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In particular, we obtain the expected numbers of simplices in the Poisson–Delaunay mosaic in dimensions n ≤ 4.","lang":"eng"}],"oa_version":"Preprint","department":[{"_id":"HeEd"}],"date_updated":"2023-09-07T12:07:12Z","type":"journal_article","status":"public","_id":"718","page":"745 - 767","doi":"10.1017/apr.2017.20","date_published":"2017-09-01T00:00:00Z","date_created":"2018-12-11T11:48:07Z","year":"2017","day":"01","publication":"Advances in Applied Probability","publisher":"Cambridge University Press","quality_controlled":"1","oa":1,"author":[{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","first_name":"Anton","last_name":"Nikitenko","full_name":"Nikitenko, Anton","orcid":"0000-0002-0659-3201"},{"last_name":"Reitzner","full_name":"Reitzner, Matthias","first_name":"Matthias"}],"publist_id":"6962","external_id":{"arxiv":["1607.05915"]},"title":"Expected sizes of poisson Delaunay mosaics and their discrete Morse functions","citation":{"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.","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.","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.","short":"H. Edelsbrunner, A. Nikitenko, M. Reitzner, Advances in Applied Probability 49 (2017) 745–767.","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.","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"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","name":"Topological Complex Systems"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}]},{"author":[{"first_name":"Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","last_name":"Nikitenko","full_name":"Nikitenko, Anton","orcid":"0000-0002-0659-3201"}],"article_processing_charge":"No","title":"Discrete Morse theory for random complexes ","citation":{"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.","mla":"Nikitenko, Anton. Discrete Morse Theory for Random Complexes . Institute of Science and Technology Austria, 2017, doi:10.15479/AT:ISTA:th_873.","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.","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"},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","page":"86","doi":"10.15479/AT:ISTA:th_873","date_published":"2017-10-27T00:00:00Z","date_created":"2019-04-09T15:04:32Z","has_accepted_license":"1","year":"2017","day":"27","publisher":"Institute of Science and Technology Austria","oa":1,"file_date_updated":"2020-07-14T12:47:26Z","department":[{"_id":"HeEd"}],"supervisor":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"}],"date_updated":"2023-09-15T12:10:34Z","ddc":["514","516","519"],"type":"dissertation","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","pubrep_id":"873","_id":"6287","related_material":{"record":[{"relation":"part_of_dissertation","id":"718","status":"public"},{"id":"5678","status":"public","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","status":"public","id":"87"}]},"publication_identifier":{"issn":["2663-337X"]},"publication_status":"published","degree_awarded":"PhD","file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","checksum":"ece7e598a2f060b263c2febf7f3fe7f9","file_id":"6289","file_size":2324870,"date_updated":"2020-07-14T12:47:26Z","creator":"dernst","file_name":"2017_Thesis_Nikitenko.pdf","date_created":"2019-04-09T14:54:51Z"},{"date_created":"2019-04-09T14:54:51Z","file_name":"2017_Thesis_Nikitenko_source.zip","date_updated":"2020-07-14T12:47:26Z","file_size":2863219,"creator":"dernst","checksum":"99b7ad76e317efd447af60f91e29b49b","file_id":"6290","content_type":"application/zip","access_level":"closed","relation":"source_file"}],"language":[{"iso":"eng"}],"alternative_title":["ISTA Thesis"],"month":"10","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"},{"project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Topological Complex Systems","grant_number":"318493"}],"citation":{"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.","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.","apa":"Bauer, U., Kerber, M., Reininghaus, J., & Wagner, H. (2017). Phat - Persistent homology algorithms toolbox. Journal of Symbolic Computation. Academic Press. https://doi.org/10.1016/j.jsc.2016.03.008","ama":"Bauer U, Kerber M, Reininghaus J, Wagner H. Phat - Persistent homology algorithms toolbox. Journal of Symbolic Computation. 2017;78:76-90. doi:10.1016/j.jsc.2016.03.008","short":"U. Bauer, M. Kerber, J. Reininghaus, H. Wagner, Journal of Symbolic Computation 78 (2017) 76–90.","ieee":"U. Bauer, M. Kerber, J. Reininghaus, and H. Wagner, “Phat - Persistent homology algorithms toolbox,” Journal of Symbolic Computation, vol. 78. Academic Press, pp. 76–90, 2017."