[{"_id":"1072","article_type":"original","type":"journal_article","status":"public","date_updated":"2023-09-20T12:05:56Z","department":[{"_id":"HeEd"}],"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."}],"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1312.1231"}],"scopus_import":"1","intvolume":" 369","month":"05","publication_status":"published","language":[{"iso":"eng"}],"ec_funded":1,"volume":369,"issue":"5","project":[{"call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","name":"Topological Complex Systems"}],"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.","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.","short":"U. Bauer, H. Edelsbrunner, Transactions of the American Mathematical Society 369 (2017) 3741–3762.","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","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."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","article_processing_charge":"No","external_id":{"arxiv":["1312.1231"],"isi":["000398030400024"]},"author":[{"first_name":"Ulrich","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9683-0724","full_name":"Bauer, Ulrich","last_name":"Bauer"},{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"}],"publist_id":"6311","title":"The Morse theory of Čech and delaunay complexes","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”.","oa":1,"publisher":"American Mathematical Society","quality_controlled":"1","year":"2017","isi":1,"publication":"Transactions of the American Mathematical Society","day":"01","page":"3741 - 3762","date_created":"2018-12-11T11:49:59Z","date_published":"2017-05-01T00:00:00Z","doi":"10.1090/tran/6991"},{"project":[{"call_identifier":"FWF","_id":"2584A770-B435-11E9-9278-68D0E5697425","grant_number":"P 23499-N23","name":"Modern Graph Algorithmic Techniques in Formal Verification"},{"call_identifier":"FWF","_id":"25863FF4-B435-11E9-9278-68D0E5697425","name":"Game Theory","grant_number":"S11407"},{"grant_number":"279307","name":"Quantitative Graph Games: Theory and Applications","_id":"2581B60A-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"title":"Pushdown reachability with constant treewidth","article_processing_charge":"No","external_id":{"isi":["000399506600005"]},"author":[{"last_name":"Chatterjee","full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","first_name":"Krishnendu"},{"id":"464B40D6-F248-11E8-B48F-1D18A9856A87","first_name":"Georg F","full_name":"Osang, Georg F","orcid":"0000-0002-8882-5116","last_name":"Osang"}],"publist_id":"6323","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"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","ieee":"K. Chatterjee and G. F. Osang, “Pushdown reachability with constant treewidth,” Information Processing Letters, vol. 122. Elsevier, pp. 25–29, 2017.","short":"K. Chatterjee, G.F. Osang, Information Processing Letters 122 (2017) 25–29.","mla":"Chatterjee, Krishnendu, and Georg F. Osang. “Pushdown Reachability with Constant Treewidth.” Information Processing Letters, vol. 122, Elsevier, 2017, pp. 25–29, doi:10.1016/j.ipl.2017.02.003.","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."},"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","has_accepted_license":"1","isi":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","access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2018-12-12T10:13:17Z","file_name":"IST-2018-991-v1+2_2018_Chatterjee_Pushdown_PREPRINT.pdf","creator":"system","date_updated":"2019-10-15T07:44:51Z","file_size":247657}],"publication_status":"published","publication_identifier":{"issn":["00200190"]}},{"publication_status":"published","publication_identifier":{"issn":["00358711"]},"language":[{"iso":"eng"}],"issue":"4","volume":465,"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"}],"oa_version":"Submitted Version","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1608.04519"}],"scopus_import":"1","intvolume":" 465","month":"01","date_updated":"2023-09-22T09:40:55Z","department":[{"_id":"HeEd"}],"_id":"1022","type":"journal_article","status":"public","year":"2017","isi":1,"publication":"Monthly Notices of the Royal Astronomical Society","day":"01","page":"4281 - 4310","date_created":"2018-12-11T11:49:44Z","date_published":"2017-01-01T00:00:00Z","doi":"10.1093/mnras/stw2862","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.","oa":1,"quality_controlled":"1","publisher":"Oxford University Press","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.","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.","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.","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","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."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","article_processing_charge":"No","external_id":{"isi":["000395170200039"]},"publist_id":"6373","author":[{"last_name":"Pranav","full_name":"Pranav, Pratyush","first_name":"Pratyush"},{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"last_name":"Van De Weygaert","full_name":"Van De Weygaert, Rien","first_name":"Rien"},{"first_name":"Gert","last_name":"Vegter","full_name":"Vegter, Gert"},{"last_name":"Kerber","full_name":"Kerber, Michael","first_name":"Michael"},{"last_name":"Jones","full_name":"Jones, Bernard","first_name":"Bernard"},{"first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","last_name":"Wintraecken"}],"title":"The topology of the cosmic web in terms of persistent Betti numbers"},{"title":"A new topology on the universal path space","external_id":{"isi":["000413889100012"]},"article_processing_charge":"No","publist_id":"6930","author":[{"id":"2E36B656-F248-11E8-B48F-1D18A9856A87","first_name":"Ziga","last_name":"Virk","full_name":"Virk, Ziga"},{"full_name":"Zastrow, Andreas","last_name":"Zastrow","first_name":"Andreas"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","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.","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","short":"Z. Virk, A. Zastrow, Topology and Its Applications 231 (2017) 186–196.","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.","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."},"date_created":"2018-12-11T11:48:14Z","doi":"10.1016/j.topol.2017.09.015","date_published":"2017-11-01T00:00:00Z","page":"186 - 196","publication":"Topology and its Applications","day":"01","year":"2017","isi":1,"publisher":"Elsevier","quality_controlled":"1","department":[{"_id":"HeEd"}],"date_updated":"2023-09-27T12:53:01Z","status":"public","type":"journal_article","_id":"737","volume":231,"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["01668641"]},"intvolume":" 231","month":"11","scopus_import":"1","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"}]},{"publisher":"Springer","quality_controlled":"1","isi":1,"year":"2017","day":"27","publication":"Special Sessions in Applications of Computer Algebra","page":"119 - 136","date_published":"2017-07-27T00:00:00Z","doi":"10.1007/978-3-319-56932-1_8","date_created":"2018-12-11T11:48:46Z","project":[{"name":"Topological Complex Systems","grant_number":"318493","call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"citation":{"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.","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.","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.","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","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."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","author":[{"last_name":"Ethier","full_name":"Ethier, Marc","first_name":"Marc"},{"last_name":"Jablonski","orcid":"0000-0002-3536-9866","full_name":"Jablonski, Grzegorz","first_name":"Grzegorz","id":"4483EF78-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Mrozek, Marian","last_name":"Mrozek","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","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","scopus_import":"1","alternative_title":["PROMS"],"month":"07","intvolume":" 198","publication_identifier":{"isbn":["978-331956930-7"]},"publication_status":"published","language":[{"iso":"eng"}],"volume":198,"ec_funded":1,"_id":"836","type":"conference","conference":{"name":"ACA: Applications of Computer Algebra","end_date":"2015-07-23","location":"Kalamata, Greece","start_date":"2015-07-20"},"status":"public","date_updated":"2023-09-26T15:50:52Z","department":[{"_id":"HeEd"}]}]