[{"external_id":{"arxiv":["1411.6337"],"isi":["000418056000005"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":37,"oa":1,"abstract":[{"lang":"eng","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."}],"oa_version":"Submitted Version","arxiv":1,"project":[{"grant_number":"318493","name":"Topological Complex Systems","call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"author":[{"last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"last_name":"Glazyrin","first_name":"Alexey","full_name":"Glazyrin, Alexey"},{"last_name":"Musin","first_name":"Oleg","full_name":"Musin, Oleg"},{"id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","first_name":"Anton","last_name":"Nikitenko","orcid":"0000-0002-0659-3201","full_name":"Nikitenko, Anton"}],"date_created":"2018-12-11T11:50:32Z","publication_identifier":{"issn":["0209-9683"]},"date_updated":"2025-06-04T08:44:44Z","intvolume":" 37","_id":"1173","year":"2017","date_published":"2017-10-01T00:00:00Z","title":"The Voronoi functional is maximized by the Delaunay triangulation in the plane","month":"10","scopus_import":"1","ec_funded":1,"status":"public","language":[{"iso":"eng"}],"article_processing_charge":"No","publisher":"Springer","publication":"Combinatorica","type":"journal_article","publication_status":"published","quality_controlled":"1","department":[{"_id":"HeEd"}],"citation":{"short":"H. Edelsbrunner, A. Glazyrin, O. Musin, A. Nikitenko, Combinatorica 37 (2017) 887–910.","ieee":"H. Edelsbrunner, A. Glazyrin, O. Musin, and A. Nikitenko, “The Voronoi functional is maximized by the Delaunay triangulation in the plane,” Combinatorica, vol. 37, no. 5. Springer, pp. 887–910, 2017.","mla":"Edelsbrunner, Herbert, et al. “The Voronoi Functional Is Maximized by the Delaunay Triangulation in the Plane.” Combinatorica, vol. 37, no. 5, Springer, 2017, pp. 887–910, doi:10.1007/s00493-016-3308-y.","chicago":"Edelsbrunner, Herbert, Alexey Glazyrin, Oleg Musin, and Anton Nikitenko. “The Voronoi Functional Is Maximized by the Delaunay Triangulation in the Plane.” Combinatorica. Springer, 2017. https://doi.org/10.1007/s00493-016-3308-y.","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.","ama":"Edelsbrunner H, Glazyrin A, Musin O, Nikitenko A. The Voronoi functional is maximized by the Delaunay triangulation in the plane. Combinatorica. 2017;37(5):887-910. doi:10.1007/s00493-016-3308-y","apa":"Edelsbrunner, H., Glazyrin, A., Musin, O., & Nikitenko, A. (2017). The Voronoi functional is maximized by the Delaunay triangulation in the plane. Combinatorica. Springer. https://doi.org/10.1007/s00493-016-3308-y"},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1411.6337"}],"isi":1,"publist_id":"6182","day":"01","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.","issue":"5","doi":"10.1007/s00493-016-3308-y","page":"887 - 910"},{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1508.07594"}],"citation":{"apa":"Akopyan, A., Bárány, I., & Robins, S. (2017). Algebraic vertices of non-convex polyhedra. Advances in Mathematics. Academic Press. https://doi.org/10.1016/j.aim.2016.12.026","ama":"Akopyan A, Bárány I, Robins S. Algebraic vertices of non-convex polyhedra. Advances in Mathematics. 2017;308:627-644. doi:10.1016/j.aim.2016.12.026","chicago":"Akopyan, Arseniy, Imre Bárány, and Sinai Robins. “Algebraic Vertices of Non-Convex Polyhedra.” Advances in Mathematics. Academic Press, 2017. https://doi.org/10.1016/j.aim.2016.12.026.","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.” Advances in Mathematics, vol. 308, Academic Press, 2017, pp. 627–44, doi:10.1016/j.aim.2016.12.026.","ieee":"A. Akopyan, I. Bárány, and S. Robins, “Algebraic vertices of non-convex polyhedra,” Advances in Mathematics, vol. 308. Academic Press, pp. 627–644, 2017.","short":"A. Akopyan, I. Bárány, S. Robins, Advances in Mathematics 308 (2017) 627–644."},"isi":1,"publist_id":"6173","day":"21","doi":"10.1016/j.aim.2016.12.026","page":"627 - 644","publisher":"Academic Press","publication":"Advances in Mathematics","type":"journal_article","publication_status":"published","quality_controlled":"1","department":[{"_id":"HeEd"}],"intvolume":" 308","_id":"1180","year":"2017","date_published":"2017-02-21T00:00:00Z","title":"Algebraic vertices of non-convex polyhedra","month":"02","scopus_import":"1","ec_funded":1,"status":"public","language":[{"iso":"eng"}],"article_processing_charge":"No","external_id":{"arxiv":["1508.07594"],"isi":["000409292900015"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":308,"oa":1,"abstract":[{"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.","lang":"eng"}],"arxiv":1,"oa_version":"Submitted Version","project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"author":[{"first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"full_name":"Bárány, Imre","last_name":"Bárány","first_name":"Imre"},{"full_name":"Robins, Sinai","first_name":"Sinai","last_name":"Robins"}],"date_created":"2018-12-11T11:50:34Z","publication_identifier":{"issn":["0001-8708"]},"date_updated":"2025-06-04T08:45:48Z"},{"title":"Phat - Persistent homology algorithms toolbox","scopus_import":"1","month":"01","date_published":"2017-01-01T00:00:00Z","year":"2017","_id":"1433","intvolume":" 78","article_type":"original","article_processing_charge":"No","language":[{"iso":"eng"}],"ec_funded":1,"status":"public","oa_version":"Published Version","abstract":[{"lang":"eng","text":"Phat is an open-source C. ++ library for the computation of persistent homology by matrix reduction, targeted towards developers of software for topological data analysis. We aim for a simple generic design that decouples algorithms from data structures without sacrificing efficiency or user-friendliness. We provide numerous different reduction strategies as well as data types to store and manipulate the boundary matrix. We compare the different combinations through extensive experimental evaluation and identify optimization techniques that work well in practical situations. We also compare our software with various other publicly available libraries for persistent homology."}],"volume":78,"oa":1,"OA_type":"free access","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"isi":["000384396000005"]},"date_updated":"2025-10-01T07:39:51Z","publication_identifier":{"issn":[" 0747-7171"]},"author":[{"first_name":"Ulrich","last_name":"Bauer","full_name":"Bauer, Ulrich"},{"full_name":"Kerber, Michael","first_name":"Michael","last_name":"Kerber"},{"last_name":"Reininghaus","first_name":"Jan","full_name":"Reininghaus, Jan"},{"id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","first_name":"Hubert","last_name":"Wagner","full_name":"Wagner, Hubert"}],"date_created":"2018-12-11T11:51:59Z","project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"318493","name":"Topological Complex Systems"}],"acknowledgement":"Michael Kerber acknowledges support by the Max Planck Center for Visual Computing and Communications (FKZ-01IMC01 and FKZ-01IM10001). Ulrich Bauer, Jan Reininghaus, and Hubert Wagner acknowledge support by the EU Project TOPOSYS (FP7-ICT-318493-STREP).","doi":"10.1016/j.jsc.2016.03.008","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1016/j.jsc.2016.03.008"}],"citation":{"mla":"Bauer, Ulrich, et al. “Phat - Persistent Homology Algorithms Toolbox.” Journal of Symbolic Computation, vol. 78, Academic Press, 2017, pp. 76–90, doi:10.1016/j.jsc.2016.03.008.","chicago":"Bauer, Ulrich, Michael Kerber, Jan Reininghaus, and Hubert Wagner. “Phat - Persistent Homology Algorithms Toolbox.” Journal of Symbolic Computation. Academic Press, 2017. https://doi.org/10.1016/j.jsc.2016.03.008.","ista":"Bauer U, Kerber M, Reininghaus J, Wagner H. 2017. Phat - Persistent homology algorithms toolbox. Journal of Symbolic Computation. 78, 76–90.","apa":"Bauer, U., Kerber, M., Reininghaus, J., & Wagner, H. (2017). Phat - Persistent homology algorithms toolbox. Journal of Symbolic Computation. 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Academic Press, pp. 76–90, 2017."