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publist_id":"5765","author":[{"first_name":"Ulrich","last_name":"Bauer","full_name":"Bauer, Ulrich"},{"full_name":"Kerber, Michael","last_name":"Kerber","first_name":"Michael"},{"last_name":"Reininghaus","full_name":"Reininghaus, Jan","first_name":"Jan"},{"last_name":"Wagner","full_name":"Wagner, Hubert","first_name":"Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","external_id":{"isi":["000384396000005"]},"title":"Phat - Persistent homology algorithms toolbox","publisher":"Academic Press","quality_controlled":"1","oa":1,"isi":1,"year":"2017","day":"01","publication":"Journal of Symbolic Computation","page":"76 - 90","doi":"10.1016/j.jsc.2016.03.008","date_published":"2017-01-01T00:00:00Z","date_created":"2018-12-11T11:51:59Z","_id":"1433","article_type":"original","type":"journal_article","status":"public","date_updated":"2023-09-20T09:42:40Z","department":[{"_id":"HeEd"}],"abstract":[{"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.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","main_file_link":[{"url":"https://doi.org/10.1016/j.jsc.2016.03.008","open_access":"1"}],"month":"01","intvolume":" 78","publication_identifier":{"issn":[" 07477171"]},"publication_status":"published","language":[{"iso":"eng"}],"volume":78,"related_material":{"record":[{"id":"10894","status":"public","relation":"earlier_version"}]},"ec_funded":1},{"project":[{"call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","grant_number":"291734"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"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.","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","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.","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."},"title":"Algebraic vertices of non-convex polyhedra","article_processing_charge":"No","external_id":{"isi":["000409292900015"]},"publist_id":"6173","author":[{"full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy"},{"last_name":"Bárány","full_name":"Bárány, Imre","first_name":"Imre"},{"first_name":"Sinai","last_name":"Robins","full_name":"Robins, Sinai"}],"oa":1,"quality_controlled":"1","publisher":"Academic Press","publication":"Advances in Mathematics","day":"21","year":"2017","isi":1,"date_created":"2018-12-11T11:50:34Z","date_published":"2017-02-21T00:00:00Z","doi":"10.1016/j.aim.2016.12.026","page":"627 - 644","_id":"1180","status":"public","type":"journal_article","date_updated":"2023-09-20T11:21:27Z","department":[{"_id":"HeEd"}],"oa_version":"Submitted Version","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."}],"intvolume":" 308","month":"02","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1508.07594"}],"scopus_import":"1","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["00018708"]},"ec_funded":1,"volume":308},{"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["02099683"]},"ec_funded":1,"issue":"5","volume":37,"oa_version":"Submitted Version","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"}],"intvolume":" 37","month":"10","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1411.6337"}],"scopus_import":"1","date_updated":"2023-09-20T11:23:53Z","department":[{"_id":"HeEd"}],"_id":"1173","status":"public","type":"journal_article","publication":"Combinatorica","day":"01","year":"2017","isi":1,"date_created":"2018-12-11T11:50:32Z","doi":"10.1007/s00493-016-3308-y","date_published":"2017-10-01T00:00:00Z","page":"887 - 910","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.","oa":1,"publisher":"Springer","quality_controlled":"1","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"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.","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.","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","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","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.","short":"H. Edelsbrunner, A. Glazyrin, O. Musin, A. Nikitenko, Combinatorica 37 (2017) 887–910.","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."},"title":"The Voronoi functional is maximized by the Delaunay triangulation in the plane","external_id":{"isi":["000418056000005"]},"article_processing_charge":"No","publist_id":"6182","author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Glazyrin","full_name":"Glazyrin, Alexey","first_name":"Alexey"},{"first_name":"Oleg","full_name":"Musin, Oleg","last_name":"Musin"},{"first_name":"Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","last_name":"Nikitenko","full_name":"Nikitenko, Anton","orcid":"0000-0002-0659-3201"}],"project":[{"name":"Topological Complex Systems","grant_number":"318493","call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425"}]},{"date_created":"2018-12-11T11:49:59Z","doi":"10.1090/tran/6991","date_published":"2017-05-01T00:00:00Z","page":"3741 - 3762","publication":"Transactions of the American Mathematical Society","day":"01","year":"2017","isi":1,"oa":1,"quality_controlled":"1","publisher":"American Mathematical Society","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”.","title":"The Morse theory of Čech and delaunay complexes","article_processing_charge":"No","external_id":{"arxiv":["1312.1231"],"isi":["000398030400024"]},"publist_id":"6311","author":[{"last_name":"Bauer","full_name":"Bauer, Ulrich","orcid":"0000-0002-9683-0724","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","first_name":"Ulrich"},{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","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.","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","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","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.","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."