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.” <i>Topology and Its Applications</i>. Elsevier, 2017. <a href=\"https://doi.org/10.1016/j.topol.2016.10.005\">https://doi.org/10.1016/j.topol.2016.10.005</a>.","ista":"Austin K, Virk Z. 2017. Higson compactification and dimension raising. Topology and its Applications. 215, 45–57.","mla":"Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.” <i>Topology and Its Applications</i>, vol. 215, Elsevier, 2017, pp. 45–57, doi:<a href=\"https://doi.org/10.1016/j.topol.2016.10.005\">10.1016/j.topol.2016.10.005</a>."},"publist_id":"7299","title":"Higson compactification and dimension raising","intvolume":"       215"},{"scopus_import":1,"intvolume":"        68","publist_id":"6118","title":"Acceleration feature points of unsteady shear flows","citation":{"apa":"Kasten, J., Reininghaus, J., Hotz, I., Hege, H., Noack, B., Daviller, G., &#38; Morzyński, M. (2016). Acceleration feature points of unsteady shear flows. <i>Archives of Mechanics</i>. Polish Academy of Sciences Publishing House.","ista":"Kasten J, Reininghaus J, Hotz I, Hege H, Noack B, Daviller G, Morzyński M. 2016. Acceleration feature points of unsteady shear flows. Archives of Mechanics. 68(1), 55–80.","mla":"Kasten, Jens, et al. “Acceleration Feature Points of Unsteady Shear Flows.” <i>Archives of Mechanics</i>, vol. 68, no. 1, Polish Academy of Sciences Publishing House, 2016, pp. 55–80.","chicago":"Kasten, Jens, Jan Reininghaus, Ingrid Hotz, Hans Hege, Bernd Noack, Guillaume Daviller, and Marek Morzyński. “Acceleration Feature Points of Unsteady Shear Flows.” <i>Archives of Mechanics</i>. Polish Academy of Sciences Publishing House, 2016.","short":"J. Kasten, J. Reininghaus, I. Hotz, H. Hege, B. Noack, G. Daviller, M. Morzyński, Archives of Mechanics 68 (2016) 55–80.","ama":"Kasten J, Reininghaus J, Hotz I, et al. Acceleration feature points of unsteady shear flows. <i>Archives of Mechanics</i>. 2016;68(1):55-80.","ieee":"J. Kasten <i>et al.</i>, “Acceleration feature points of unsteady shear flows,” <i>Archives of Mechanics</i>, vol. 68, no. 1. Polish Academy of Sciences Publishing House, pp. 55–80, 2016."},"date_created":"2018-12-11T11:50:46Z","issue":"1","year":"2016","oa":1,"date_updated":"2021-01-12T06:49:09Z","acknowledgement":"The authors acknowledge funding of the German Re-\r\nsearch  Foundation  (DFG)  via  the  Collaborative  Re-\r\nsearch  Center  (SFB  557)  \\Control  of  Complex  Turbu-\r\nlent  Shear  Flows\"  and  the  Emmy  Noether  Program.\r\nFurther  funding  was  provided  by  the  Zuse  Institute\r\nBerlin  (ZIB),  the  DFG-CNRS  research  group  \\Noise\r\nGeneration in Turbulent Flows\" (2003{2010), the Chaire\r\nd'Excellence 'Closed-loop control of turbulent shear  ows\r\nusing reduced-order models' (TUCOROM) of the French\r\nAgence Nationale de la Recherche (ANR), and the Eu-\r\nropean  Social  Fund  (ESF  App.   No.   100098251).   We\r\nthank  the  Ambrosys  Ltd.  Society  for  Complex  Sys-\r\ntems  Management  and  the  Bernd  R.  Noack  Cybernet-\r\nics  Foundation  for  additional  support.   A  part  of  this\r\nwork was performed using HPC resources from GENCI-[CCRT/CINES/IDRIS]  supported  by  the  Grant  2011-\r\n[x2011020912","publication":"Archives of Mechanics","_id":"1216","language":[{"iso":"eng"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","abstract":[{"text":"A framework fo r extracting features in 2D transient flows, based on the acceleration field to ensure Galilean invariance is proposed in this paper. The minima of the acceleration magnitude (a superset of acceleration zeros) are extracted and discriminated into vortices and saddle points, based on the spectral properties of the velocity Jacobian. The extraction of topological features is performed with purely combinatorial algorithms from discrete computational topology. The feature points are prioritized with persistence, as a physically meaningful importance measure. These feature points are tracked in time with a robust algorithm for tracking features. Thus, a space-time hierarchy of the minima is built and vortex merging events are detected. We apply the acceleration feature extraction strategy to three two-dimensional shear flows: (1) an incompressible periodic cylinder wake, (2) an incompressible planar mixing layer and (3) a weakly compressible planar jet. The vortex-like acceleration feature points are shown to be well aligned with acceleration zeros, maxima of the vorticity magnitude, minima of the pressure field and minima of λ2.","lang":"eng"}],"main_file_link":[{"open_access":"1","url":"http://am.ippt.pan.pl/am/article/viewFile/v68p55/pdf"}],"day":"01","oa_version":"Published Version","month":"01","author":[{"last_name":"Kasten","first_name":"Jens","full_name":"Kasten, Jens"},{"first_name":"Jan","full_name":"Reininghaus, Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","last_name":"Reininghaus"},{"first_name":"Ingrid","full_name":"Hotz, Ingrid","last_name":"Hotz"},{"first_name":"Hans","full_name":"Hege, Hans","last_name":"Hege"},{"full_name":"Noack, Bernd","first_name":"Bernd","last_name":"Noack"},{"full_name":"Daviller, Guillaume","first_name":"Guillaume","last_name":"Daviller"},{"last_name":"Morzyński","first_name":"Marek","full_name":"Morzyński, Marek"}],"publication_status":"published","volume":68,"quality_controlled":"1","page":"55 - 80","department":[{"_id":"HeEd"}],"status":"public","date_published":"2016-01-01T00:00:00Z","type":"journal_article","publisher":"Polish Academy of Sciences Publishing House"},{"year":"2016","acknowledgement":"We wish to thank Alexey Tarasov, Vladislav Volkov and Brittany Fasy for some useful comments and remarks, and especially Thom Sulanke for modifying surftri to suit our purposes. Oleg R. Musin was partially supported by the NSF Grant DMS-1400876 and by the RFBR Grant 15-01-99563. Anton V. Nikitenko was supported by the Chebyshev Laboratory (Department of Mathematics and Mechanics, St. Petersburg State University) under RF Government Grant 11.G34.31.0026.","publist_id":"6111","citation":{"apa":"Musin, O., &#38; Nikitenko, A. (2016). Optimal packings of congruent circles on a square flat torus. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/s00454-015-9742-6\">https://doi.org/10.1007/s00454-015-9742-6</a>","ieee":"O. Musin and A. Nikitenko, “Optimal packings of congruent circles on a square flat torus,” <i>Discrete &#38; Computational Geometry</i>, vol. 55, no. 1. Springer, pp. 1–20, 2016.","ama":"Musin O, Nikitenko A. Optimal packings of congruent circles on a square flat torus. <i>Discrete &#38; Computational Geometry</i>. 2016;55(1):1-20. doi:<a href=\"https://doi.org/10.1007/s00454-015-9742-6\">10.1007/s00454-015-9742-6</a>","short":"O. Musin, A. Nikitenko, Discrete &#38; Computational Geometry 55 (2016) 1–20.","chicago":"Musin, Oleg, and Anton Nikitenko. “Optimal Packings of Congruent Circles on a Square Flat Torus.” <i>Discrete &#38; Computational Geometry</i>. Springer, 2016. <a href=\"https://doi.org/10.1007/s00454-015-9742-6\">https://doi.org/10.1007/s00454-015-9742-6</a>.","ista":"Musin O, Nikitenko A. 2016. Optimal packings of congruent circles on a square flat torus. Discrete &#38; Computational Geometry. 55(1), 1–20.","mla":"Musin, Oleg, and Anton Nikitenko. “Optimal Packings of Congruent Circles on a Square Flat Torus.” <i>Discrete &#38; Computational Geometry</i>, vol. 55, no. 1, Springer, 2016, pp. 1–20, doi:<a href=\"https://doi.org/10.1007/s00454-015-9742-6\">10.1007/s00454-015-9742-6</a>."},"date_created":"2018-12-11T11:50:48Z","_id":"1222","doi":"10.1007/s00454-015-9742-6","publication_status":"published","abstract":[{"lang":"eng","text":"We consider packings of congruent circles on a square flat torus, i.e., periodic (w.r.t. a square lattice) planar circle packings, with the maximal circle radius. This problem is interesting due to a practical reason—the problem of “super resolution of images.” We have found optimal arrangements for N=6, 7 and 8 circles. Surprisingly, for the case N=7 there are three different optimal arrangements. Our proof is based on a computer enumeration of toroidal irreducible contact graphs."}],"date_published":"2016-01-01T00:00:00Z","publisher":"Springer","volume":55,"quality_controlled":"1","page":"1 - 20","department":[{"_id":"HeEd"}],"issue":"1","date_updated":"2021-01-12T06:49:11Z","oa":1,"title":"Optimal packings of congruent circles on a square flat torus","intvolume":"        55","scopus_import":1,"language":[{"iso":"eng"}],"publication":"Discrete & Computational Geometry","author":[{"last_name":"Musin","first_name":"Oleg","full_name":"Musin, Oleg"},{"full_name":"Nikitenko, Anton","first_name":"Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","last_name":"Nikitenko"}],"month":"01","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","day":"01","oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1212.0649"}],"status":"public","type":"journal_article"},{"publication_status":"published","abstract":[{"text":"Bitmap images of arbitrary dimension may be formally perceived as unions of m-dimensional boxes aligned with respect to a rectangular grid in ℝm. Cohomology and homology groups are well known topological invariants of such sets. Cohomological operations, such as the cup product, provide higher-order algebraic topological invariants, especially important for digital images of dimension higher than 3. If such an operation is determined at the level of simplicial chains [see e.g. González-Díaz, Real, Homology, Homotopy Appl, 2003, 83-93], then it is effectively computable. However, decomposing a cubical complex into a simplicial one deleteriously affects the efficiency of such an approach. In order to avoid this overhead, a direct cubical approach was applied in [Pilarczyk, Real, Adv. Comput. Math., 2015, 253-275] for the cup product in cohomology, and implemented in the ChainCon software package [http://www.pawelpilarczyk.com/chaincon/]. We establish a formula for the Steenrod square operations [see Steenrod, Annals of Mathematics. Second Series, 1947, 290-320] directly at the level of cubical chains, and we prove the correctness of this formula. An implementation of this formula is programmed in C++ within the ChainCon software framework. We provide a few examples and discuss the effectiveness of this approach. One specific application follows from the fact that Steenrod squares yield tests for the topological extension problem: Can a given map A → Sd to a sphere Sd be extended to a given super-complex X of A? In particular, the ROB-SAT problem, which is to decide for a given function f: X → ℝm and a value r &gt; 0 whether every g: X → ℝm with ∥g - f ∥∞ ≤ r has a root, reduces to the extension problem.","lang":"eng"}],"project":[{"name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734"},{"grant_number":"622033","_id":"255F06BE-B435-11E9-9278-68D0E5697425","name":"Persistent Homology - Images, Data and Maps","call_identifier":"FP7"}],"department":[{"_id":"UlWa"},{"_id":"HeEd"}],"page":"140 - 