},"day":"01","publist_id":"5765","isi":1,"page":"76 - 90","publication":"Journal of Symbolic Computation","related_material":{"record":[{"relation":"earlier_version","status":"public","id":"10894"}]},"publisher":"Academic Press","corr_author":"1","department":[{"_id":"HeEd"}],"quality_controlled":"1","type":"journal_article","publication_status":"published"},{"status":"public","ec_funded":1,"article_processing_charge":"No","language":[{"iso":"eng"}],"pubrep_id":"991","_id":"1065","year":"2017","intvolume":" 122","scopus_import":"1","month":"06","title":"Pushdown reachability with constant treewidth","date_published":"2017-06-01T00:00:00Z","date_created":"2018-12-11T11:49:57Z","author":[{"full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X","last_name":"Chatterjee","first_name":"Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Osang, Georg F","orcid":"0000-0002-8882-5116","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","last_name":"Osang","first_name":"Georg F"}],"project":[{"call_identifier":"FWF","_id":"2584A770-B435-11E9-9278-68D0E5697425","grant_number":"P 23499-N23","name":"Modern Graph Algorithmic Techniques in Formal Verification"},{"grant_number":"S11407","name":"Game Theory","_id":"25863FF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"grant_number":"279307","name":"Quantitative Graph Games: Theory and Applications","call_identifier":"FP7","_id":"2581B60A-B435-11E9-9278-68D0E5697425"}],"date_updated":"2025-07-10T11:49:53Z","publication_identifier":{"issn":["0020-0190"]},"volume":122,"oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"isi":["000399506600005"]},"oa_version":"Submitted Version","abstract":[{"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.","lang":"eng"}],"page":"25 - 29","file_date_updated":"2019-10-15T07:44:51Z","publist_id":"6323","day":"01","isi":1,"citation":{"short":"K. Chatterjee, G.F. Osang, Information Processing Letters 122 (2017) 25–29.","ieee":"K. Chatterjee and G. F. Osang, “Pushdown reachability with constant treewidth,” Information Processing Letters, vol. 122. Elsevier, pp. 25–29, 2017.","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.” Information Processing Letters. Elsevier, 2017. https://doi.org/10.1016/j.ipl.2017.02.003.","ama":"Chatterjee K, Osang GF. Pushdown reachability with constant treewidth. Information Processing Letters. 2017;122:25-29. doi:10.1016/j.ipl.2017.02.003","apa":"Chatterjee, K., & Osang, G. F. (2017). Pushdown reachability with constant treewidth. Information Processing Letters. Elsevier. https://doi.org/10.1016/j.ipl.2017.02.003","mla":"Chatterjee, Krishnendu, and Georg F. Osang. “Pushdown Reachability with Constant Treewidth.” Information Processing Letters, vol. 122, Elsevier, 2017, pp. 25–29, doi:10.1016/j.ipl.2017.02.003."},"doi":"10.1016/j.ipl.2017.02.003","quality_controlled":"1","publication_status":"published","type":"journal_article","file":[{"content_type":"application/pdf","file_size":247657,"file_id":"4998","access_level":"open_access","creator":"system","file_name":"IST-2018-991-v1+2_2018_Chatterjee_Pushdown_PREPRINT.pdf","date_updated":"2019-10-15T07:44:51Z","date_created":"2018-12-12T10:13:17Z","relation":"main_file"}],"department":[{"_id":"KrCh"},{"_id":"HeEd"}],"has_accepted_license":"1","publisher":"Elsevier","publication":"Information Processing Letters","ddc":["000"]},{"year":"2017","_id":"1072","intvolume":" 369","title":"The Morse theory of Čech and delaunay complexes","scopus_import":"1","month":"05","date_published":"2017-05-01T00:00:00Z","ec_funded":1,"status":"public","article_type":"original","article_processing_charge":"No","language":[{"iso":"eng"}],"oa":1,"volume":369,"external_id":{"isi":["000398030400024"],"arxiv":["1312.1231"]},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa_version":"Preprint","arxiv":1,"abstract":[{"lang":"eng","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."}],"author":[{"orcid":"0000-0002-9683-0724","full_name":"Bauer, Ulrich","first_name":"Ulrich","last_name":"Bauer","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"}],"date_created":"2018-12-11T11:49:59Z","project":[{"call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425","name":"Topological Complex Systems","grant_number":"318493"}],"date_updated":"2025-04-15T08:37:54Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1312.1231"}],"citation":{"mla":"Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay Complexes.” Transactions of the American Mathematical Society, vol. 369, no. 5, American Mathematical Society, 2017, pp. 3741–62, doi:10.1090/tran/6991.","chicago":"Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay Complexes.” Transactions of the American Mathematical Society. American Mathematical Society, 2017. https://doi.org/10.1090/tran/6991.","ista":"Bauer U, Edelsbrunner H. 2017. The Morse theory of Čech and delaunay complexes. Transactions of the American Mathematical Society. 369(5), 3741–3762.","ama":"Bauer U, Edelsbrunner H. The Morse theory of Čech and delaunay complexes. Transactions of the American Mathematical Society. 2017;369(5):3741-3762. doi:10.1090/tran/6991","apa":"Bauer, U., & Edelsbrunner, H. (2017). The Morse theory of Čech and delaunay complexes. Transactions of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/tran/6991","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,” Transactions of the American Mathematical Society, vol. 369, no. 5. American Mathematical Society, pp. 3741–3762, 2017."},"day":"01","isi":1,"publist_id":"6311","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”.","doi":"10.1090/tran/6991","issue":"5","page":"3741 - 3762","publisher":"American Mathematical Society","publication":"Transactions of the American Mathematical Society","quality_controlled":"1","type":"journal_article","publication_status":"published","department":[{"_id":"HeEd"}]},{"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."}],"oa_version":"Submitted Version","arxiv":1,"external_id":{"isi":["000395170200039"],"arxiv":["1608.04519"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"volume":465,"publication_identifier":{"issn":["0035-8711"]},"date_updated":"2025-06-04T08:10:31Z","author":[{"full_name":"Pranav, Pratyush","last_name":"Pranav","first_name":"Pratyush"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Van De Weygaert, Rien","first_name":"Rien","last_name":"Van De Weygaert"},{"full_name":"Vegter, Gert","first_name":"Gert","last_name":"Vegter"},{"full_name":"Kerber, Michael","first_name":"Michael","last_name":"Kerber"},{"full_name":"Jones, Bernard","first_name":"Bernard","last_name":"Jones"},{"orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs","last_name":"Wintraecken"}],"date_created":"2018-12-11T11:49:44Z","date_published":"2017-01-01T00:00:00Z","title":"The topology of the cosmic web in terms of persistent Betti numbers","month":"01","scopus_import":"1","intvolume":" 465","year":"2017","_id":"1022","language":[{"iso":"eng"}],"article_processing_charge":"No","status":"public","publication":"Monthly Notices of the Royal Astronomical Society","publisher":"Oxford University Press","department":[{"_id":"HeEd"}],"type":"journal_article","publication_status":"published","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.","issue":"4","doi":"10.1093/mnras/stw2862","citation":{"mla":"Pranav, Pratyush, et al. “The Topology of the Cosmic Web in Terms of Persistent Betti Numbers.” Monthly Notices of the Royal Astronomical Society, vol. 465, no. 4, Oxford University Press, 2017, pp. 4281–310, doi:10.1093/mnras/stw2862.","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.” Monthly Notices of the Royal Astronomical Society. Oxford University Press, 2017. https://doi.org/10.1093/mnras/stw2862.","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.","ama":"Pranav P, Edelsbrunner H, Van De Weygaert R, et al. The topology of the cosmic web in terms of persistent Betti numbers. Monthly Notices of the Royal Astronomical Society. 