},"project":[{"grant_number":"318493","name":"Topological Complex Systems","_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"ec_funded":1,"volume":369,"issue":"5","language":[{"iso":"eng"}],"publication_status":"published","intvolume":" 369","month":"05","main_file_link":[{"url":"https://arxiv.org/abs/1312.1231","open_access":"1"}],"scopus_import":"1","oa_version":"Preprint","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"}],"department":[{"_id":"HeEd"}],"date_updated":"2023-09-20T12:05:56Z","status":"public","article_type":"original","type":"journal_article","_id":"1072"},{"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","call_identifier":"FWF","_id":"25863FF4-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FP7","_id":"2581B60A-B435-11E9-9278-68D0E5697425","name":"Quantitative Graph Games: Theory and Applications","grant_number":"279307"}],"title":"Pushdown reachability with constant treewidth","article_processing_charge":"No","external_id":{"isi":["000399506600005"]},"publist_id":"6323","author":[{"last_name":"Chatterjee","full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X","first_name":"Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","full_name":"Osang, Georg F","orcid":"0000-0002-8882-5116","last_name":"Osang"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"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.","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.","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","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.","ista":"Chatterjee K, Osang GF. 2017. Pushdown reachability with constant treewidth. Information Processing Letters. 122, 25–29."},"oa":1,"publisher":"Elsevier","quality_controlled":"1","date_created":"2018-12-11T11:49:57Z","date_published":"2017-06-01T00:00:00Z","doi":"10.1016/j.ipl.2017.02.003","page":"25 - 29","publication":"Information Processing Letters","day":"01","year":"2017","isi":1,"has_accepted_license":"1","pubrep_id":"991","status":"public","type":"journal_article","_id":"1065","file_date_updated":"2019-10-15T07:44:51Z","department":[{"_id":"KrCh"},{"_id":"HeEd"}],"ddc":["000"],"date_updated":"2023-09-20T12:08:18Z","intvolume":" 122","month":"06","scopus_import":"1","oa_version":"Submitted Version","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."}],"ec_funded":1,"volume":122,"language":[{"iso":"eng"}],"file":[{"file_id":"4998","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_name":"IST-2018-991-v1+2_2018_Chatterjee_Pushdown_PREPRINT.pdf","date_created":"2018-12-12T10:13:17Z","file_size":247657,"date_updated":"2019-10-15T07:44:51Z","creator":"system"}],"publication_status":"published","publication_identifier":{"issn":["00200190"]}},{"quality_controlled":"1","publisher":"Oxford University Press","oa":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.","doi":"10.1093/mnras/stw2862","date_published":"2017-01-01T00:00:00Z","date_created":"2018-12-11T11:49:44Z","page":"4281 - 4310","day":"01","publication":"Monthly Notices of the Royal Astronomical Society","isi":1,"year":"2017","title":"The topology of the cosmic web in terms of persistent Betti numbers","publist_id":"6373","author":[{"last_name":"Pranav","full_name":"Pranav, Pratyush","first_name":"Pratyush"},{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"first_name":"Rien","last_name":"Van De Weygaert","full_name":"Van De Weygaert, Rien"},{"first_name":"Gert","full_name":"Vegter, Gert","last_name":"Vegter"},{"full_name":"Kerber, Michael","last_name":"Kerber","first_name":"Michael"},{"last_name":"Jones","full_name":"Jones, Bernard","first_name":"Bernard"},{"last_name":"Wintraecken","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"external_id":{"isi":["000395170200039"]},"article_processing_charge":"No","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"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.","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.","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.","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","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"},"month":"01","intvolume":" 465","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1608.04519"}],"oa_version":"Submitted Version","abstract":[{"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.","lang":"eng"}],"volume":465,"issue":"4","language":[{"iso":"eng"}],"publication_identifier":{"issn":["00358711"]},"publication_status":"published","status":"public","type":"journal_article","_id":"1022","department":[{"_id":"HeEd"}],"date_updated":"2023-09-22T09:40:55Z"},{"page":"186 - 196","doi":"10.1016/j.topol.2017.09.015","date_published":"2017-11-01T00:00:00Z","date_created":"2018-12-11T11:48:14Z","isi":1,"year":"2017","day":"01","publication":"Topology and its