151","volume":9667,"quality_controlled":"1","publisher":"Springer","date_published":"2016-06-02T00:00:00Z","citation":{"apa":"Krcál, M., &#38; Pilarczyk, P. (2016). Computation of cubical Steenrod squares (Vol. 9667, pp. 140–151). Presented at the CTIC: Computational Topology in Image Context, Marseille, France: Springer. <a href=\"https://doi.org/10.1007/978-3-319-39441-1_13\">https://doi.org/10.1007/978-3-319-39441-1_13</a>","ieee":"M. Krcál and P. Pilarczyk, “Computation of cubical Steenrod squares,” presented at the CTIC: Computational Topology in Image Context, Marseille, France, 2016, vol. 9667, pp. 140–151.","ama":"Krcál M, Pilarczyk P. Computation of cubical Steenrod squares. In: Vol 9667. Springer; 2016:140-151. doi:<a href=\"https://doi.org/10.1007/978-3-319-39441-1_13\">10.1007/978-3-319-39441-1_13</a>","short":"M. Krcál, P. Pilarczyk, in:, Springer, 2016, pp. 140–151.","ista":"Krcál M, Pilarczyk P. 2016. Computation of cubical Steenrod squares. CTIC: Computational Topology in Image Context, LNCS, vol. 9667, 140–151.","mla":"Krcál, Marek, and Pawel Pilarczyk. <i>Computation of Cubical Steenrod Squares</i>. Vol. 9667, Springer, 2016, pp. 140–51, doi:<a href=\"https://doi.org/10.1007/978-3-319-39441-1_13\">10.1007/978-3-319-39441-1_13</a>.","chicago":"Krcál, Marek, and Pawel Pilarczyk. “Computation of Cubical Steenrod Squares,” 9667:140–51. Springer, 2016. <a href=\"https://doi.org/10.1007/978-3-319-39441-1_13\">https://doi.org/10.1007/978-3-319-39441-1_13</a>."},"date_created":"2018-12-11T11:50:52Z","publist_id":"6096","acknowledgement":"The research conducted by both authors has received funding from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreements no. 291734 (for M. K.) and no. 622033 (for P. P.).","year":"2016","ec_funded":1,"_id":"1237","doi":"10.1007/978-3-319-39441-1_13","author":[{"last_name":"Krcál","id":"33E21118-F248-11E8-B48F-1D18A9856A87","full_name":"Krcál, Marek","first_name":"Marek"},{"full_name":"Pilarczyk, Pawel","first_name":"Pawel","id":"3768D56A-F248-11E8-B48F-1D18A9856A87","last_name":"Pilarczyk"}],"day":"02","oa_version":"None","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","conference":{"name":"CTIC: Computational Topology in Image Context","start_date":"2016-06-15","location":"Marseille, France","end_date":"2016-06-17"},"month":"06","alternative_title":["LNCS"],"status":"public","type":"conference","title":"Computation of cubical Steenrod squares","date_updated":"2021-01-12T06:49:18Z","scopus_import":1,"intvolume":"      9667","language":[{"iso":"eng"}]},{"publist_id":"6075","citation":{"apa":"Harker, S., Kokubu, H., Mischaikow, K., &#38; Pilarczyk, P. (2016). Inducing a map on homology from a correspondence. <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/proc/12812\">https://doi.org/10.1090/proc/12812</a>","mla":"Harker, Shaun, et al. “Inducing a Map on Homology from a Correspondence.” <i>Proceedings of the American Mathematical Society</i>, vol. 144, no. 4, American Mathematical Society, 2016, pp. 1787–801, doi:<a href=\"https://doi.org/10.1090/proc/12812\">10.1090/proc/12812</a>.","ista":"Harker S, Kokubu H, Mischaikow K, Pilarczyk P. 2016. Inducing a map on homology from a correspondence. Proceedings of the American Mathematical Society. 144(4), 1787–1801.","chicago":"Harker, Shaun, Hiroshi Kokubu, Konstantin Mischaikow, and Pawel Pilarczyk. “Inducing a Map on Homology from a Correspondence.” <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society, 2016. <a href=\"https://doi.org/10.1090/proc/12812\">https://doi.org/10.1090/proc/12812</a>.","ieee":"S. Harker, H. Kokubu, K. Mischaikow, and P. Pilarczyk, “Inducing a map on homology from a correspondence,” <i>Proceedings of the American Mathematical Society</i>, vol. 144, no. 4. American Mathematical Society, pp. 1787–1801, 2016.","ama":"Harker S, Kokubu H, Mischaikow K, Pilarczyk P. Inducing a map on homology from a correspondence. <i>Proceedings of the American Mathematical Society</i>. 2016;144(4):1787-1801. doi:<a href=\"https://doi.org/10.1090/proc/12812\">10.1090/proc/12812</a>","short":"S. Harker, H. Kokubu, K. Mischaikow, P. Pilarczyk, Proceedings of the American Mathematical Society 144 (2016) 1787–1801."},"date_created":"2018-12-11T11:50:57Z","year":"2016","acknowledgement":"The authors gratefully acknowledge the support of the Lorenz Center which\r\nprovided an opportunity for us to discuss in depth the work of this paper. Research leading to these results has received funding from Fundo Europeu de Desenvolvimento Regional (FEDER) through COMPETE—Programa Operacional Factores de Competitividade (POFC) and from the Portuguese national funds through Funda¸c˜ao para a Ciˆencia e a Tecnologia (FCT) in the framework of the research\r\nproject FCOMP-01-0124-FEDER-010645 (ref. FCT PTDC/MAT/098871/2008),\r\nas well as from the People Programme (Marie Curie Actions) of the European\r\nUnion’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement no. 622033 (supporting PP). The work of the first and third author has\r\nbeen partially supported by NSF grants NSF-DMS-0835621, 0915019, 1125174,\r\n1248071, and contracts from AFOSR and DARPA. The work of the second author\r\nwas supported by Grant-in-Aid for Scientific Research (No. 25287029), Ministry of\r\nEducation, Science, Technology, Culture and Sports, Japan.","ec_funded":1,"_id":"1252","article_type":"original","doi":"10.1090/proc/12812","publication_status":"published","abstract":[{"lang":"eng","text":"We study the homomorphism induced in homology by a closed correspondence between topological spaces, using projections from the graph of the correspondence to its domain and codomain. We provide assumptions under which the homomorphism induced by an outer approximation of a continuous map coincides with the homomorphism induced in homology by the map. In contrast to more classical results we do not require that the projection to the domain have acyclic preimages. Moreover, we show that it is possible to retrieve correct homological information from a correspondence even if some data is missing or perturbed. Finally, we describe an application to combinatorial maps that are either outer approximations of continuous maps or reconstructions of such maps from a finite set of data points."