2017;465(4):4281-4310. doi:10.1093/mnras/stw2862","apa":"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. Oxford University Press. https://doi.org/10.1093/mnras/stw2862","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.","ieee":"P. Pranav et al., “The topology of the cosmic web in terms of persistent Betti numbers,” Monthly Notices of the Royal Astronomical Society, vol. 465, no. 4. Oxford University Press, pp. 4281–4310, 2017."},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1608.04519"}],"isi":1,"day":"01","publist_id":"6373","page":"4281 - 4310"},{"publisher":"Springer","publication_status":"published","type":"conference","quality_controlled":"1","department":[{"_id":"HeEd"}],"alternative_title":["LNCS"],"corr_author":"1","day":"28","publist_id":"6815","isi":1,"main_file_link":[{"url":"https://arxiv.org/abs/1705.02045","open_access":"1"}],"citation":{"ieee":"T. Heiss and H. Wagner, “Streaming algorithm for Euler characteristic curves of multidimensional images,” presented at the CAIP: Computer Analysis of Images and Patterns, Ystad, Sweden, 2017, vol. 10424, pp. 397–409.","short":"T. Heiss, H. Wagner, in:, M. Felsberg, A. Heyden, N. Krüger (Eds.), Springer, 2017, pp. 397–409.","mla":"Heiss, Teresa, and Hubert Wagner. Streaming Algorithm for Euler Characteristic Curves of Multidimensional Images. Edited by Michael Felsberg et al., vol. 10424, Springer, 2017, pp. 397–409, doi:10.1007/978-3-319-64689-3_32.","ama":"Heiss T, Wagner H. Streaming algorithm for Euler characteristic curves of multidimensional images. In: Felsberg M, Heyden A, Krüger N, eds. Vol 10424. Springer; 2017:397-409. doi:10.1007/978-3-319-64689-3_32","apa":"Heiss, T., & Wagner, H. (2017). Streaming algorithm for Euler characteristic curves of multidimensional images. In M. Felsberg, A. Heyden, & N. Krüger (Eds.) (Vol. 10424, pp. 397–409). Presented at the CAIP: Computer Analysis of Images and Patterns, Ystad, Sweden: Springer. https://doi.org/10.1007/978-3-319-64689-3_32","ista":"Heiss T, Wagner H. 2017. Streaming algorithm for Euler characteristic curves of multidimensional images. CAIP: Computer Analysis of Images and Patterns, LNCS, vol. 10424, 397–409.","chicago":"Heiss, Teresa, and Hubert Wagner. “Streaming Algorithm for Euler Characteristic Curves of Multidimensional Images.” edited by Michael Felsberg, Anders Heyden, and Norbert Krüger, 10424:397–409. Springer, 2017. https://doi.org/10.1007/978-3-319-64689-3_32."},"doi":"10.1007/978-3-319-64689-3_32","page":"397 - 409","conference":{"start_date":"2017-08-22","location":"Ystad, Sweden","name":"CAIP: Computer Analysis of Images and Patterns","end_date":"2017-08-24"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["1705.02045"],"isi":["000432085900032"]},"oa":1,"volume":10424,"abstract":[{"text":"We present an efficient algorithm to compute Euler characteristic curves of gray scale images of arbitrary dimension. In various applications the Euler characteristic curve is used as a descriptor of an image. Our algorithm is the first streaming algorithm for Euler characteristic curves. The usage of streaming removes the necessity to store the entire image in RAM. Experiments show that our implementation handles terabyte scale images on commodity hardware. Due to lock-free parallelism, it scales well with the number of processor cores. Additionally, we put the concept of the Euler characteristic curve in the wider context of computational topology. In particular, we explain the connection with persistence diagrams.","lang":"eng"}],"oa_version":"Submitted Version","arxiv":1,"editor":[{"full_name":"Felsberg, Michael","first_name":"Michael","last_name":"Felsberg"},{"full_name":"Heyden, Anders","first_name":"Anders","last_name":"Heyden"},{"first_name":"Norbert","last_name":"Krüger","full_name":"Krüger, Norbert"}],"date_created":"2018-12-11T11:48:45Z","author":[{"first_name":"Teresa","last_name":"Heiss","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1780-2689","full_name":"Heiss, Teresa"},{"last_name":"Wagner","first_name":"Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","full_name":"Wagner, Hubert"}],"publication_identifier":{"issn":["0302-9743"]},"date_updated":"2025-06-04T09:54:22Z","intvolume":" 10424","year":"2017","_id":"833","date_published":"2017-07-28T00:00:00Z","month":"07","scopus_import":"1","title":"Streaming algorithm for Euler characteristic curves of multidimensional images","status":"public","language":[{"iso":"eng"}],"article_processing_charge":"No"},{"publication_identifier":{"isbn":["978-331956930-7"]},"date_updated":"2025-04-15T08:37:55Z","project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Topological Complex Systems","grant_number":"318493"}],"author":[{"first_name":"Marc","last_name":"Ethier","full_name":"Ethier, Marc"},{"full_name":"Jablonski, Grzegorz","orcid":"0000-0002-3536-9866","last_name":"Jablonski","first_name":"Grzegorz","id":"4483EF78-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Mrozek","first_name":"Marian","full_name":"Mrozek, Marian"}],"date_created":"2018-12-11T11:48:46Z","abstract":[{"text":"Recent research has examined how to study the topological features of a continuous self-map by means of the persistence of the eigenspaces, for given eigenvalues, of the endomorphism induced in homology over a field. This raised the question of how to select dynamically significant eigenvalues. The present paper aims to answer this question, giving an algorithm that computes the persistence of eigenspaces for every eigenvalue simultaneously, also expressing said eigenspaces as direct sums of “finite” and “singular” subspaces.","lang":"eng"}],"oa_version":"None","external_id":{"isi":["000434088200008"]},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","volume":198,"language":[{"iso":"eng"}],"article_processing_charge":"No","ec_funded":1,"status":"public","date_published":"2017-07-27T00:00:00Z","title":"Finding eigenvalues of self-maps with the Kronecker canonical form","scopus_import":"1","month":"07","intvolume":" 198","year":"2017","_id":"836","department":[{"_id":"HeEd"}],"alternative_title":["PROMS"],"type":"conference","publication_status":"published","quality_controlled":"1","publication":"Special Sessions in Applications of Computer Algebra","publisher":"Springer","conference":{"start_date":"2015-07-20","location":"Kalamata, Greece","end_date":"2015-07-23","name":"ACA: Applications of Computer Algebra"},"page":"119 - 136","doi":"10.1007/978-3-319-56932-1_8","citation":{"chicago":"Ethier, Marc, Grzegorz Jablonski, and Marian Mrozek. “Finding Eigenvalues of Self-Maps with the Kronecker Canonical Form.” In Special Sessions in Applications of Computer Algebra, 198:119–36. Springer, 2017. https://doi.org/10.1007/978-3-319-56932-1_8.","ista":"Ethier M, Jablonski G, Mrozek M. 2017. Finding eigenvalues of self-maps with the Kronecker canonical form. Special Sessions in Applications of Computer Algebra. ACA: Applications of Computer Algebra, PROMS, vol. 198, 119–136.","ama":"Ethier M, Jablonski G, Mrozek M. Finding eigenvalues of self-maps with the Kronecker canonical form. In: Special Sessions in Applications of Computer Algebra. Vol 198. Springer; 2017:119-136. doi:10.1007/978-3-319-56932-1_8","apa":"Ethier, M., Jablonski, G., & Mrozek, M. (2017). Finding eigenvalues of self-maps with the Kronecker canonical form. In Special Sessions in Applications of Computer Algebra (Vol. 198, pp. 119–136). Kalamata, Greece: Springer. https://doi.org/10.1007/978-3-319-56932-1_8","mla":"Ethier, Marc, et al. “Finding Eigenvalues of Self-Maps with the Kronecker Canonical Form.” Special Sessions in Applications of Computer Algebra, vol. 198, Springer, 2017, pp. 119–36, doi:10.1007/978-3-319-56932-1_8.","short":"M. Ethier, G. Jablonski, M. Mrozek, in:, Special Sessions in Applications of Computer Algebra, Springer, 2017, pp. 119–136.","ieee":"M. Ethier, G. Jablonski, and M. Mrozek, “Finding eigenvalues of self-maps with the Kronecker canonical form,” in Special Sessions in Applications of Computer Algebra, Kalamata, Greece, 2017, vol. 198, pp. 119–136."