--- _id: '718' abstract: - lang: eng text: Mapping every simplex in the Delaunay mosaic of a discrete point set to the radius of the smallest empty circumsphere gives a generalized discrete Morse function. Choosing the points from a Poisson point process in ℝ n , we study the expected number of simplices in the Delaunay mosaic as well as the expected number of critical simplices and nonsingular intervals in the corresponding generalized discrete gradient. Observing connections with other probabilistic models, we obtain precise expressions for the expected numbers in low dimensions. In particular, we obtain the expected numbers of simplices in the Poisson–Delaunay mosaic in dimensions n ≤ 4. author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Anton full_name: Nikitenko, Anton id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87 last_name: Nikitenko orcid: 0000-0002-0659-3201 - first_name: Matthias full_name: Reitzner, Matthias last_name: Reitzner citation: ama: Edelsbrunner H, Nikitenko A, Reitzner M. Expected sizes of poisson Delaunay mosaics and their discrete Morse functions. Advances in Applied Probability. 2017;49(3):745-767. doi:10.1017/apr.2017.20 apa: Edelsbrunner, H., Nikitenko, A., & Reitzner, M. (2017). Expected sizes of poisson Delaunay mosaics and their discrete Morse functions. Advances in Applied Probability. Cambridge University Press. https://doi.org/10.1017/apr.2017.20 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. 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. 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. date_created: 2018-12-11T11:48:07Z date_published: 2017-09-01T00:00:00Z date_updated: 2023-09-07T12:07:12Z day: '01' department: - _id: HeEd doi: 10.1017/apr.2017.20 ec_funded: 1 external_id: arxiv: - '1607.05915' intvolume: ' 49' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1607.05915 month: '09' oa: 1 oa_version: Preprint page: 745 - 767 project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication: Advances in Applied Probability publication_identifier: issn: - '00018678' publication_status: published publisher: Cambridge University Press publist_id: '6962' quality_controlled: '1' related_material: record: - id: '6287' relation: dissertation_contains status: public scopus_import: 1 status: public title: Expected sizes of poisson Delaunay mosaics and their discrete Morse functions type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 49 year: '2017' ... --- _id: '6287' abstract: - lang: eng text: The main objects considered in the present work are simplicial and CW-complexes with vertices forming a random point cloud. In particular, we consider a Poisson point process in R^n and study Delaunay and Voronoi complexes of the first and higher orders and weighted Delaunay complexes obtained as sections of Delaunay complexes, as well as the Čech complex. Further, we examine theDelaunay complex of a Poisson point process on the sphere S^n, as well as of a uniform point cloud, which is equivalent to the convex hull, providing a connection to the theory of random polytopes. Each of the complexes in question can be endowed with a radius function, which maps its cells to the radii of appropriately chosen circumspheres, called the radius of the cell. Applying and developing discrete Morse theory for these functions, joining it together with probabilistic and sometimes analytic machinery, and developing several integral geometric tools, we aim at getting the distributions of circumradii of typical cells. For all considered complexes, we are able to generalize and obtain up to constants the distribution of radii of typical intervals of all types. In low dimensions the constants can be computed explicitly, thus providing the explicit expressions for the expected numbers of cells. In particular, it allows to find the expected density of simplices of every dimension for a Poisson point process in R^4, whereas the result for R^3 was known already in 1970's. alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Anton full_name: Nikitenko, Anton id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87 last_name: Nikitenko orcid: 0000-0002-0659-3201 citation: ama: Nikitenko A. Discrete Morse theory for random complexes . 2017. doi:10.15479/AT:ISTA:th_873 apa: Nikitenko, A. (2017). Discrete Morse theory for random complexes . Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:th_873 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. ieee: A. Nikitenko, “Discrete Morse theory for random complexes ,” Institute of Science and Technology Austria, 2017. ista: Nikitenko A. 2017. Discrete Morse theory for random complexes . Institute of Science and Technology Austria. mla: Nikitenko, Anton. Discrete Morse Theory for Random Complexes . Institute of Science and Technology Austria, 2017, doi:10.15479/AT:ISTA:th_873. short: A. Nikitenko, Discrete Morse Theory for Random Complexes , Institute of Science and Technology Austria, 2017. date_created: 2019-04-09T15:04:32Z date_published: 2017-10-27T00:00:00Z date_updated: 2023-09-15T12:10:34Z day: '27' ddc: - '514' - '516' - '519' degree_awarded: PhD department: - _id: HeEd doi: 10.15479/AT:ISTA:th_873 file: - access_level: open_access checksum: ece7e598a2f060b263c2febf7f3fe7f9 content_type: application/pdf creator: dernst date_created: 2019-04-09T14:54:51Z date_updated: 2020-07-14T12:47:26Z file_id: '6289' file_name: 2017_Thesis_Nikitenko.pdf file_size: 2324870 relation: main_file - access_level: closed checksum: 99b7ad76e317efd447af60f91e29b49b content_type: application/zip creator: dernst date_created: 2019-04-09T14:54:51Z date_updated: 2020-07-14T12:47:26Z file_id: '6290' file_name: 2017_Thesis_Nikitenko_source.zip file_size: 2863219 relation: source_file file_date_updated: 2020-07-14T12:47:26Z has_accepted_license: '1' language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: '86' publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria pubrep_id: '873' related_material: record: - id: '718' relation: part_of_dissertation status: public - id: '5678' relation: part_of_dissertation status: public - id: '87' relation: part_of_dissertation status: public status: public supervisor: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 title: 'Discrete Morse theory for random complexes ' tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: dissertation user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2017' ... --- _id: '1433' abstract: - lang: eng text: Phat is an open-source C. ++ library for the computation of persistent homology by matrix reduction, targeted towards developers of software for topological data analysis. We aim for a simple generic design that decouples algorithms from data structures without sacrificing efficiency or user-friendliness. We provide numerous different reduction strategies as well as data types to store and manipulate the boundary matrix. We compare the different combinations through extensive experimental evaluation and identify optimization techniques that work well in practical situations. We also compare our software with various other publicly available libraries for persistent homology. article_processing_charge: No article_type: original author: - first_name: Ulrich full_name: Bauer, Ulrich last_name: Bauer - first_name: Michael full_name: Kerber, Michael last_name: Kerber - first_name: Jan full_name: Reininghaus, Jan last_name: Reininghaus - first_name: Hubert full_name: Wagner, Hubert id: 379CA8B8-F248-11E8-B48F-1D18A9856A87 last_name: Wagner citation: 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 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 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. 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. 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. short: U. Bauer, M. Kerber, J. Reininghaus, H. Wagner, Journal of Symbolic Computation 78 (2017) 76–90. date_created: 2018-12-11T11:51:59Z date_published: 2017-01-01T00:00:00Z date_updated: 2023-09-20T09:42:40Z day: '01' department: - _id: HeEd doi: 10.1016/j.jsc.2016.03.008 ec_funded: 1 external_id: isi: - '000384396000005' intvolume: ' 78' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1016/j.jsc.2016.03.008 month: '01' oa: 1 oa_version: Published Version page: 76 - 90 project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems publication: Journal of Symbolic Computation publication_identifier: issn: - ' 07477171' publication_status: published publisher: Academic Press publist_id: '5765' quality_controlled: '1' related_material: record: - id: '10894' relation: earlier_version status: public scopus_import: '1' status: public title: Phat - Persistent homology algorithms toolbox type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 78 year: '2017' ... --- _id: '1180' 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. article_processing_charge: No author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Imre full_name: Bárány, Imre last_name: Bárány - first_name: Sinai full_name: Robins, Sinai last_name: Robins citation: 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 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 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. 