}],"external_id":{"arxiv":["1411.7563"]},"project":[{"_id":"255F06BE-B435-11E9-9278-68D0E5697425","grant_number":"622033","call_identifier":"FP7","name":"Persistent Homology - Images, Data and Maps"}],"quality_controlled":"1","volume":144,"department":[{"_id":"HeEd"}],"page":"1787 - 1801","date_published":"2016-04-01T00:00:00Z","publisher":"American Mathematical Society","title":"Inducing a map on homology from a correspondence","issue":"4","article_processing_charge":"No","date_updated":"2022-05-24T09:35:58Z","oa":1,"intvolume":"       144","scopus_import":"1","language":[{"iso":"eng"}],"publication":"Proceedings of the American Mathematical Society","arxiv":1,"author":[{"last_name":"Harker","full_name":"Harker, Shaun","first_name":"Shaun"},{"last_name":"Kokubu","full_name":"Kokubu, Hiroshi","first_name":"Hiroshi"},{"full_name":"Mischaikow, Konstantin","first_name":"Konstantin","last_name":"Mischaikow"},{"full_name":"Pilarczyk, Pawel","first_name":"Pawel","last_name":"Pilarczyk","id":"3768D56A-F248-11E8-B48F-1D18A9856A87"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"01","main_file_link":[{"url":"https://arxiv.org/abs/1411.7563","open_access":"1"}],"oa_version":"Preprint","month":"04","publication_identifier":{"issn":["1088-6826"]},"status":"public","type":"journal_article"},{"author":[{"last_name":"Golmakani","full_name":"Golmakani, Ali","first_name":"Ali"},{"last_name":"Luzzatto","full_name":"Luzzatto, Stefano","first_name":"Stefano"},{"first_name":"Pawel","full_name":"Pilarczyk, Pawel","last_name":"Pilarczyk","id":"3768D56A-F248-11E8-B48F-1D18A9856A87"}],"month":"04","main_file_link":[{"url":"https://arxiv.org/abs/1504.00116","open_access":"1"}],"day":"02","oa_version":"Preprint","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","status":"public","type":"journal_article","oa":1,"date_updated":"2021-01-12T06:49:25Z","issue":"2","title":"Uniform expansivity outside a critical neighborhood in the quadratic family","intvolume":"        25","scopus_import":1,"language":[{"iso":"eng"}],"publication":"Experimental Mathematics","publication_status":"published","abstract":[{"text":"We use rigorous numerical techniques to compute a lower bound for the exponent of expansivity outside a neighborhood of the critical point for thousands of intervals of parameter values in the quadratic family. We first compute a radius of the critical neighborhood outside which the map is uniformly expanding. This radius is taken as small as possible, yet large enough for our numerical procedure to succeed in proving that the expansivity exponent outside this neighborhood is positive. Then, for each of the intervals, we compute a lower bound for this expansivity exponent, valid for all the parameters in that interval. We illustrate and study the distribution of the radii and the expansivity exponents. The results of our computations are mathematically rigorous. The source code of the software and the results of the computations are made publicly available at http://www.pawelpilarczyk.com/quadratic/.","lang":"eng"}],"project":[{"_id":"255F06BE-B435-11E9-9278-68D0E5697425","grant_number":"622033","name":"Persistent Homology - Images, Data and Maps","call_identifier":"FP7"}],"publisher":"Taylor and Francis","date_published":"2016-04-02T00:00:00Z","page":"116 - 124","department":[{"_id":"HeEd"}],"volume":25,"quality_controlled":"1","acknowledgement":"AG and PP were partially supported by Abdus Salam International Centre for Theoretical Physics (ICTP). Additionally, AG was supported by BREUDS, and research conducted by PP has received funding from Fundo Europeu de Desenvolvimento Regional (FEDER) through COMPETE—Programa Operacional Factores de Competitividade (POFC) and from the Portuguese national funds through Fundação para a Ciência e a Tecnologia (FCT) in the framework of the research project FCOMP-01-0124-FEDER-010645 (ref. FCT PTDC/MAT/098871/2008); and from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement no. 622033. The  authors  gratefully  acknowledge  the  Department  of\r\nMathematics  of  Kyoto  University  for  providing  access\r\nto  their  server  for  conducting  computations  for  this\r\nproject.","year":"2016","date_created":"2018-12-11T11:50:58Z","citation":{"apa":"Golmakani, A., Luzzatto, S., &#38; Pilarczyk, P. (2016). Uniform expansivity outside a critical neighborhood in the quadratic family. <i>Experimental Mathematics</i>. Taylor and Francis. <a href=\"https://doi.org/10.1080/10586458.2015.1048011\">https://doi.org/10.1080/10586458.2015.1048011</a>","short":"A. Golmakani, S. Luzzatto, P. Pilarczyk, Experimental Mathematics 25 (2016) 116–124.","ama":"Golmakani A, Luzzatto S, Pilarczyk P. Uniform expansivity outside a critical neighborhood in the quadratic family. <i>Experimental Mathematics</i>. 