},"isi":1,"publist_id":"6812","day":"27"},{"publication_status":"published","editor":[{"full_name":"Toth, Csaba","last_name":"Toth","first_name":"Csaba"},{"full_name":"O'Rourke, Joseph","first_name":"Joseph","last_name":"O'Rourke"},{"full_name":"Goodman, Jacob","last_name":"Goodman","first_name":"Jacob"}],"type":"book_chapter","date_created":"2018-12-11T11:44:32Z","quality_controlled":"1","author":[{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"last_name":"Koehl","first_name":"Patrice","full_name":"Koehl, Patrice"}],"series_title":"Handbook of Discrete and Computational Geometry","publication_identifier":{"eisbn":["9781498711425"]},"department":[{"_id":"HeEd"}],"date_updated":"2023-10-16T11:15:22Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Taylor & Francis","publication":"Handbook of Discrete and Computational Geometry, Third Edition","abstract":[{"text":"The advent of high-throughput technologies and the concurrent advances in information sciences have led to a data revolution in biology. This revolution is most significant in molecular biology, with an increase in the number and scale of the “omics” projects over the last decade. Genomics projects, for example, have produced impressive advances in our knowledge of the information concealed into genomes, from the many genes that encode for the proteins that are responsible for most if not all cellular functions, to the noncoding regions that are now known to provide regulatory functions. Proteomics initiatives help to decipher the role of post-translation modifications on the protein structures and provide maps of protein-protein interactions, while functional genomics is the field that attempts to make use of the data produced by these projects to understand protein functions. The biggest challenge today is to assimilate the wealth of information provided by these initiatives into a conceptual framework that will help us decipher life. For example, the current views of the relationship between protein structure and function remain fragmented. We know of their sequences, more and more about their structures, we have information on their biological activities, but we have difficulties connecting this dotted line into an informed whole. We lack the experimental and computational tools for directly studying protein structure, function, and dynamics at the molecular and supra-molecular levels. In this chapter, we review some of the current developments in building the computational tools that are needed, focusing on the role that geometry and topology play in these efforts. One of our goals is to raise the general awareness about the importance of geometric methods in elucidating the mysterious foundations of our very existence. Another goal is the broadening of what we consider a geometric algorithm. There is plenty of valuable no-man’s-land between combinatorial and numerical algorithms, and it seems opportune to explore this land with a computational-geometric frame of mind.","lang":"eng"}],"oa_version":"None","page":"1709 - 1735","status":"public","language":[{"iso":"eng"}],"article_processing_charge":"No","publist_id":"7970","day":"09","year":"2017","_id":"84","citation":{"ieee":"H. Edelsbrunner and P. Koehl, “Computational topology for structural molecular biology,” in Handbook of Discrete and Computational Geometry, Third Edition, C. Toth, J. O’Rourke, and J. Goodman, Eds. Taylor & Francis, 2017, pp. 1709–1735.","short":"H. Edelsbrunner, P. Koehl, in:, C. Toth, J. O’Rourke, J. Goodman (Eds.), Handbook of Discrete and Computational Geometry, Third Edition, Taylor & Francis, 2017, pp. 1709–1735.","mla":"Edelsbrunner, Herbert, and Patrice Koehl. “Computational Topology for Structural Molecular Biology.” Handbook of Discrete and Computational Geometry, Third Edition, edited by Csaba Toth et al., Taylor & Francis, 2017, pp. 1709–35, doi:10.1201/9781315119601.","apa":"Edelsbrunner, H., & Koehl, P. (2017). Computational topology for structural molecular biology. In C. Toth, J. O’Rourke, & J. Goodman (Eds.), Handbook of Discrete and Computational Geometry, Third Edition (pp. 1709–1735). Taylor & Francis. https://doi.org/10.1201/9781315119601","ama":"Edelsbrunner H, Koehl P. Computational topology for structural molecular biology. In: Toth C, O’Rourke J, Goodman J, eds. Handbook of Discrete and Computational Geometry, Third Edition. Handbook of Discrete and Computational Geometry. Taylor & Francis; 2017:1709-1735. doi:10.1201/9781315119601","chicago":"Edelsbrunner, Herbert, and Patrice Koehl. “Computational Topology for Structural Molecular Biology.” In Handbook of Discrete and Computational Geometry, Third Edition, edited by Csaba Toth, Joseph O’Rourke, and Jacob Goodman, 1709–35. Handbook of Discrete and Computational Geometry. Taylor & Francis, 2017. https://doi.org/10.1201/9781315119601.","ista":"Edelsbrunner H, Koehl P. 2017.Computational topology for structural molecular biology. In: Handbook of Discrete and Computational Geometry, Third Edition. , 1709–1735."},"date_published":"2017-11-09T00:00:00Z","month":"11","doi":"10.1201/9781315119601","scopus_import":"1","title":"Computational topology for structural molecular biology"},{"page":"588 - 596","citation":{"mla":"Akopyan, Arseniy, and Vladislav Vysotsky. “On the Lengths of Curves Passing through Boundary Points of a Planar Convex Shape.” The American Mathematical Monthly, vol. 124, no. 7, Mathematical Association of America, 2017, pp. 588–96, doi:10.4169/amer.math.monthly.124.7.588.","ista":"Akopyan A, Vysotsky V. 2017. On the lengths of curves passing through boundary points of a planar convex shape. The American Mathematical Monthly. 124(7), 588–596.","chicago":"Akopyan, Arseniy, and Vladislav Vysotsky. “On the Lengths of Curves Passing through Boundary Points of a Planar Convex Shape.” The American Mathematical Monthly. Mathematical Association of America, 2017. https://doi.org/10.4169/amer.math.monthly.124.7.588.","ama":"Akopyan A, Vysotsky V. On the lengths of curves passing through boundary points of a planar convex shape. The American Mathematical Monthly. 2017;124(7):588-596. doi:10.4169/amer.math.monthly.124.7.588","apa":"Akopyan, A., & Vysotsky, V. (2017). On the lengths of curves passing through boundary points of a planar convex shape. The American Mathematical Monthly. Mathematical Association of America. https://doi.org/10.4169/amer.math.monthly.124.7.588","short":"A. Akopyan, V. Vysotsky, The American Mathematical Monthly 124 (2017) 588–596.","ieee":"A. Akopyan and V. Vysotsky, “On the lengths of curves passing through boundary points of a planar convex shape,” The American Mathematical Monthly, vol. 124, no. 7. Mathematical Association of America, pp. 588–596, 2017."},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1605.07997"}],"isi":1,"day":"01","publist_id":"6534","issue":"7","doi":"10.4169/amer.math.monthly.124.7.588","type":"journal_article","publication_status":"published","quality_controlled":"1","department":[{"_id":"HeEd"}],"publisher":"Mathematical Association of America","publication":"The American Mathematical Monthly","ec_funded":1,"status":"public","language":[{"iso":"eng"}],"article_type":"original","article_processing_charge":"No","intvolume":" 124","year":"2017","_id":"909","date_published":"2017-01-01T00:00:00Z","title":"On the lengths of curves passing through boundary points of a planar convex shape","scopus_import":"1","month":"01","project":[{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"author":[{"orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","last_name":"Akopyan"},{"first_name":"Vladislav","last_name":"Vysotsky","full_name":"Vysotsky, Vladislav"}],"date_created":"2018-12-11T11:49:09Z","publication_identifier":{"issn":["0002-9890"]},"date_updated":"2025-07-10T12:01:35Z","external_id":{"arxiv":["1605.07997"],"isi":["000413947300002"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":124,"oa":1,"abstract":[{"text":"We study the lengths of curves passing through a fixed number of points on the boundary of a convex shape in the plane. We show that, for any convex shape K, there exist four points on the boundary of K such that the length of any curve passing through these points is at least half of the perimeter of K. It is also shown that the same statement does not remain valid with the additional constraint that the points are extreme points of K. Moreover, the factor &#xbd; cannot be achieved with any fixed number of extreme points. We conclude the paper with a few other inequalities related to the perimeter of a convex shape.","lang":"eng"}],"oa_version":"Submitted Version","arxiv":1},{"date_updated":"2025-09-29T13:22:54Z","date_created":"2018-12-11T11:46:43Z","author":[{"full_name":"Biedl, Therese","first_name":"Therese","last_name":"Biedl"},{"orcid":"0000-0002-8871-5814","full_name":"Huber, Stefan","id":"4700A070-F248-11E8-B48F-1D18A9856A87","first_name":"Stefan","last_name":"Huber"},{"first_name":"Peter","last_name":"Palfrader","full_name":"Palfrader, Peter"}],"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."