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. ista: Akopyan A, Bárány I, Robins S. 2017. Algebraic vertices of non-convex polyhedra. Advances in Mathematics. 308, 627–644. mla: Akopyan, Arseniy, et al. “Algebraic Vertices of Non-Convex Polyhedra.” Advances in Mathematics, vol. 308, Academic Press, 2017, pp. 627–44, doi:10.1016/j.aim.2016.12.026. short: A. Akopyan, I. Bárány, S. Robins, Advances in Mathematics 308 (2017) 627–644. date_created: 2018-12-11T11:50:34Z date_published: 2017-02-21T00:00:00Z date_updated: 2023-09-20T11:21:27Z day: '21' department: - _id: HeEd doi: 10.1016/j.aim.2016.12.026 ec_funded: 1 external_id: isi: - '000409292900015' intvolume: ' 308' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1508.07594 month: '02' oa: 1 oa_version: Submitted Version page: 627 - 644 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Advances in Mathematics publication_identifier: issn: - '00018708' publication_status: published publisher: Academic Press publist_id: '6173' quality_controlled: '1' scopus_import: '1' status: public title: Algebraic vertices of non-convex polyhedra type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 308 year: '2017' ... --- _id: '1173' abstract: - lang: eng text: We introduce the Voronoi functional of a triangulation of a finite set of points in the Euclidean plane and prove that among all geometric triangulations of the point set, the Delaunay triangulation maximizes the functional. This result neither extends to topological triangulations in the plane nor to geometric triangulations in three and higher dimensions. 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. article_processing_charge: No author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Alexey full_name: Glazyrin, Alexey last_name: Glazyrin - first_name: Oleg full_name: Musin, Oleg last_name: Musin - first_name: Anton full_name: Nikitenko, Anton id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87 last_name: Nikitenko orcid: 0000-0002-0659-3201 citation: ama: Edelsbrunner H, Glazyrin A, Musin O, Nikitenko A. The Voronoi functional is maximized by the Delaunay triangulation in the plane. Combinatorica. 2017;37(5):887-910. doi:10.1007/s00493-016-3308-y apa: Edelsbrunner, H., Glazyrin, A., Musin, O., & Nikitenko, A. (2017). The Voronoi functional is maximized by the Delaunay triangulation in the plane. Combinatorica. Springer. https://doi.org/10.1007/s00493-016-3308-y 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. 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. ista: Edelsbrunner H, Glazyrin A, Musin O, Nikitenko A. 2017. The Voronoi functional is maximized by the Delaunay triangulation in the plane. Combinatorica. 37(5), 887–910. mla: Edelsbrunner, Herbert, et al. “The Voronoi Functional Is Maximized by the Delaunay Triangulation in the Plane.” Combinatorica, vol. 37, no. 5, Springer, 2017, pp. 887–910, doi:10.1007/s00493-016-3308-y. short: H. Edelsbrunner, A. Glazyrin, O. Musin, A. Nikitenko, Combinatorica 37 (2017) 887–910. date_created: 2018-12-11T11:50:32Z date_published: 2017-10-01T00:00:00Z date_updated: 2023-09-20T11:23:53Z day: '01' department: - _id: HeEd doi: 10.1007/s00493-016-3308-y ec_funded: 1 external_id: isi: - '000418056000005' intvolume: ' 37' isi: 1 issue: '5' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1411.6337 month: '10' oa: 1 oa_version: Submitted Version page: 887 - 910 project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems publication: Combinatorica publication_identifier: issn: - '02099683' publication_status: published publisher: Springer publist_id: '6182' quality_controlled: '1' scopus_import: '1' status: public title: The Voronoi functional is maximized by the Delaunay triangulation in the plane type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 37 year: '2017' ... --- _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' ... --- _id: '833' 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. alternative_title: - LNCS article_processing_charge: No author: - first_name: Teresa full_name: Heiss, Teresa id: 4879BB4E-F248-11E8-B48F-1D18A9856A87 last_name: Heiss orcid: 0000-0002-1780-2689 - first_name: Hubert full_name: Wagner, Hubert id: 379CA8B8-F248-11E8-B48F-1D18A9856A87 last_name: Wagner citation: 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' 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. 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.' 