Applications","publisher":"Elsevier","quality_controlled":"1","publist_id":"6930","author":[{"last_name":"Virk","full_name":"Virk, Ziga","first_name":"Ziga","id":"2E36B656-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Andreas","last_name":"Zastrow","full_name":"Zastrow, Andreas"}],"article_processing_charge":"No","external_id":{"isi":["000413889100012"]},"title":"A new topology on the universal path space","citation":{"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.","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.","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","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","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.","ista":"Virk Z, Zastrow A. 2017. A new topology on the universal path space. Topology and its Applications. 231, 186–196."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","volume":231,"publication_identifier":{"issn":["01668641"]},"publication_status":"published","language":[{"iso":"eng"}],"scopus_import":"1","month":"11","intvolume":" 231","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"}],"oa_version":"None","department":[{"_id":"HeEd"}],"date_updated":"2023-09-27T12:53:01Z","type":"journal_article","status":"public","_id":"737"},{"volume":198,"ec_funded":1,"publication_identifier":{"isbn":["978-331956930-7"]},"publication_status":"published","language":[{"iso":"eng"}],"alternative_title":["PROMS"],"scopus_import":"1","month":"07","intvolume":" 198","abstract":[{"lang":"eng","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."}],"oa_version":"None","department":[{"_id":"HeEd"}],"date_updated":"2023-09-26T15:50:52Z","type":"conference","conference":{"name":"ACA: Applications of Computer Algebra","end_date":"2015-07-23","location":"Kalamata, Greece","start_date":"2015-07-20"},"status":"public","_id":"836","page":"119 - 136","doi":"10.1007/978-3-319-56932-1_8","date_published":"2017-07-27T00:00:00Z","date_created":"2018-12-11T11:48:46Z","isi":1,"year":"2017","day":"27","publication":"Special Sessions in Applications of Computer Algebra","publisher":"Springer","quality_controlled":"1","author":[{"last_name":"Ethier","full_name":"Ethier, Marc","first_name":"Marc"},{"id":"4483EF78-F248-11E8-B48F-1D18A9856A87","first_name":"Grzegorz","orcid":"0000-0002-3536-9866","full_name":"Jablonski, Grzegorz","last_name":"Jablonski"},{"last_name":"Mrozek","full_name":"Mrozek, Marian","first_name":"Marian"}],"publist_id":"6812","article_processing_charge":"No","external_id":{"isi":["000434088200008"]},"title":"Finding eigenvalues of self-maps with the Kronecker canonical form","citation":{"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.","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.","short":"M. Ethier, G. Jablonski, M. Mrozek, in:, Special Sessions in Applications of Computer Algebra, Springer, 2017, pp. 119–136.","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","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","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."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","project":[{"call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","name":"Topological Complex Systems"}]},{"oa":1,"publisher":"Springer","quality_controlled":"1","date_created":"2018-12-11T11:48:45Z","doi":"10.1007/978-3-319-64689-3_32","date_published":"2017-07-28T00:00:00Z","page":"397 - 409","day":"28","year":"2017","isi":1,"title":"Streaming algorithm for Euler characteristic curves of multidimensional images","editor":[{"first_name":"Michael","last_name":"Felsberg","full_name":"Felsberg, Michael"},{"first_name":"Anders","last_name":"Heyden","full_name":"Heyden, Anders"},{"first_name":"Norbert","full_name":"Krüger, Norbert","last_name":"Krüger"}],"article_processing_charge":"No","external_id":{"isi":["000432085900032"]},"publist_id":"6815","author":[{"first_name":"Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","last_name":"Heiss","full_name":"Heiss, Teresa","orcid":"0000-0002-1780-2689"},{"full_name":"Wagner, Hubert","last_name":"Wagner","first_name":"Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"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","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.","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.","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."},"intvolume":" 10424","month":"07","main_file_link":[{"url":"https://arxiv.org/abs/1705.02045","open_access":"1"}],"scopus_import":"1","alternative_title":["LNCS"],"oa_version":"Submitted Version","abstract":[{"lang":"eng","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."