}],"oa_version":"Published Version","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","volume":26,"oa":1,"language":[{"iso":"eng"}],"status":"public","date_published":"2017-04-13T00:00:00Z","month":"04","scopus_import":1,"title":"Planar matchings for weighted straight skeletons","intvolume":" 26","_id":"481","year":"2017","pubrep_id":"949","department":[{"_id":"HeEd"}],"file":[{"creator":"system","checksum":"f79e8558bfe4b368dfefeb8eec2e3a5e","access_level":"open_access","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","relation":"main_file","file_size":769296,"content_type":"application/pdf","file_id":"4758"}],"corr_author":"1","publication_status":"published","type":"journal_article","quality_controlled":"1","publication":"International Journal of Computational Geometry and Applications","ddc":["004","514","516"],"publisher":"World Scientific Publishing","related_material":{"record":[{"relation":"earlier_version","id":"10892","status":"public"}]},"has_accepted_license":"1","file_date_updated":"2020-07-14T12:46:35Z","page":"211 - 229","license":"https://creativecommons.org/licenses/by/4.0/","doi":"10.1142/S0218195916600050","issue":"3-4","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"acknowledgement":"Supported by NSERC and the Ross and Muriel Cheriton Fellowship. Research supported by Austrian Science Fund (FWF): P25816-N15.","publist_id":"7338","day":"13","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.","chicago":"Biedl, Therese, Stefan Huber, and Peter Palfrader. “Planar Matchings for Weighted Straight Skeletons.” International Journal of Computational Geometry and Applications. World Scientific Publishing, 2017. https://doi.org/10.1142/S0218195916600050.","ama":"Biedl T, Huber S, Palfrader P. Planar matchings for weighted straight skeletons. International Journal of Computational Geometry and Applications. 2017;26(3-4):211-229. doi:10.1142/S0218195916600050","apa":"Biedl, T., Huber, S., & Palfrader, P. (2017). Planar matchings for weighted straight skeletons. International Journal of Computational Geometry and Applications. World Scientific Publishing. https://doi.org/10.1142/S0218195916600050","mla":"Biedl, Therese, et al. “Planar Matchings for Weighted Straight Skeletons.” International Journal of Computational Geometry and Applications, vol. 26, no. 3–4, World Scientific Publishing, 2017, pp. 211–29, doi:10.1142/S0218195916600050.","short":"T. Biedl, S. Huber, P. Palfrader, International Journal of Computational Geometry and Applications 26 (2017) 211–229.","ieee":"T. Biedl, S. Huber, and P. Palfrader, “Planar matchings for weighted straight skeletons,” International Journal of Computational Geometry and Applications, vol. 26, no. 3–4. World Scientific Publishing, pp. 211–229, 2017."}},{"publication":"Topology and its Applications","publisher":"Elsevier","corr_author":"1","department":[{"_id":"HeEd"}],"quality_controlled":"1","type":"journal_article","publication_status":"published","doi":"10.1016/j.topol.2016.10.005","main_file_link":[{"url":"https://arxiv.org/abs/1608.03954","open_access":"1"}],"citation":{"mla":"Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.” Topology and Its Applications, vol. 215, Elsevier, 2017, pp. 45–57, doi:10.1016/j.topol.2016.10.005.","apa":"Austin, K., & Virk, Z. (2017). Higson compactification and dimension raising. Topology and Its Applications. Elsevier. https://doi.org/10.1016/j.topol.2016.10.005","ama":"Austin K, Virk Z. Higson compactification and dimension raising. Topology and its Applications. 2017;215:45-57. doi:10.1016/j.topol.2016.10.005","ista":"Austin K, Virk Z. 2017. Higson compactification and dimension raising. Topology and its Applications. 215, 45–57.","chicago":"Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.” Topology and Its Applications. Elsevier, 2017. https://doi.org/10.1016/j.topol.2016.10.005.","ieee":"K. Austin and Z. Virk, “Higson compactification and dimension raising,” Topology and its Applications, vol. 215. Elsevier, pp. 45–57, 2017.","short":"K. Austin, Z. Virk, Topology and Its Applications 215 (2017) 45–57."},"isi":1,"publist_id":"7299","day":"01","page":"45 - 57","oa_version":"Submitted Version","arxiv":1,"abstract":[{"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.","lang":"eng"}],"oa":1,"volume":215,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","external_id":{"arxiv":["1608.03954"],"isi":["000390501400005"]},"date_updated":"2025-09-18T09:47:04Z","publication_identifier":{"issn":["0166-8641"]},"author":[{"full_name":"Austin, Kyle","first_name":"Kyle","last_name":"Austin"},{"last_name":"Virk","first_name":"Ziga","id":"2E36B656-F248-11E8-B48F-1D18A9856A87","full_name":"Virk, Ziga"}],"date_created":"2018-12-11T11:46:56Z","title":"Higson compactification and dimension raising","scopus_import":"1","month":"01","date_published":"2017-01-01T00:00:00Z","year":"2017","_id":"521","intvolume":" 215","article_processing_charge":"No","language":[{"iso":"eng"}],"status":"public"},{"issue":"2","doi":"10.4310/HHA.2017.v19.n2.a16","day":"01","publist_id":"7246","isi":1,"citation":{"short":"P. Franek, M. Krcál, Homology, Homotopy and Applications 19 (2017) 313–342.","ieee":"P. Franek and M. Krcál, “Persistence of zero sets,” Homology, Homotopy and Applications, vol. 19, no. 2. International Press, pp. 313–342, 2017.","mla":"Franek, Peter, and Marek Krcál. “Persistence of Zero Sets.” Homology, Homotopy and Applications, vol. 19, no. 2, International Press, 2017, pp. 313–42, doi:10.4310/HHA.2017.v19.n2.a16.","chicago":"Franek, Peter, and Marek Krcál. “Persistence of Zero Sets.” Homology, Homotopy and Applications. International Press, 2017. https://doi.org/10.4310/HHA.2017.v19.n2.a16.","ista":"Franek P, Krcál M. 2017. Persistence of zero sets. Homology, Homotopy and Applications. 19(2), 313–342.","ama":"Franek P, Krcál M. Persistence of zero sets. Homology, Homotopy and Applications. 2017;19(2):313-342. doi:10.4310/HHA.2017.v19.n2.a16","apa":"Franek, P., & Krcál, M. (2017). Persistence of zero sets. Homology, Homotopy and Applications. International Press. https://doi.org/10.4310/HHA.2017.v19.n2.a16"},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1507.04310"}],"page":"313 - 342","publication":"Homology, Homotopy and Applications","publisher":"International Press","corr_author":"1","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"quality_controlled":"1","publication_status":"published","type":"journal_article","scopus_import":"1","month":"01","title":"Persistence of zero sets","date_published":"2017-01-01T00:00:00Z","_id":"568","year":"2017","intvolume":" 19","article_processing_charge":"No","language":[{"iso":"eng"}],"status":"public","ec_funded":1,"arxiv":1,"oa_version":"Submitted Version","abstract":[{"lang":"eng","text":"We study robust properties of zero sets of continuous maps f: X → ℝn. Formally, we analyze the family Z< r(f) := (g-1(0): ||g - f|| < r) of all zero sets of all continuous maps g closer to f than r in the max-norm. All of these sets are outside A := (x: |f(x)| ≥ r) and we claim that Z< r(f) is fully determined by A and an element of a certain cohomotopy group which (by a recent result) is computable whenever the dimension of X is at most 2n - 3. By considering all r > 0 simultaneously, the pointed cohomotopy groups form a persistence module-a structure leading to persistence diagrams as in the case of persistent homology or well groups. Eventually, we get a descriptor of persistent robust properties of zero sets that has better descriptive power (Theorem A) and better computability status (Theorem B) than the established well diagrams. Moreover, if we endow every point of each zero set with gradients of the perturbation, the robust description of the zero sets by elements of cohomotopy groups is in some sense the best possible (Theorem C)."