2016;25(2):116-124. doi:<a href=\"https://doi.org/10.1080/10586458.2015.1048011\">10.1080/10586458.2015.1048011</a>","ieee":"A. Golmakani, S. Luzzatto, and P. Pilarczyk, “Uniform expansivity outside a critical neighborhood in the quadratic family,” <i>Experimental Mathematics</i>, vol. 25, no. 2. Taylor and Francis, pp. 116–124, 2016.","mla":"Golmakani, Ali, et al. “Uniform Expansivity Outside a Critical Neighborhood in the Quadratic Family.” <i>Experimental Mathematics</i>, vol. 25, no. 2, Taylor and Francis, 2016, pp. 116–24, doi:<a href=\"https://doi.org/10.1080/10586458.2015.1048011\">10.1080/10586458.2015.1048011</a>.","chicago":"Golmakani, Ali, Stefano Luzzatto, and Pawel Pilarczyk. “Uniform Expansivity Outside a Critical Neighborhood in the Quadratic Family.” <i>Experimental Mathematics</i>. Taylor and Francis, 2016. <a href=\"https://doi.org/10.1080/10586458.2015.1048011\">https://doi.org/10.1080/10586458.2015.1048011</a>.","ista":"Golmakani A, Luzzatto S, Pilarczyk P. 2016. Uniform expansivity outside a critical neighborhood in the quadratic family. Experimental Mathematics. 25(2), 116–124."},"publist_id":"6071","ec_funded":1,"_id":"1254","doi":"10.1080/10586458.2015.1048011"},{"month":"09","file":[{"file_size":1678369,"relation":"main_file","content_type":"application/pdf","access_level":"open_access","creator":"system","date_created":"2018-12-12T10:16:20Z","date_updated":"2020-07-14T12:44:42Z","file_name":"IST-2016-694-v1+1_Generalized_offsetting_of_planar_structures_using_skeletons.pdf","file_id":"5206","checksum":"c746f3a48edb62b588d92ea5d0fd2c0e"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","day":"02","oa_version":"Published Version","author":[{"full_name":"Held, Martin","first_name":"Martin","last_name":"Held"},{"id":"4700A070-F248-11E8-B48F-1D18A9856A87","last_name":"Huber","orcid":"0000-0002-8871-5814","first_name":"Stefan","full_name":"Huber, Stefan"},{"first_name":"Peter","full_name":"Palfrader, Peter","last_name":"Palfrader"}],"status":"public","type":"journal_article","has_accepted_license":"1","intvolume":"        13","scopus_import":1,"issue":"5","pubrep_id":"694","date_updated":"2021-01-12T06:49:32Z","oa":1,"title":"Generalized offsetting of planar structures using skeletons","publication":"Computer-Aided Design and Applications","language":[{"iso":"eng"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png","short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)"},"ddc":["004","516"],"abstract":[{"lang":"eng","text":"We study different means to extend offsetting based on skeletal structures beyond the well-known constant-radius and mitered offsets supported by Voronoi diagrams and straight skeletons, for which the orthogonal distance of offset elements to their respective input elements is constant and uniform over all input elements. Our main contribution is a new geometric structure, called variable-radius Voronoi diagram, which supports the computation of variable-radius offsets, i.e., offsets whose distance to the input is allowed to vary along the input. We discuss properties of this structure and sketch a prototype implementation that supports the computation of variable-radius offsets based on this new variant of Voronoi diagrams."}],"publication_status":"published","license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","date_published":"2016-09-02T00:00:00Z","publisher":"Taylor and Francis","volume":13,"quality_controlled":"1","department":[{"_id":"HeEd"}],"page":"712 - 721","year":"2016","acknowledgement":"This work was supported by Austrian Science Fund (FWF): P25816-N15.","publist_id":"6048","citation":{"chicago":"Held, Martin, Stefan Huber, and Peter Palfrader. “Generalized Offsetting of Planar Structures Using Skeletons.” <i>Computer-Aided Design and Applications</i>. Taylor and Francis, 2016. <a href=\"https://doi.org/10.1080/16864360.2016.1150718\">https://doi.org/10.1080/16864360.2016.1150718</a>.","mla":"Held, Martin, et al. “Generalized Offsetting of Planar Structures Using Skeletons.” <i>Computer-Aided Design and Applications</i>, vol. 13, no. 5, Taylor and Francis, 2016, pp. 712–21, doi:<a href=\"https://doi.org/10.1080/16864360.2016.1150718\">10.1080/16864360.2016.1150718</a>.","ista":"Held M, Huber S, Palfrader P. 2016. Generalized offsetting of planar structures using skeletons. Computer-Aided Design and Applications. 13(5), 712–721.","short":"M. Held, S. Huber, P. Palfrader, Computer-Aided Design and Applications 13 (2016) 712–721.","ama":"Held M, Huber S, Palfrader P. Generalized offsetting of planar structures using skeletons. <i>Computer-Aided Design and Applications</i>. 2016;13(5):712-721. doi:<a href=\"https://doi.org/10.1080/16864360.2016.1150718\">10.1080/16864360.2016.1150718</a>","ieee":"M. Held, S. Huber, and P. Palfrader, “Generalized offsetting of planar structures using skeletons,” <i>Computer-Aided Design and Applications</i>, vol. 13, no. 5. Taylor and Francis, pp. 712–721, 2016.","apa":"Held, M., Huber, S., &#38; Palfrader, P. (2016). Generalized offsetting of planar structures using skeletons. <i>Computer-Aided Design and Applications</i>. Taylor and Francis. <a href=\"https://doi.org/10.1080/16864360.2016.1150718\">https://doi.org/10.1080/16864360.2016.1150718</a>"},"date_created":"2018-12-11T11:51:04Z","doi":"10.1080/16864360.2016.1150718","_id":"1272","file_date_updated":"2020-07-14T12:44:42Z"},{"publication":"Pattern Recognition Letters","language":[{"iso":"eng"}],"has_accepted_license":"1","scopus_import":1,"intvolume":"        83","title":"The classification of endoscopy images with persistent