--- _id: '1072' 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. 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”. article_processing_charge: No article_type: original author: - first_name: Ulrich full_name: Bauer, Ulrich id: 2ADD483A-F248-11E8-B48F-1D18A9856A87 last_name: Bauer orcid: 0000-0002-9683-0724 - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 citation: ama: Bauer U, Edelsbrunner H. The Morse theory of Čech and delaunay complexes. Transactions of the American Mathematical Society. 2017;369(5):3741-3762. doi:10.1090/tran/6991 apa: Bauer, U., & Edelsbrunner, H. (2017). The Morse theory of Čech and delaunay complexes. Transactions of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/tran/6991 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. 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. ista: Bauer U, Edelsbrunner H. 2017. The Morse theory of Čech and delaunay complexes. Transactions of the American Mathematical Society. 369(5), 3741–3762. mla: Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay Complexes.” Transactions of the American Mathematical Society, vol. 369, no. 5, American Mathematical Society, 2017, pp. 3741–62, doi:10.1090/tran/6991. short: U. Bauer, H. Edelsbrunner, Transactions of the American Mathematical Society 369 (2017) 3741–3762. date_created: 2018-12-11T11:49:59Z date_published: 2017-05-01T00:00:00Z date_updated: 2023-09-20T12:05:56Z day: '01' department: - _id: HeEd doi: 10.1090/tran/6991 ec_funded: 1 external_id: arxiv: - '1312.1231' isi: - '000398030400024' intvolume: ' 369' isi: 1 issue: '5' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1312.1231 month: '05' oa: 1 oa_version: Preprint page: 3741 - 3762 project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems publication: Transactions of the American Mathematical Society publication_status: published publisher: American Mathematical Society publist_id: '6311' quality_controlled: '1' scopus_import: '1' status: public title: The Morse theory of Čech and delaunay complexes type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 369 year: '2017' ... --- _id: '1065' 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.' article_processing_charge: No author: - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Georg F full_name: Osang, Georg F id: 464B40D6-F248-11E8-B48F-1D18A9856A87 last_name: Osang orcid: 0000-0002-8882-5116 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 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. ieee: K. Chatterjee and G. F. Osang, “Pushdown reachability with constant treewidth,” Information Processing Letters, vol. 122. Elsevier, pp. 25–29, 2017. ista: Chatterjee K, Osang GF. 2017. Pushdown reachability with constant treewidth. Information Processing Letters. 122, 25–29. 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. date_created: 2018-12-11T11:49:57Z date_published: 2017-06-01T00:00:00Z date_updated: 2023-09-20T12:08:18Z day: '01' ddc: - '000' department: - _id: KrCh - _id: HeEd doi: 10.1016/j.ipl.2017.02.003 ec_funded: 1 external_id: isi: - '000399506600005' file: - access_level: open_access content_type: application/pdf creator: system date_created: 2018-12-12T10:13:17Z date_updated: 2019-10-15T07:44:51Z file_id: '4998' file_name: IST-2018-991-v1+2_2018_Chatterjee_Pushdown_PREPRINT.pdf file_size: 247657 relation: main_file file_date_updated: 2019-10-15T07:44:51Z has_accepted_license: '1' intvolume: ' 122' isi: 1 language: - iso: eng month: '06' oa: 1 oa_version: Submitted Version page: 25 - 29 project: - _id: 2584A770-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P 23499-N23 name: Modern Graph Algorithmic Techniques in Formal Verification - _id: 25863FF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S11407 name: Game Theory - _id: 2581B60A-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '279307' name: 'Quantitative Graph Games: Theory and Applications' publication: Information Processing Letters publication_identifier: issn: - '00200190' publication_status: published publisher: Elsevier publist_id: '6323' pubrep_id: '991' quality_controlled: '1' scopus_import: '1' status: public title: Pushdown reachability with constant treewidth type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 122 year: '2017' ... --- _id: '1022' abstract: - lang: eng text: We introduce a multiscale topological description of the Megaparsec web-like cosmic matter distribution. Betti numbers and topological persistence offer a powerful means of describing the rich connectivity structure of the cosmic web and of its multiscale arrangement of matter and galaxies. Emanating from algebraic topology and Morse theory, Betti numbers and persistence diagrams represent an extension and deepening of the cosmologically familiar topological genus measure and the related geometric Minkowski functionals. In addition to a description of the mathematical background, this study presents the computational procedure for computing Betti numbers and persistence diagrams for density field filtrations. The field may be computed starting from a discrete spatial distribution of galaxies or simulation particles. The main emphasis of this study concerns an extensive and systematic exploration of the imprint of different web-like morphologies and different levels of multiscale clustering in the corresponding computed Betti numbers and persistence diagrams. To this end, we use Voronoi clustering models as templates for a rich variety of web-like configurations and the fractal-like Soneira-Peebles models exemplify a range of multiscale configurations. We have identified the clear imprint of cluster nodes, filaments, walls, and voids in persistence diagrams, along with that of the nested hierarchy of structures in multiscale point distributions. We conclude by outlining the potential of persistent topology for understanding the connectivity structure of the cosmic web, in large simulations of cosmic structure formation and in the challenging context of the observed galaxy distribution in large galaxy surveys. 