}],"oa":1,"volume":19,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","external_id":{"arxiv":["1507.04310"],"isi":["000440749400010"]},"date_updated":"2025-09-11T07:41:51Z","publication_identifier":{"issn":["1532-0073"]},"date_created":"2018-12-11T11:47:14Z","author":[{"id":"473294AE-F248-11E8-B48F-1D18A9856A87","first_name":"Peter","last_name":"Franek","orcid":"0000-0001-8878-8397","full_name":"Franek, Peter"},{"full_name":"Krcál, Marek","last_name":"Krcál","first_name":"Marek","id":"33E21118-F248-11E8-B48F-1D18A9856A87"}],"project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"},{"call_identifier":"H2020","_id":"2590DB08-B435-11E9-9278-68D0E5697425","grant_number":"701309","name":"Atomic Resolution Structures of Mitochondrial Respiratory Chain Supercomplexes"}]},{"article_processing_charge":"No","language":[{"iso":"eng"}],"status":"public","title":"Construction of persistent Voronoi diagram on 3D digital plane","month":"05","extern":"1","date_published":"2017-05-17T00:00:00Z","place":"Cham","_id":"5803","year":"2017","intvolume":" 10256","date_updated":"2022-01-28T07:48:24Z","publication_identifier":{"isbn":["978-3-319-59107-0","978-3-319-59108-7"],"issn":["0302-9743","1611-3349"]},"author":[{"full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","last_name":"Biswas","first_name":"Ranita"},{"full_name":"Bhowmick, Partha","last_name":"Bhowmick","first_name":"Partha"}],"date_created":"2019-01-08T20:42:56Z","oa_version":"None","abstract":[{"text":"Different distance metrics produce Voronoi diagrams with different properties. It is a well-known that on the (real) 2D plane or even on any 3D plane, a Voronoi diagram (VD) based on the Euclidean distance metric produces convex Voronoi regions. In this paper, we first show that this metric produces a persistent VD on the 2D digital plane, as it comprises digitally convex Voronoi regions and hence correctly approximates the corresponding VD on the 2D real plane. Next, we show that on a 3D digital plane D, the Euclidean metric spanning over its voxel set does not guarantee a digital VD which is persistent with the real-space VD. As a solution, we introduce a novel concept of functional-plane-convexity, which is ensured by the Euclidean metric spanning over the pedal set of D. Necessary proofs and some visual result have been provided to adjudge the merit and usefulness of the proposed concept.","lang":"eng"}],"volume":10256,"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","page":"93-104","conference":{"start_date":"2017-06-19","end_date":"2017-06-21","name":"IWCIA: International Workshop on Combinatorial Image Analysis","location":"Plovdiv, Bulgaria"},"doi":"10.1007/978-3-319-59108-7_8","citation":{"short":"R. Biswas, P. Bhowmick, in:, Combinatorial Image Analysis, Springer Nature, Cham, 2017, pp. 93–104.","ieee":"R. Biswas and P. Bhowmick, “Construction of persistent Voronoi diagram on 3D digital plane,” in Combinatorial image analysis, vol. 10256, Cham: Springer Nature, 2017, pp. 93–104.","mla":"Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi Diagram on 3D Digital Plane.” Combinatorial Image Analysis, vol. 10256, Springer Nature, 2017, pp. 93–104, doi:10.1007/978-3-319-59108-7_8.","ista":"Biswas R, Bhowmick P. 2017.Construction of persistent Voronoi diagram on 3D digital plane. In: Combinatorial image analysis. LNCS, vol. 10256, 93–104.","chicago":"Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi Diagram on 3D Digital Plane.” In Combinatorial Image Analysis, 10256:93–104. Cham: Springer Nature, 2017. https://doi.org/10.1007/978-3-319-59108-7_8.","apa":"Biswas, R., & Bhowmick, P. (2017). Construction of persistent Voronoi diagram on 3D digital plane. In Combinatorial image analysis (Vol. 10256, pp. 93–104). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-59108-7_8","ama":"Biswas R, Bhowmick P. Construction of persistent Voronoi diagram on 3D digital plane. In: Combinatorial Image Analysis. Vol 10256. Cham: Springer Nature; 2017:93-104. doi:10.1007/978-3-319-59108-7_8"},"day":"17","alternative_title":["LNCS"],"department":[{"_id":"HeEd"}],"quality_controlled":"1","type":"book_chapter","publication_status":"published","publication":"Combinatorial image analysis","publisher":"Springer Nature"},{"date_updated":"2025-07-10T11:53:56Z","publication_identifier":{"issn":["1868-8969"]},"date_created":"2018-12-11T11:47:56Z","author":[{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Wagner, Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","first_name":"Hubert","last_name":"Wagner"}],"oa_version":"Published Version","abstract":[{"lang":"eng","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. "}],"volume":77,"oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","language":[{"iso":"eng"}],"status":"public","month":"06","scopus_import":"1","title":"Topological data analysis with Bregman divergences","date_published":"2017-06-01T00:00:00Z","_id":"688","year":"2017","pubrep_id":"895","intvolume":" 77","corr_author":"1","alternative_title":["LIPIcs"],"file":[{"date_created":"2018-12-12T10:11:03Z","relation":"main_file","access_level":"open_access","checksum":"067ab0cb3f962bae6c3af6bf0094e0f3","creator":"system","file_name":"IST-2017-895-v1+1_LIPIcs-SoCG-2017-39.pdf","date_updated":"2020-07-14T12:47:42Z","file_id":"4856","content_type":"application/pdf","file_size":990546}],"department":[{"_id":"HeEd"},{"_id":"UlWa"}],"quality_controlled":"1","publication_status":"published","type":"conference","ddc":["514","516"],"has_accepted_license":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","file_date_updated":"2020-07-14T12:47:42Z","conference":{"location":"Brisbane, Australia","name":"Symposium on Computational Geometry, SoCG","end_date":"2017-07-07","start_date":"2017-07-04"},"page":"391-3916","doi":"10.4230/LIPIcs.SoCG.2017.39","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publist_id":"7021","day":"01","citation":{"mla":"Edelsbrunner, Herbert, and Hubert Wagner. 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Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. https://doi.org/10.4230/LIPIcs.SoCG.2017.39.","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."}},{"language":[{"iso":"eng"}],"article_processing_charge":"No","status":"public","ec_funded":1,"date_published":"2017-08-01T00:00:00Z","scopus_import":"1","month":"08","title":"A tight estimate for the waist of the ball ","intvolume":" 49","year":"2017","_id":"707","publication_identifier":{"issn":["0024-6093"]},"date_updated":"2025-09-10T11:04:43Z","project":[{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"date_created":"2018-12-11T11:48:02Z","author":[{"full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","first_name":"Arseniy"},{"first_name":"Roman","last_name":"Karasev","full_name":"Karasev, Roman"}],"abstract":[{"lang":"eng","text":"We answer a question of M. Gromov on the waist of the unit ball."