homology","issue":"1","article_processing_charge":"No","oa":1,"pubrep_id":"975","date_updated":"2023-02-23T10:04:40Z","type":"journal_article","status":"public","file":[{"file_name":"2016-Edelsbrunner_The_classification.pdf","checksum":"33458bbb8c32a339e1adeca6d5a1112d","file_id":"6334","date_updated":"2020-07-14T12:44:42Z","date_created":"2019-04-17T07:55:51Z","creator":"dernst","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_size":1921113}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Submitted Version","day":"01","month":"11","author":[{"first_name":"Olga","full_name":"Dunaeva, Olga","last_name":"Dunaeva"},{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner"},{"first_name":"Anton","full_name":"Lukyanov, Anton","last_name":"Lukyanov"},{"first_name":"Michael","full_name":"Machin, Michael","last_name":"Machin"},{"last_name":"Malkova","first_name":"Daria","full_name":"Malkova, Daria"},{"first_name":"Roman","full_name":"Kuvaev, Roman","last_name":"Kuvaev"},{"full_name":"Kashin, Sergey","first_name":"Sergey","last_name":"Kashin"}],"doi":"10.1016/j.patrec.2015.12.012","_id":"1289","file_date_updated":"2020-07-14T12:44:42Z","related_material":{"record":[{"relation":"earlier_version","id":"1568","status":"public"}]},"citation":{"chicago":"Dunaeva, Olga, Herbert Edelsbrunner, Anton Lukyanov, Michael Machin, Daria Malkova, Roman Kuvaev, and Sergey Kashin. “The Classification of Endoscopy Images with Persistent Homology.” <i>Pattern Recognition Letters</i>. Elsevier, 2016. <a href=\"https://doi.org/10.1016/j.patrec.2015.12.012\">https://doi.org/10.1016/j.patrec.2015.12.012</a>.","mla":"Dunaeva, Olga, et al. “The Classification of Endoscopy Images with Persistent Homology.” <i>Pattern Recognition Letters</i>, vol. 83, no. 1, Elsevier, 2016, pp. 13–22, doi:<a href=\"https://doi.org/10.1016/j.patrec.2015.12.012\">10.1016/j.patrec.2015.12.012</a>.","ista":"Dunaeva O, Edelsbrunner H, Lukyanov A, Machin M, Malkova D, Kuvaev R, Kashin S. 2016. The classification of endoscopy images with persistent homology. Pattern Recognition Letters. 83(1), 13–22.","ieee":"O. Dunaeva <i>et al.</i>, “The classification of endoscopy images with persistent homology,” <i>Pattern Recognition Letters</i>, vol. 83, no. 1. Elsevier, pp. 13–22, 2016.","ama":"Dunaeva O, Edelsbrunner H, Lukyanov A, et al. The classification of endoscopy images with persistent homology. <i>Pattern Recognition Letters</i>. 2016;83(1):13-22. doi:<a href=\"https://doi.org/10.1016/j.patrec.2015.12.012\">10.1016/j.patrec.2015.12.012</a>","short":"O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, D. Malkova, R. Kuvaev, S. Kashin, Pattern Recognition Letters 83 (2016) 13–22.","apa":"Dunaeva, O., Edelsbrunner, H., Lukyanov, A., Machin, M., Malkova, D., Kuvaev, R., &#38; Kashin, S. (2016). The classification of endoscopy images with persistent homology. <i>Pattern Recognition Letters</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.patrec.2015.12.012\">https://doi.org/10.1016/j.patrec.2015.12.012</a>"},"publist_id":"6027","date_created":"2018-12-11T11:51:10Z","year":"2016","quality_controlled":"1","volume":83,"page":"13 - 22","department":[{"_id":"HeEd"}],"date_published":"2016-11-01T00:00:00Z","publisher":"Elsevier","abstract":[{"text":"Aiming at the automatic diagnosis of tumors using narrow band imaging (NBI) magnifying endoscopic (ME) images of the stomach, we combine methods from image processing, topology, geometry, and machine learning to classify patterns into three classes: oval, tubular and irregular. Training the algorithm on a small number of images of each type, we achieve a high rate of correct classifications. The analysis of the learning algorithm reveals that a handful of geometric and topological features are responsible for the overwhelming majority of decisions.","lang":"eng"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png","short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)"},"ddc":["004","514"],"publication_status":"published"},{"_id":"1292","doi":"10.1007/s10474-016-0648-4","year":"2016","acknowledgement":"The authors are veryg rateful to Hansj ̈org Geiges \r\nfor fruitful discussions and advice and Christian Evers for helpful remarks on a draft version.","publist_id":"6023","citation":{"apa":"Durst, S., Kegel, M., &#38; Klukas, M. D. (2016). Computing the Thurston–Bennequin invariant in open books. <i>Acta Mathematica Hungarica</i>. Springer. <a href=\"https://doi.org/10.1007/s10474-016-0648-4\">https://doi.org/10.1007/s10474-016-0648-4</a>","chicago":"Durst, Sebastian, Marc Kegel, and Mirko D Klukas. “Computing the Thurston–Bennequin Invariant in Open Books.” <i>Acta Mathematica Hungarica</i>. Springer, 2016. <a href=\"https://doi.org/10.1007/s10474-016-0648-4\">https://doi.org/10.1007/s10474-016-0648-4</a>.","mla":"Durst, Sebastian, et al. “Computing the Thurston–Bennequin Invariant in Open Books.” <i>Acta Mathematica Hungarica</i>, vol. 150, no. 2, Springer, 2016, pp. 441–55, doi:<a href=\"https://doi.org/10.1007/s10474-016-0648-4\">10.1007/s10474-016-0648-4</a>.","ista":"Durst S, Kegel M, Klukas MD. 2016. Computing the Thurston–Bennequin invariant in open books. Acta Mathematica Hungarica. 150(2), 441–455.","ieee":"S. Durst, M. Kegel, and M. D. Klukas, “Computing the Thurston–Bennequin invariant in open books,” <i>Acta Mathematica Hungarica</i>, vol. 150, no. 2. Springer, pp. 441–455, 2016.","ama":"Durst S, Kegel M, Klukas MD. Computing the Thurston–Bennequin invariant in open books. <i>Acta Mathematica Hungarica</i>. 