}],"volume":10424,"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["03029743"]},"status":"public","conference":{"name":"CAIP: Computer Analysis of Images and Patterns","start_date":"2017-08-22","end_date":"2017-08-24","location":"Ystad, Sweden"},"type":"conference","_id":"833","department":[{"_id":"HeEd"}],"date_updated":"2023-09-26T16:10:03Z"},{"series_title":"Handbook of Discrete and Computational Geometry","_id":"84","type":"book_chapter","status":"public","date_updated":"2023-10-16T11:15:22Z","citation":{"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.","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","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","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.","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.","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"full_name":"Koehl, Patrice","last_name":"Koehl","first_name":"Patrice"}],"publist_id":"7970","department":[{"_id":"HeEd"}],"editor":[{"first_name":"Csaba","last_name":"Toth","full_name":"Toth, Csaba"},{"first_name":"Joseph","full_name":"O'Rourke, Joseph","last_name":"O'Rourke"},{"full_name":"Goodman, Jacob","last_name":"Goodman","first_name":"Jacob"}],"title":"Computational topology for structural molecular biology","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","scopus_import":"1","publisher":"Taylor & Francis","quality_controlled":"1","month":"11","publication_status":"published","year":"2017","publication_identifier":{"eisbn":["9781498711425"]},"publication":"Handbook of Discrete and Computational Geometry, Third Edition","language":[{"iso":"eng"}],"day":"09","page":"1709 - 1735","date_created":"2018-12-11T11:44:32Z","date_published":"2017-11-09T00:00:00Z","doi":"10.1201/9781315119601"},{"department":[{"_id":"HeEd"}],"date_updated":"2023-10-17T11:24:57Z","status":"public","type":"journal_article","article_type":"original","_id":"909","ec_funded":1,"volume":124,"issue":"7","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["00029890"]},"intvolume":" 124","month":"01","main_file_link":[{"url":"https://arxiv.org/abs/1605.07997","open_access":"1"}],"scopus_import":"1","oa_version":"Submitted Version","abstract":[{"lang":"eng","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 ½ 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."}],"title":"On the lengths of curves passing through boundary points of a planar convex shape","article_processing_charge":"No","external_id":{"arxiv":["1605.07997"],"isi":["000413947300002"]},"author":[{"last_name":"Akopyan","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Vysotsky, Vladislav","last_name":"Vysotsky","first_name":"Vladislav"}],"publist_id":"6534","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","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.","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","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.","short":"A. Akopyan, V. Vysotsky, The American Mathematical Monthly 124 (2017) 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.","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."},"project":[{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"date_created":"2018-12-11T11:49:09Z","doi":"10.4169/amer.math.monthly.124.7.588","date_published":"2017-01-01T00:00:00Z","page":"588 - 596","publication":"The American Mathematical Monthly","day":"01","year":"2017","isi":1,"oa":1,"publisher":"Mathematical Association of America","quality_controlled":"1"},{"_id":"1149","status":"public","project":[{"call_identifier":"FP7","_id":"255F06BE-B435-11E9-9278-68D0E5697425","grant_number":"622033","name":"Persistent Homology - Images, Data and Maps"}],"type":"journal_article","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T06:48:38Z","citation":{"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.","short":"T. Miyaji, P. Pilarczyk, M. Gameiro, H. Kokubu, K. Mischaikow, Applied Numerical Mathematics 107 (2016) 34–47.","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.","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","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","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."},"title":"A study of rigorous ODE integrators for multi scale set oriented computations","department":[{"_id":"HeEd"}],"publist_id":"6209","author":[{"last_name":"Miyaji","full_name":"Miyaji, Tomoyuki","first_name":"Tomoyuki"},{"full_name":"Pilarczyk, Pawel","last_name":"Pilarczyk","id":"3768D56A-F248-11E8-B48F-1D18A9856A87","first_name":"Pawel"},{"first_name":"Marcio","full_name":"Gameiro, Marcio","last_name":"Gameiro"},{"first_name":"Hiroshi","last_name":"Kokubu","full_name":"Kokubu, Hiroshi"},{"last_name":"Mischaikow","full_name":"Mischaikow, Konstantin","first_name":"Konstantin"}],"oa_version":"None","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.","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."}],"month":"09","intvolume":" 107","publisher":"Elsevier","quality_controlled":"1","scopus_import":1,"day":"01","publication":"Applied Numerical Mathematics","language":[{"iso":"eng"}],"publication_status":"published","year":"2016","volume":107,"doi":"10.1016/j.apnum.2016.04.005","date_published":"2016-09-01T00:00:00Z","ec_funded":1,"date_created":"2018-12-11T11:50:25Z","page":"34 - 47"},{"_id":"1216","type":"journal_article","status":"public","citation":{"chicago":"Kasten, Jens, Jan Reininghaus, Ingrid Hotz, Hans Hege, Bernd Noack, Guillaume Daviller, and Marek Morzyński. “Acceleration Feature Points of Unsteady Shear Flows.” Archives of Mechanics. Polish Academy of Sciences Publishing House, 2016.","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.” Archives of Mechanics, vol. 68, no. 1, Polish Academy of Sciences Publishing House, 2016, pp. 55–80.","ama":"Kasten J, Reininghaus J, Hotz I, et al. Acceleration feature points of unsteady shear flows. Archives of Mechanics. 