}],"arxiv":1,"oa_version":"Preprint","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","external_id":{"isi":["000407045900012"],"arxiv":["1608.06279"]},"oa":1,"volume":49,"page":"690 - 693","doi":"10.1112/blms.12062","issue":"4","publist_id":"6982","isi":1,"day":"01","citation":{"ieee":"A. Akopyan and R. Karasev, “A tight estimate for the waist of the ball ,” Bulletin of the London Mathematical Society, vol. 49, no. 4. Wiley, pp. 690–693, 2017.","short":"A. Akopyan, R. Karasev, Bulletin of the London Mathematical Society 49 (2017) 690–693.","apa":"Akopyan, A., & Karasev, R. (2017). A tight estimate for the waist of the ball . Bulletin of the London Mathematical Society. Wiley. https://doi.org/10.1112/blms.12062","ama":"Akopyan A, Karasev R. A tight estimate for the waist of the ball . Bulletin of the London Mathematical Society. 2017;49(4):690-693. doi:10.1112/blms.12062","ista":"Akopyan A, Karasev R. 2017. A tight estimate for the waist of the ball . Bulletin of the London Mathematical Society. 49(4), 690–693.","chicago":"Akopyan, Arseniy, and Roman Karasev. “A Tight Estimate for the Waist of the Ball .” Bulletin of the London Mathematical Society. Wiley, 2017. https://doi.org/10.1112/blms.12062.","mla":"Akopyan, Arseniy, and Roman Karasev. “A Tight Estimate for the Waist of the Ball .” Bulletin of the London Mathematical Society, vol. 49, no. 4, Wiley, 2017, pp. 690–93, doi:10.1112/blms.12062."},"main_file_link":[{"url":"https://arxiv.org/abs/1608.06279","open_access":"1"}],"department":[{"_id":"HeEd"}],"corr_author":"1","publication_status":"published","type":"journal_article","quality_controlled":"1","publication":"Bulletin of the London Mathematical Society","publisher":"Wiley"},{"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","oa":1,"abstract":[{"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.","lang":"eng"}],"oa_version":"Published Version","author":[{"first_name":"Anton","last_name":"Nikitenko","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0659-3201","full_name":"Nikitenko, Anton"}],"date_created":"2019-04-09T15:04:32Z","publication_identifier":{"issn":["2663-337X"]},"date_updated":"2026-04-08T14:19:31Z","degree_awarded":"PhD","_id":"6287","year":"2017","pubrep_id":"873","date_published":"2017-10-27T00:00:00Z","title":"Discrete Morse theory for random complexes ","month":"10","status":"public","language":[{"iso":"eng"}],"article_processing_charge":"No","publisher":"Institute of Science and Technology Austria","has_accepted_license":"1","related_material":{"record":[{"id":"87","status":"public","relation":"part_of_dissertation"},{"status":"public","id":"5678","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"718","status":"public"}]},"OA_place":"publisher","ddc":["514","516","519"],"type":"dissertation","publication_status":"published","department":[{"_id":"HeEd"}],"file":[{"date_created":"2019-04-09T14:54:51Z","relation":"main_file","creator":"dernst","access_level":"open_access","checksum":"ece7e598a2f060b263c2febf7f3fe7f9","date_updated":"2020-07-14T12:47:26Z","file_name":"2017_Thesis_Nikitenko.pdf","file_id":"6289","file_size":2324870,"content_type":"application/pdf"},{"date_updated":"2020-07-14T12:47:26Z","file_name":"2017_Thesis_Nikitenko_source.zip","creator":"dernst","access_level":"closed","checksum":"99b7ad76e317efd447af60f91e29b49b","relation":"source_file","date_created":"2019-04-09T14:54:51Z","file_size":2863219,"content_type":"application/zip","file_id":"6290"}],"alternative_title":["ISTA Thesis"],"corr_author":"1","citation":{"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.","mla":"Nikitenko, Anton. Discrete Morse Theory for Random Complexes . Institute of Science and Technology Austria, 2017, doi:10.15479/AT:ISTA:th_873.","apa":"Nikitenko, A. (2017). Discrete Morse theory for random complexes . Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:th_873","ama":"Nikitenko A. Discrete Morse theory for random complexes . 2017. doi:10.15479/AT:ISTA:th_873","chicago":"Nikitenko, Anton. “Discrete Morse Theory for Random Complexes .” Institute of Science and Technology Austria, 2017. https://doi.org/10.15479/AT:ISTA:th_873.","ista":"Nikitenko A. 2017. Discrete Morse theory for random complexes . Institute of Science and Technology Austria."},"day":"27","supervisor":[{"last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"}],"tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"doi":"10.15479/AT:ISTA:th_873","page":"86","file_date_updated":"2020-07-14T12:47:26Z"},{"abstract":[{"text":"Mapping every simplex in the Delaunay mosaic of a discrete point set to the radius of the smallest empty circumsphere gives a generalized discrete Morse function. Choosing the points from a Poisson point process in ℝ n , we study the expected number of simplices in the Delaunay mosaic as well as the expected number of critical simplices and nonsingular intervals in the corresponding generalized discrete gradient. Observing connections with other probabilistic models, we obtain precise expressions for the expected numbers in low dimensions. In particular, we obtain the expected numbers of simplices in the Poisson–Delaunay mosaic in dimensions n ≤ 4.","lang":"eng"}],"oa_version":"Preprint","arxiv":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","external_id":{"arxiv":["1607.05915"],"isi":["000416417500004"]},"volume":49,"oa":1,"publication_identifier":{"issn":["0001-8678"]},"date_updated":"2026-04-08T14:19:30Z","project":[{"grant_number":"318493","name":"Topological Complex Systems","call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"first_name":"Anton","last_name":"Nikitenko","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0659-3201","full_name":"Nikitenko, Anton"},{"full_name":"Reitzner, Matthias","last_name":"Reitzner","first_name":"Matthias"}],"date_created":"2018-12-11T11:48:07Z","date_published":"2017-09-01T00:00:00Z","title":"Expected sizes of poisson Delaunay mosaics and their discrete Morse functions","month":"09","scopus_import":"1","intvolume":" 49","year":"2017","_id":"718","language":[{"iso":"eng"}],"article_processing_charge":"No","ec_funded":1,"status":"public","publication":"Advances in Applied Probability","publisher":"Cambridge University Press","related_material":{"record":[{"id":"6287","status":"public","relation":"dissertation_contains"}]},"department":[{"_id":"HeEd"}],"type":"journal_article","publication_status":"published","quality_controlled":"1","doi":"10.1017/apr.2017.20","issue":"3","citation":{"ama":"Edelsbrunner H, Nikitenko A, Reitzner M. Expected sizes of poisson Delaunay mosaics and their discrete Morse functions. Advances in Applied Probability. 2017;49(3):745-767. doi:10.1017/apr.2017.20","apa":"Edelsbrunner, H., Nikitenko, A., & Reitzner, M. (2017). Expected sizes of poisson Delaunay mosaics and their discrete Morse functions. Advances in Applied Probability. Cambridge University Press. https://doi.org/10.1017/apr.2017.20","ista":"Edelsbrunner H, Nikitenko A, Reitzner M. 2017. Expected sizes of poisson Delaunay mosaics and their discrete Morse functions. Advances in Applied Probability. 49(3), 745–767.","chicago":"Edelsbrunner, Herbert, Anton Nikitenko, and Matthias Reitzner. “Expected Sizes of Poisson Delaunay Mosaics and Their Discrete Morse Functions.” Advances in Applied Probability. Cambridge University Press, 2017. https://doi.org/10.1017/apr.2017.20.","mla":"Edelsbrunner, Herbert, et al. “Expected Sizes of Poisson Delaunay Mosaics and Their Discrete Morse Functions.” Advances in Applied Probability, vol. 49, no. 3, Cambridge University Press, 2017, pp. 745–67, doi:10.1017/apr.2017.20.","ieee":"H. Edelsbrunner, A. Nikitenko, and M. Reitzner, “Expected sizes of poisson Delaunay mosaics and their discrete Morse functions,” Advances in Applied Probability, vol. 49, no. 3. Cambridge University Press, pp. 745–767, 2017.","short":"H. Edelsbrunner, A. Nikitenko, M. Reitzner, Advances in Applied Probability 49 (2017) 745–767."