2016;150(2):441-455. doi:<a href=\"https://doi.org/10.1007/s10474-016-0648-4\">10.1007/s10474-016-0648-4</a>","short":"S. Durst, M. Kegel, M.D. Klukas, Acta Mathematica Hungarica 150 (2016) 441–455."},"date_created":"2018-12-11T11:51:11Z","date_published":"2016-12-01T00:00:00Z","publisher":"Springer","volume":150,"quality_controlled":"1","page":"441 - 455","department":[{"_id":"HeEd"}],"publication_status":"published","abstract":[{"text":"We give explicit formulas and algorithms for the computation of the Thurston–Bennequin invariant of a nullhomologous Legendrian knot on a page of a contact open book and on Heegaard surfaces in convex position. Furthermore, we extend the results to rationally nullhomologous knots in arbitrary 3-manifolds.","lang":"eng"}],"language":[{"iso":"eng"}],"publication":"Acta Mathematica Hungarica","issue":"2","oa":1,"date_updated":"2021-01-12T06:49:40Z","title":"Computing the Thurston–Bennequin invariant in open books","scopus_import":1,"intvolume":"       150","status":"public","type":"journal_article","author":[{"full_name":"Durst, Sebastian","first_name":"Sebastian","last_name":"Durst"},{"first_name":"Marc","full_name":"Kegel, Marc","last_name":"Kegel"},{"full_name":"Klukas, Mirko D","first_name":"Mirko D","last_name":"Klukas","id":"34927512-F248-11E8-B48F-1D18A9856A87"}],"month":"12","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1605.00794"}],"day":"01","oa_version":"Preprint"},{"doi":"10.1016/j.endm.2016.09.030","publication":"Electronic Notes in Discrete Mathematics","language":[{"iso":"eng"}],"_id":"1295","intvolume":"        54","scopus_import":1,"ec_funded":1,"date_created":"2018-12-11T11:51:12Z","publist_id":"5976","title":"Multiple covers with balls II: Weighted averages","citation":{"apa":"Edelsbrunner, H., &#38; Iglesias Ham, M. (2016). Multiple covers with balls II: Weighted averages. <i>Electronic Notes in Discrete Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.endm.2016.09.030\">https://doi.org/10.1016/j.endm.2016.09.030</a>","ama":"Edelsbrunner H, Iglesias Ham M. Multiple covers with balls II: Weighted averages. <i>Electronic Notes in Discrete Mathematics</i>. 2016;54:169-174. doi:<a href=\"https://doi.org/10.1016/j.endm.2016.09.030\">10.1016/j.endm.2016.09.030</a>","ieee":"H. Edelsbrunner and M. Iglesias Ham, “Multiple covers with balls II: Weighted averages,” <i>Electronic Notes in Discrete Mathematics</i>, vol. 54. Elsevier, pp. 169–174, 2016.","short":"H. Edelsbrunner, M. Iglesias Ham, Electronic Notes in Discrete Mathematics 54 (2016) 169–174.","chicago":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls II: Weighted Averages.” <i>Electronic Notes in Discrete Mathematics</i>. Elsevier, 2016. <a href=\"https://doi.org/10.1016/j.endm.2016.09.030\">https://doi.org/10.1016/j.endm.2016.09.030</a>.","ista":"Edelsbrunner H, Iglesias Ham M. 2016. Multiple covers with balls II: Weighted averages. Electronic Notes in Discrete Mathematics. 54, 169–174.","mla":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls II: Weighted Averages.” <i>Electronic Notes in Discrete Mathematics</i>, vol. 54, Elsevier, 2016, pp. 169–74, doi:<a href=\"https://doi.org/10.1016/j.endm.2016.09.030\">10.1016/j.endm.2016.09.030</a>."},"year":"2016","date_updated":"2021-01-12T06:49:41Z","acknowledgement":"This work is partially supported by the Toposys project FP7-ICT-318493-STREP, and by ESF under the ACAT Research Network Programme.","volume":54,"quality_controlled":"1","department":[{"_id":"HeEd"}],"page":"169 - 174","date_published":"2016-10-01T00:00:00Z","type":"journal_article","status":"public","publisher":"Elsevier","project":[{"name":"Topological Complex Systems","call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493"}],"abstract":[{"lang":"eng","text":"Voronoi diagrams and Delaunay triangulations have been extensively used to represent and compute geometric features of point configurations. We introduce a generalization to poset diagrams and poset complexes, which contain order-k and degree-k Voronoi diagrams and their duals as special cases. Extending a result of Aurenhammer from 1990, we show how to construct poset diagrams as weighted Voronoi diagrams of average balls."}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","day":"01","oa_version":"None","month":"10","publication_status":"published","author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833"},{"last_name":"Iglesias Ham","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","first_name":"Mabel","full_name":"Iglesias Ham, Mabel"}]},{"intvolume":"       216","scopus_import":1,"oa":1,"date_updated":"2021-01-12T06:49:56Z","issue":"2","title":"Billiards in convex bodies with acute angles","publication":"Israel Journal of Mathematics","language":[{"iso":"eng"}],"month":"10","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1506.06014"}],"oa_version":"Preprint","day":"15","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Akopyan, Arseniy","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","orcid":"0000-0002-2548-617X"},{"last_name":"Balitskiy","full_name":"Balitskiy, Alexey","first_name":"Alexey"}],"status":"public","type":"journal_article","ec_funded":1,"acknowledgement":"Supported by People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement n°[291734]. Supported by the Russian Foundation for Basic Research grant 15-31-20403 (mol a ved), by the Russian Foundation for Basic Research grant 15-01-99563 A, in part by the Moebius Contest Foundation for Young Scientists, and in part by the Simons Foundation.","year":"2016","publist_id":"5938","citation":{"apa":"Akopyan, A., &#38; Balitskiy, A. (2016). Billiards in convex bodies with acute angles. <i>Israel Journal of Mathematics</i>. Springer. <a href=\"https://doi.org/10.1007/s11856-016-1429-z\">https://doi.org/10.1007/s11856-016-1429-z</a>","ista":"Akopyan A, Balitskiy A. 2016. Billiards in convex bodies with acute angles. Israel Journal of Mathematics. 