2016;68(1):55-80.","apa":"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. Polish Academy of Sciences Publishing House.","ieee":"J. Kasten et al., “Acceleration feature points of unsteady shear flows,” Archives of Mechanics, vol. 68, no. 1. Polish Academy of Sciences Publishing House, pp. 55–80, 2016.","short":"J. Kasten, J. Reininghaus, I. Hotz, H. Hege, B. Noack, G. Daviller, M. Morzyński, Archives of Mechanics 68 (2016) 55–80."},"date_updated":"2021-01-12T06:49:09Z","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Kasten, Jens","last_name":"Kasten","first_name":"Jens"},{"id":"4505473A-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","last_name":"Reininghaus","full_name":"Reininghaus, Jan"},{"last_name":"Hotz","full_name":"Hotz, Ingrid","first_name":"Ingrid"},{"full_name":"Hege, Hans","last_name":"Hege","first_name":"Hans"},{"first_name":"Bernd","last_name":"Noack","full_name":"Noack, Bernd"},{"first_name":"Guillaume","full_name":"Daviller, Guillaume","last_name":"Daviller"},{"first_name":"Marek","full_name":"Morzyński, Marek","last_name":"Morzyński"}],"publist_id":"6118","title":"Acceleration feature points of unsteady shear flows","department":[{"_id":"HeEd"}],"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"}],"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","oa_version":"Published Version","main_file_link":[{"url":"http://am.ippt.pan.pl/am/article/viewFile/v68p55/pdf","open_access":"1"}],"oa":1,"quality_controlled":"1","publisher":"Polish Academy of Sciences Publishing House","scopus_import":1,"intvolume":" 68","month":"01","publication_status":"published","year":"2016","publication":"Archives of Mechanics","language":[{"iso":"eng"}],"day":"01","page":"55 - 80","date_created":"2018-12-11T11:50:46Z","volume":68,"issue":"1","date_published":"2016-01-01T00:00:00Z"},{"department":[{"_id":"HeEd"}],"date_updated":"2021-01-12T06:49:11Z","type":"journal_article","status":"public","_id":"1222","volume":55,"issue":"1","publication_status":"published","language":[{"iso":"eng"}],"scopus_import":1,"main_file_link":[{"url":"https://arxiv.org/abs/1212.0649","open_access":"1"}],"month":"01","intvolume":" 55","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."}],"oa_version":"Preprint","author":[{"first_name":"Oleg","last_name":"Musin","full_name":"Musin, Oleg"},{"full_name":"Nikitenko, Anton","last_name":"Nikitenko","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","first_name":"Anton"}],"publist_id":"6111","title":"Optimal packings of congruent circles on a square flat torus","citation":{"mla":"Musin, Oleg, and Anton Nikitenko. “Optimal Packings of Congruent Circles on a Square Flat Torus.” Discrete & Computational Geometry, vol. 55, no. 1, Springer, 2016, pp. 1–20, doi:10.1007/s00454-015-9742-6.","short":"O. Musin, A. Nikitenko, Discrete & Computational Geometry 55 (2016) 1–20.","ieee":"O. Musin and A. Nikitenko, “Optimal packings of congruent circles on a square flat torus,” Discrete & Computational Geometry, vol. 55, no. 1. Springer, pp. 1–20, 2016.","apa":"Musin, O., & Nikitenko, A. (2016). Optimal packings of congruent circles on a square flat torus. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-015-9742-6","ama":"Musin O, Nikitenko A. Optimal packings of congruent circles on a square flat torus. Discrete & Computational Geometry. 2016;55(1):1-20. doi:10.1007/s00454-015-9742-6","chicago":"Musin, Oleg, and Anton Nikitenko. “Optimal Packings of Congruent Circles on a Square Flat Torus.” Discrete & Computational Geometry. Springer, 2016. https://doi.org/10.1007/s00454-015-9742-6.","ista":"Musin O, Nikitenko A. 2016. Optimal packings of congruent circles on a square flat torus. Discrete & Computational Geometry. 55(1), 1–20."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","page":"1 - 20","date_published":"2016-01-01T00:00:00Z","doi":"10.1007/s00454-015-9742-6","date_created":"2018-12-11T11:50:48Z","year":"2016","day":"01","publication":"Discrete & Computational Geometry","quality_controlled":"1","publisher":"Springer","oa":1,"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."