},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1607.05915"}],"publist_id":"6962","day":"01","isi":1,"page":"745 - 767"},{"corr_author":"1","department":[{"_id":"HeEd"}],"quality_controlled":"1","type":"journal_article","publication_status":"published","publication":"Topology and its Applications","publisher":"Elsevier","page":"186 - 196","doi":"10.1016/j.topol.2017.09.015","citation":{"ieee":"Z. Virk and A. Zastrow, “A new topology on the universal path space,” Topology and its Applications, vol. 231. Elsevier, pp. 186–196, 2017.","short":"Z. Virk, A. Zastrow, Topology and Its Applications 231 (2017) 186–196.","ama":"Virk Z, Zastrow A. A new topology on the universal path space. Topology and its Applications. 2017;231:186-196. doi:10.1016/j.topol.2017.09.015","apa":"Virk, Z., & Zastrow, A. (2017). A new topology on the universal path space. Topology and Its Applications. Elsevier. https://doi.org/10.1016/j.topol.2017.09.015","ista":"Virk Z, Zastrow A. 2017. A new topology on the universal path space. Topology and its Applications. 231, 186–196.","chicago":"Virk, Ziga, and Andreas Zastrow. “A New Topology on the Universal Path Space.” Topology and Its Applications. Elsevier, 2017. https://doi.org/10.1016/j.topol.2017.09.015.","mla":"Virk, Ziga, and Andreas Zastrow. “A New Topology on the Universal Path Space.” Topology and Its Applications, vol. 231, Elsevier, 2017, pp. 186–96, doi:10.1016/j.topol.2017.09.015."},"publist_id":"6930","day":"01","isi":1,"date_updated":"2026-04-16T10:04:39Z","publication_identifier":{"issn":["0166-8641"]},"author":[{"full_name":"Virk, Ziga","id":"2E36B656-F248-11E8-B48F-1D18A9856A87","first_name":"Ziga","last_name":"Virk"},{"full_name":"Zastrow, Andreas","first_name":"Andreas","last_name":"Zastrow"}],"date_created":"2018-12-11T11:48:14Z","oa_version":"None","abstract":[{"text":"We generalize Brazas’ topology on the fundamental group to the whole universal path space X˜ i.e., to the set of homotopy classes of all based paths. We develop basic properties of the new notion and provide a complete comparison of the obtained topology with the established topologies, in particular with the Lasso topology and the CO topology, i.e., the topology that is induced by the compact-open topology. It turns out that the new topology is the finest topology contained in the CO topology, for which the action of the fundamental group on the universal path space is a continuous group action.","lang":"eng"}],"volume":231,"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","external_id":{"isi":["000413889100012"]},"article_processing_charge":"No","language":[{"iso":"eng"}],"status":"public","title":"A new topology on the universal path space","scopus_import":"1","month":"11","date_published":"2017-11-01T00:00:00Z","year":"2017","_id":"737","intvolume":" 231"},{"publication":"Applied Numerical Mathematics","publisher":"Elsevier","department":[{"_id":"HeEd"}],"publication_status":"published","type":"journal_article","quality_controlled":"1","doi":"10.1016/j.apnum.2016.04.005","acknowledgement":"MG was partially supported by FAPESP grants 2013/07460-7 and 2010/00875-9, and by CNPq grants 305860/2013-5 and 306453/2009-6, Brazil. The work of HK was partially supported by Grant-in-Aid for Scientific Research (Nos.24654022, 25287029), Ministry of Education, Science, Technology, Culture and Sports, Japan. KM was supported by NSF grants NSF-DMS-0835621, 0915019, 1125174, 1248071, and contracts from AFOSR and DARPA. TM was supported by Grant-in-Aid for JSPS Fellows No. 245312. A part of the research of TM and HK was also supported by JST, CREST.\r\n\r\nResearch 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); from the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/2007-2013) under REA grant agreement No. 622033; and from the same sources as HK.\r\n\r\nThe authors express their gratitude to the Department of Mathematics of Kyoto University for making their server available for conducting the computations described in the paper, and to the reviewers for helpful comments that contributed towards increasing the quality of the paper.","isi":1,"publist_id":"6209","day":"01","citation":{"ieee":"T. Miyaji, P. Pilarczyk, M. Gameiro, H. Kokubu, and K. Mischaikow, “A study of rigorous ODE integrators for multi scale set oriented computations,” Applied Numerical Mathematics, vol. 107. Elsevier, pp. 34–47, 2016.","short":"T. Miyaji, P. Pilarczyk, M. Gameiro, H. Kokubu, K. Mischaikow, Applied Numerical Mathematics 107 (2016) 34–47.","mla":"Miyaji, Tomoyuki, et al. “A Study of Rigorous ODE Integrators for Multi Scale Set Oriented Computations.” Applied Numerical Mathematics, vol. 107, Elsevier, 2016, pp. 34–47, doi:10.1016/j.apnum.2016.04.005.","ama":"Miyaji T, Pilarczyk P, Gameiro M, Kokubu H, Mischaikow K. A study of rigorous ODE integrators for multi scale set oriented computations. Applied Numerical Mathematics. 2016;107:34-47. doi:10.1016/j.apnum.2016.04.005","apa":"Miyaji, T., Pilarczyk, P., Gameiro, M., Kokubu, H., & Mischaikow, K. (2016). A study of rigorous ODE integrators for multi scale set oriented computations. Applied Numerical Mathematics. Elsevier. https://doi.org/10.1016/j.apnum.2016.04.005","chicago":"Miyaji, Tomoyuki, Pawel Pilarczyk, Marcio Gameiro, Hiroshi Kokubu, and Konstantin Mischaikow. “A Study of Rigorous ODE Integrators for Multi Scale Set Oriented Computations.” Applied Numerical Mathematics. Elsevier, 2016. https://doi.org/10.1016/j.apnum.2016.04.005.","ista":"Miyaji T, Pilarczyk P, Gameiro M, Kokubu H, Mischaikow K. 2016. A study of rigorous ODE integrators for multi scale set oriented computations. Applied Numerical Mathematics. 107, 34–47."},"page":"34 - 47","abstract":[{"lang":"eng","text":"We study the usefulness of two most prominent publicly available rigorous ODE integrators: one provided by the CAPD group (capd.ii.uj.edu.pl), the other based on the COSY Infinity project (cosyinfinity.org). Both integrators are capable of handling entire sets of initial conditions and provide tight rigorous outer enclosures of the images under a time-T map. We conduct extensive benchmark computations using the well-known Lorenz system, and compare the computation time against the final accuracy achieved. We also discuss the effect of a few technical parameters, such as the order of the numerical integration method, the value of T, and the phase space resolution. We conclude that COSY may provide more precise results due to its ability of avoiding the variable dependency problem. However, the overall cost of computations conducted using CAPD is typically lower, especially when intervals of parameters are involved. Moreover, access to COSY is limited (registration required) and the rigorous ODE integrators are not publicly available, while CAPD is an open source free software project. Therefore, we recommend the latter integrator for this kind of computations. Nevertheless, proper choice of the various integration parameters turns out to be of even greater importance than the choice of the integrator itself. © 2016 IMACS. Published by Elsevier B.V. All rights reserved."}],"oa_version":"None","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","external_id":{"isi":["000378447000003"]},"volume":107,"date_updated":"2025-09-22T09:58:16Z","project":[{"grant_number":"622033","name":"Persistent Homology - Images, Data and Maps","_id":"255F06BE-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"date_created":"2018-12-11T11:50:25Z","author":[{"full_name":"Miyaji, Tomoyuki","last_name":"Miyaji","first_name":"Tomoyuki"},{"full_name":"Pilarczyk, Pawel","first_name":"Pawel","last_name":"Pilarczyk","id":"3768D56A-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Gameiro, Marcio","first_name":"Marcio","last_name":"Gameiro"},{"first_name":"Hiroshi","last_name":"Kokubu","full_name":"Kokubu, Hiroshi"},{"first_name":"Konstantin","last_name":"Mischaikow","full_name":"Mischaikow, Konstantin"}],"date_published":"2016-09-01T00:00:00Z","month":"09","scopus_import":"1","title":"A study of rigorous ODE integrators for multi scale set oriented computations","intvolume":" 107","_id":"1149","year":"2016","language":[{"iso":"eng"}],"article_processing_charge":"No","status":"public","ec_funded":1}]