216(2), 833–845.","chicago":"Akopyan, Arseniy, and Alexey Balitskiy. “Billiards in Convex Bodies with Acute Angles.” <i>Israel Journal of Mathematics</i>. Springer, 2016. <a href=\"https://doi.org/10.1007/s11856-016-1429-z\">https://doi.org/10.1007/s11856-016-1429-z</a>.","mla":"Akopyan, Arseniy, and Alexey Balitskiy. “Billiards in Convex Bodies with Acute Angles.” <i>Israel Journal of Mathematics</i>, vol. 216, no. 2, Springer, 2016, pp. 833–45, doi:<a href=\"https://doi.org/10.1007/s11856-016-1429-z\">10.1007/s11856-016-1429-z</a>.","ieee":"A. Akopyan and A. Balitskiy, “Billiards in convex bodies with acute angles,” <i>Israel Journal of Mathematics</i>, vol. 216, no. 2. Springer, pp. 833–845, 2016.","ama":"Akopyan A, Balitskiy A. Billiards in convex bodies with acute angles. <i>Israel Journal of Mathematics</i>. 2016;216(2):833-845. doi:<a href=\"https://doi.org/10.1007/s11856-016-1429-z\">10.1007/s11856-016-1429-z</a>","short":"A. Akopyan, A. Balitskiy, Israel Journal of Mathematics 216 (2016) 833–845."},"date_created":"2018-12-11T11:51:24Z","doi":"10.1007/s11856-016-1429-z","_id":"1330","abstract":[{"text":"In this paper we investigate the existence of closed billiard trajectories in not necessarily smooth convex bodies. In particular, we show that if a body K ⊂ Rd has the property that the tangent cone of every non-smooth point q ∉ ∂K is acute (in a certain sense), then there is a closed billiard trajectory in K.","lang":"eng"}],"publication_status":"published","publisher":"Springer","date_published":"2016-10-15T00:00:00Z","department":[{"_id":"HeEd"}],"page":"833 - 845","quality_controlled":"1","volume":216,"project":[{"call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734"}]},{"intvolume":"        33","scopus_import":1,"date_created":"2018-12-11T11:53:03Z","title":"On the discrepancy of jittered sampling","publist_id":"5549","citation":{"chicago":"Pausinger, Florian, and Stefan Steinerberger. “On the Discrepancy of Jittered Sampling.” <i>Journal of Complexity</i>. Academic Press, 2016. <a href=\"https://doi.org/10.1016/j.jco.2015.11.003\">https://doi.org/10.1016/j.jco.2015.11.003</a>.","ista":"Pausinger F, Steinerberger S. 2016. On the discrepancy of jittered sampling. Journal of Complexity. 33, 199–216.","mla":"Pausinger, Florian, and Stefan Steinerberger. “On the Discrepancy of Jittered Sampling.” <i>Journal of Complexity</i>, vol. 33, Academic Press, 2016, pp. 199–216, doi:<a href=\"https://doi.org/10.1016/j.jco.2015.11.003\">10.1016/j.jco.2015.11.003</a>.","ama":"Pausinger F, Steinerberger S. On the discrepancy of jittered sampling. <i>Journal of Complexity</i>. 2016;33:199-216. doi:<a href=\"https://doi.org/10.1016/j.jco.2015.11.003\">10.1016/j.jco.2015.11.003</a>","ieee":"F. Pausinger and S. Steinerberger, “On the discrepancy of jittered sampling,” <i>Journal of Complexity</i>, vol. 33. Academic Press, pp. 199–216, 2016.","short":"F. Pausinger, S. Steinerberger, Journal of Complexity 33 (2016) 199–216.","apa":"Pausinger, F., &#38; Steinerberger, S. (2016). On the discrepancy of jittered sampling. <i>Journal of Complexity</i>. Academic Press. <a href=\"https://doi.org/10.1016/j.jco.2015.11.003\">https://doi.org/10.1016/j.jco.2015.11.003</a>"},"acknowledgement":"We are grateful to the referee whose suggestions greatly improved the quality and clarity of the exposition.","date_updated":"2021-01-12T06:52:02Z","oa":1,"year":"2016","doi":"10.1016/j.jco.2015.11.003","publication":"Journal of Complexity","_id":"1617","language":[{"iso":"eng"}],"oa_version":"Submitted Version","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1510.00251"}],"day":"01","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","abstract":[{"lang":"eng","text":"We study the discrepancy of jittered sampling sets: such a set P⊂ [0,1]d is generated for fixed m∈ℕ by partitioning [0,1]d into md axis aligned cubes of equal measure and placing a random point inside each of the N=md cubes. We prove that, for N sufficiently large, 1/10 d/N1/2+1/2d ≤EDN∗(P)≤ √d(log N) 1/2/N1/2+1/2d, where the upper bound with an unspecified constant Cd was proven earlier by Beck. Our proof makes crucial use of the sharp Dvoretzky-Kiefer-Wolfowitz inequality and a suitably taylored Bernstein inequality; we have reasons to believe that the upper bound has the sharp scaling in N. Additional heuristics suggest that jittered sampling should be able to improve known bounds on the inverse of the star-discrepancy in the regime N≳dd. We also prove a partition principle showing that every partition of [0,1]d combined with a jittered sampling construction gives rise to a set whose expected squared L2-discrepancy is smaller than that of purely random points."}],"month":"04","publication_status":"published","author":[{"full_name":"Pausinger, Florian","first_name":"Florian","orcid":"0000-0002-8379-3768","last_name":"Pausinger","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Steinerberger","full_name":"Steinerberger, Stefan","first_name":"Stefan"}],"page":"199 - 216","department":[{"_id":"HeEd"}],"volume":33,"quality_controlled":"1","publisher":"Academic Press","type":"journal_article","status":"public","date_published":"2016-04-01T00:00:00Z"}]