},{"publisher":"Springer","quality_controlled":"1","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.).","page":"140 - 151","date_created":"2018-12-11T11:50:52Z","date_published":"2016-06-02T00:00:00Z","doi":"10.1007/978-3-319-39441-1_13","year":"2016","day":"02","project":[{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"call_identifier":"FP7","_id":"255F06BE-B435-11E9-9278-68D0E5697425","grant_number":"622033","name":"Persistent Homology - Images, Data and Maps"}],"author":[{"full_name":"Krcál, Marek","last_name":"Krcál","id":"33E21118-F248-11E8-B48F-1D18A9856A87","first_name":"Marek"},{"last_name":"Pilarczyk","full_name":"Pilarczyk, Pawel","first_name":"Pawel","id":"3768D56A-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"6096","title":"Computation of cubical Steenrod squares","citation":{"short":"M. Krcál, P. Pilarczyk, in:, Springer, 2016, pp. 140–151.","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.","apa":"Krcál, M., & 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. https://doi.org/10.1007/978-3-319-39441-1_13","ama":"Krcál M, Pilarczyk P. Computation of cubical Steenrod squares. In: Vol 9667. Springer; 2016:140-151. doi:10.1007/978-3-319-39441-1_13","mla":"Krcál, Marek, and Pawel Pilarczyk. Computation of Cubical Steenrod Squares. Vol. 9667, Springer, 2016, pp. 140–51, doi:10.1007/978-3-319-39441-1_13.","ista":"Krcál M, Pilarczyk P. 2016. Computation of cubical Steenrod squares. CTIC: Computational Topology in Image Context, LNCS, vol. 9667, 140–151.","chicago":"Krcál, Marek, and Pawel Pilarczyk. “Computation of Cubical Steenrod Squares,” 9667:140–51. Springer, 2016. https://doi.org/10.1007/978-3-319-39441-1_13."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","alternative_title":["LNCS"],"scopus_import":1,"intvolume":" 9667","month":"06","abstract":[{"lang":"eng","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 > 0 whether every g: X → ℝm with ∥g - f ∥∞ ≤ r has a root, reduces to the extension problem."}],"oa_version":"None","ec_funded":1,"volume":9667,"publication_status":"published","language":[{"iso":"eng"}],"conference":{"name":"CTIC: Computational Topology in Image Context","start_date":"2016-06-15","end_date":"2016-06-17","location":"Marseille, France"},"type":"conference","status":"public","_id":"1237","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"date_updated":"2021-01-12T06:49:18Z"},{"type":"journal_article","article_type":"original","status":"public","_id":"1252","department":[{"_id":"HeEd"}],"date_updated":"2022-05-24T09:35:58Z","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1411.7563","open_access":"1"}],"month":"04","intvolume":" 144","abstract":[{"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.","lang":"eng"}],"oa_version":"Preprint","volume":144,"issue":"4","ec_funded":1,"publication_identifier":{"issn":["1088-6826"]},"publication_status":"published","language":[{"iso":"eng"}],"project":[{"name":"Persistent Homology - Images, Data and Maps","grant_number":"622033","call_identifier":"FP7","_id":"255F06BE-B435-11E9-9278-68D0E5697425"}],"author":[{"first_name":"Shaun","full_name":"Harker, Shaun","last_name":"Harker"},{"first_name":"Hiroshi","full_name":"Kokubu, Hiroshi","last_name":"Kokubu"},{"first_name":"Konstantin","full_name":"Mischaikow, Konstantin","last_name":"Mischaikow"},{"last_name":"Pilarczyk","full_name":"Pilarczyk, Pawel","first_name":"Pawel","id":"3768D56A-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"6075","external_id":{"arxiv":["1411.7563"]},"article_processing_charge":"No","title":"Inducing a map on homology from a correspondence","citation":{"mla":"Harker, Shaun, et al. “Inducing a Map on Homology from a Correspondence.” Proceedings of the American Mathematical Society, vol. 144, no. 4, American Mathematical Society, 2016, pp. 1787–801, doi:10.1090/proc/12812.","apa":"Harker, S., Kokubu, H., Mischaikow, K., & Pilarczyk, P. (2016). Inducing a map on homology from a correspondence. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/12812","ama":"Harker S, Kokubu H, Mischaikow K, Pilarczyk P. Inducing a map on homology from a correspondence. Proceedings of the American Mathematical Society. 2016;144(4):1787-1801. doi:10.1090/proc/12812","short":"S. Harker, H. Kokubu, K. Mischaikow, P. Pilarczyk, Proceedings of the American Mathematical Society 144 (2016) 1787–1801.","ieee":"S. Harker, H. Kokubu, K. Mischaikow, and P. Pilarczyk, “Inducing a map on homology from a correspondence,” Proceedings of the American Mathematical Society, vol. 144, no. 4. American Mathematical Society, pp. 1787–1801, 2016.","chicago":"Harker, Shaun, Hiroshi Kokubu, Konstantin Mischaikow, and Pawel Pilarczyk. “Inducing a Map on Homology from a Correspondence.” Proceedings of the American Mathematical Society. American Mathematical Society, 2016. https://doi.org/10.1090/proc/12812.","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","publisher":"American Mathematical Society","oa":1,"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.","page":"1787 - 1801","doi":"10.1090/proc/12812","date_published":"2016-04-01T00:00:00Z","date_created":"2018-12-11T11:50:57Z","year":"2016","day":"01","publication":"Proceedings of the American Mathematical Society"},{"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.","oa":1,"publisher":"Taylor and Francis","quality_controlled":"1","publication":"Experimental Mathematics","day":"02","year":"2016","date_created":"2018-12-11T11:50:58Z","doi":"10.1080/10586458.2015.1048011","date_published":"2016-04-02T00:00:00Z","page":"116 - 124","project":[{"call_identifier":"FP7","_id":"255F06BE-B435-11E9-9278-68D0E5697425","grant_number":"622033","name":"Persistent Homology - Images, Data and Maps"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Golmakani, Ali, Stefano Luzzatto, and Pawel Pilarczyk. “Uniform Expansivity Outside a Critical Neighborhood in the Quadratic Family.” Experimental Mathematics. Taylor and Francis, 2016. https://doi.org/10.1080/10586458.2015.1048011.","ista":"Golmakani A, Luzzatto S, Pilarczyk P. 2016. Uniform expansivity outside a critical neighborhood in the quadratic family. Experimental Mathematics. 