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. article_processing_charge: No author: - first_name: Pratyush full_name: Pranav, Pratyush last_name: Pranav - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Rien full_name: Van De Weygaert, Rien last_name: Van De Weygaert - first_name: Gert full_name: Vegter, Gert last_name: Vegter - first_name: Michael full_name: Kerber, Michael last_name: Kerber - first_name: Bernard full_name: Jones, Bernard last_name: Jones - first_name: Mathijs full_name: Wintraecken, Mathijs id: 307CFBC8-F248-11E8-B48F-1D18A9856A87 last_name: Wintraecken orcid: 0000-0002-7472-2220 citation: 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. 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. 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. date_created: 2018-12-11T11:49:44Z date_published: 2017-01-01T00:00:00Z date_updated: 2023-09-22T09:40:55Z day: '01' department: - _id: HeEd doi: 10.1093/mnras/stw2862 external_id: isi: - '000395170200039' intvolume: ' 465' isi: 1 issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1608.04519 month: '01' oa: 1 oa_version: Submitted Version page: 4281 - 4310 publication: Monthly Notices of the Royal Astronomical Society publication_identifier: issn: - '00358711' publication_status: published publisher: Oxford University Press publist_id: '6373' quality_controlled: '1' scopus_import: '1' status: public title: The topology of the cosmic web in terms of persistent Betti numbers type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 465 year: '2017' ... --- _id: '737' abstract: - lang: eng 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. article_processing_charge: No author: - first_name: Ziga full_name: Virk, Ziga id: 2E36B656-F248-11E8-B48F-1D18A9856A87 last_name: Virk - first_name: Andreas full_name: Zastrow, Andreas last_name: Zastrow citation: 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 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. 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. ista: Virk Z, Zastrow A. 2017. A new topology on the universal path space. Topology and its Applications. 231, 186–196. 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. short: Z. Virk, A. Zastrow, Topology and Its Applications 231 (2017) 186–196. date_created: 2018-12-11T11:48:14Z date_published: 2017-11-01T00:00:00Z date_updated: 2023-09-27T12:53:01Z day: '01' department: - _id: HeEd doi: 10.1016/j.topol.2017.09.015 external_id: isi: - '000413889100012' intvolume: ' 231' isi: 1 language: - iso: eng month: '11' oa_version: None page: 186 - 196 publication: Topology and its Applications publication_identifier: issn: - '01668641' publication_status: published publisher: Elsevier publist_id: '6930' quality_controlled: '1' scopus_import: '1' status: public title: A new topology on the universal path space type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 231 year: '2017' ... --- _id: '836' 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. alternative_title: - PROMS article_processing_charge: No author: - first_name: Marc full_name: Ethier, Marc last_name: Ethier - first_name: Grzegorz full_name: Jablonski, Grzegorz id: 4483EF78-F248-11E8-B48F-1D18A9856A87 last_name: Jablonski orcid: 0000-0002-3536-9866 - first_name: Marian full_name: Mrozek, Marian last_name: Mrozek citation: ama: 'Ethier M, Jablonski G, Mrozek M. Finding eigenvalues of self-maps with the Kronecker canonical form. In: Special Sessions in Applications of Computer Algebra. Vol 198. Springer; 2017:119-136. doi:10.1007/978-3-319-56932-1_8' apa: 'Ethier, M., Jablonski, G., & Mrozek, M. (2017). Finding eigenvalues of self-maps with the Kronecker canonical form. In Special Sessions in Applications of Computer Algebra (Vol. 198, pp. 119–136). Kalamata, Greece: Springer. https://doi.org/10.1007/978-3-319-56932-1_8' 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. 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. 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.' mla: Ethier, Marc, et al. “Finding Eigenvalues of Self-Maps with the Kronecker Canonical Form.” Special Sessions in Applications of Computer Algebra, vol. 198, Springer, 2017, pp. 119–36, doi:10.1007/978-3-319-56932-1_8. short: M. Ethier, G. Jablonski, M. Mrozek, in:, Special Sessions in Applications of Computer Algebra, Springer, 2017, pp. 119–136. conference: end_date: 2015-07-23 location: Kalamata, Greece name: 'ACA: Applications of Computer Algebra' start_date: 2015-07-20 date_created: 2018-12-11T11:48:46Z date_published: 2017-07-27T00:00:00Z date_updated: 2023-09-26T15:50:52Z day: '27' department: - _id: HeEd doi: 10.1007/978-3-319-56932-1_8 ec_funded: 1 external_id: isi: - '000434088200008' intvolume: ' 198' isi: 1 language: - iso: eng month: '07' oa_version: None page: 119 - 136 project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems publication: Special Sessions in Applications of Computer Algebra publication_identifier: isbn: - 978-331956930-7 publication_status: published publisher: Springer publist_id: '6812' quality_controlled: '1' scopus_import: '1' status: public title: Finding eigenvalues of self-maps with the Kronecker canonical form type: conference user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 198 year: '2017' ...