25(2), 116–124.","mla":"Golmakani, Ali, et al. “Uniform Expansivity Outside a Critical Neighborhood in the Quadratic Family.” Experimental Mathematics, vol. 25, no. 2, Taylor and Francis, 2016, pp. 116–24, doi:10.1080/10586458.2015.1048011.","ama":"Golmakani A, Luzzatto S, Pilarczyk P. Uniform expansivity outside a critical neighborhood in the quadratic family. Experimental Mathematics. 2016;25(2):116-124. doi:10.1080/10586458.2015.1048011","apa":"Golmakani, A., Luzzatto, S., & Pilarczyk, P. (2016). Uniform expansivity outside a critical neighborhood in the quadratic family. Experimental Mathematics. Taylor and Francis. https://doi.org/10.1080/10586458.2015.1048011","ieee":"A. Golmakani, S. Luzzatto, and P. Pilarczyk, “Uniform expansivity outside a critical neighborhood in the quadratic family,” Experimental Mathematics, vol. 25, no. 2. Taylor and Francis, pp. 116–124, 2016.","short":"A. Golmakani, S. Luzzatto, P. Pilarczyk, Experimental Mathematics 25 (2016) 116–124."},"title":"Uniform expansivity outside a critical neighborhood in the quadratic family","publist_id":"6071","author":[{"full_name":"Golmakani, Ali","last_name":"Golmakani","first_name":"Ali"},{"full_name":"Luzzatto, Stefano","last_name":"Luzzatto","first_name":"Stefano"},{"last_name":"Pilarczyk","full_name":"Pilarczyk, Pawel","first_name":"Pawel","id":"3768D56A-F248-11E8-B48F-1D18A9856A87"}],"oa_version":"Preprint","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"}],"intvolume":" 25","month":"04","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1504.00116"}],"scopus_import":1,"language":[{"iso":"eng"}],"publication_status":"published","ec_funded":1,"volume":25,"issue":"2","_id":"1254","status":"public","type":"journal_article","date_updated":"2021-01-12T06:49:25Z","department":[{"_id":"HeEd"}]},{"file":[{"date_created":"2018-12-12T10:16:20Z","file_name":"IST-2016-694-v1+1_Generalized_offsetting_of_planar_structures_using_skeletons.pdf","creator":"system","date_updated":"2020-07-14T12:44:42Z","file_size":1678369,"file_id":"5206","checksum":"c746f3a48edb62b588d92ea5d0fd2c0e","access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"publication_status":"published","issue":"5","volume":13,"license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","oa_version":"Published Version","abstract":[{"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.","lang":"eng"}],"month":"09","intvolume":" 13","scopus_import":1,"ddc":["004","516"],"date_updated":"2021-01-12T06:49:32Z","file_date_updated":"2020-07-14T12:44:42Z","department":[{"_id":"HeEd"}],"_id":"1272","status":"public","pubrep_id":"694","type":"journal_article","tmp":{"short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png"},"day":"02","publication":"Computer-Aided Design and Applications","has_accepted_license":"1","year":"2016","date_published":"2016-09-02T00:00:00Z","doi":"10.1080/16864360.2016.1150718","date_created":"2018-12-11T11:51:04Z","page":"712 - 721","acknowledgement":"This work was supported by Austrian Science Fund (FWF): P25816-N15.","publisher":"Taylor and Francis","quality_controlled":"1","oa":1,"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Held, Martin, Stefan Huber, and Peter Palfrader. “Generalized Offsetting of Planar Structures Using Skeletons.” Computer-Aided Design and Applications. Taylor and Francis, 2016. https://doi.org/10.1080/16864360.2016.1150718.","ista":"Held M, Huber S, Palfrader P. 2016. Generalized offsetting of planar structures using skeletons. Computer-Aided Design and Applications. 13(5), 712–721.","mla":"Held, Martin, et al. “Generalized Offsetting of Planar Structures Using Skeletons.” Computer-Aided Design and Applications, vol. 13, no. 5, Taylor and Francis, 2016, pp. 712–21, doi:10.1080/16864360.2016.1150718.","ieee":"M. Held, S. Huber, and P. Palfrader, “Generalized offsetting of planar structures using skeletons,” Computer-Aided Design and Applications, vol. 13, no. 5. Taylor and Francis, pp. 712–721, 2016.","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. Computer-Aided Design and Applications. 2016;13(5):712-721. doi:10.1080/16864360.2016.1150718","apa":"Held, M., Huber, S., & Palfrader, P. (2016). Generalized offsetting of planar structures using skeletons. Computer-Aided Design and Applications. Taylor and Francis. https://doi.org/10.1080/16864360.2016.1150718"},"title":"Generalized offsetting of planar structures using skeletons","publist_id":"6048","author":[{"first_name":"Martin","full_name":"Held, Martin","last_name":"Held"},{"first_name":"Stefan","id":"4700A070-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8871-5814","full_name":"Huber, Stefan","last_name":"Huber"},{"last_name":"Palfrader","full_name":"Palfrader, Peter","first_name":"Peter"}]}]