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.' 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. short: T. Heiss, H. Wagner, in:, M. Felsberg, A. Heyden, N. Krüger (Eds.), Springer, 2017, pp. 397–409. conference: end_date: 2017-08-24 location: Ystad, Sweden name: 'CAIP: Computer Analysis of Images and Patterns' start_date: 2017-08-22 date_created: 2018-12-11T11:48:45Z date_published: 2017-07-28T00:00:00Z date_updated: 2023-09-26T16:10:03Z day: '28' department: - _id: HeEd doi: 10.1007/978-3-319-64689-3_32 editor: - first_name: Michael full_name: Felsberg, Michael last_name: Felsberg - first_name: Anders full_name: Heyden, Anders last_name: Heyden - first_name: Norbert full_name: Krüger, Norbert last_name: Krüger external_id: isi: - '000432085900032' intvolume: ' 10424' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1705.02045 month: '07' oa: 1 oa_version: Submitted Version page: 397 - 409 publication_identifier: issn: - '03029743' publication_status: published publisher: Springer publist_id: '6815' quality_controlled: '1' scopus_import: '1' status: public title: Streaming algorithm for Euler characteristic curves of multidimensional images type: conference user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 10424 year: '2017' ... --- _id: '84' abstract: - lang: eng 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. article_processing_charge: No author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Patrice full_name: Koehl, Patrice last_name: Koehl citation: 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 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. 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. ista: 'Edelsbrunner H, Koehl P. 2017.Computational topology for structural molecular biology. In: Handbook of Discrete and Computational Geometry, Third Edition. , 1709–1735.' mla: Edelsbrunner, Herbert, and Patrice Koehl. “Computational Topology for Structural Molecular Biology.” Handbook of Discrete and Computational Geometry, Third Edition, edited by Csaba Toth et al., Taylor & Francis, 2017, pp. 1709–35, doi:10.1201/9781315119601. 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. date_created: 2018-12-11T11:44:32Z date_published: 2017-11-09T00:00:00Z date_updated: 2023-10-16T11:15:22Z day: '09' department: - _id: HeEd doi: 10.1201/9781315119601 editor: - first_name: Csaba full_name: Toth, Csaba last_name: Toth - first_name: Joseph full_name: O'Rourke, Joseph last_name: O'Rourke - first_name: Jacob full_name: Goodman, Jacob last_name: Goodman language: - iso: eng month: '11' oa_version: None page: 1709 - 1735 publication: Handbook of Discrete and Computational Geometry, Third Edition publication_identifier: eisbn: - '9781498711425' publication_status: published publisher: Taylor & Francis publist_id: '7970' quality_controlled: '1' scopus_import: '1' series_title: Handbook of Discrete and Computational Geometry status: public title: Computational topology for structural molecular biology type: book_chapter user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2017' ... --- _id: '909' 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 &#xbd; cannot be achieved with any fixed number of extreme points. We conclude the paper with a few other inequalities related to the perimeter of a convex shape. article_processing_charge: No article_type: original author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Vladislav full_name: Vysotsky, Vladislav last_name: Vysotsky citation: 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 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. 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. 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. 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. short: A. Akopyan, V. Vysotsky, The American Mathematical Monthly 124 (2017) 588–596. date_created: 2018-12-11T11:49:09Z date_published: 2017-01-01T00:00:00Z date_updated: 2023-10-17T11:24:57Z day: '01' department: - _id: HeEd doi: 10.4169/amer.math.monthly.124.7.588 ec_funded: 1 external_id: arxiv: - '1605.07997' isi: - '000413947300002' intvolume: ' 124' isi: 1 issue: '7' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1605.07997 month: '01' oa: 1 oa_version: Submitted Version page: 588 - 596 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: The American Mathematical Monthly publication_identifier: issn: - '00029890' publication_status: published publisher: Mathematical Association of America publist_id: '6534' quality_controlled: '1' scopus_import: '1' status: public title: On the lengths of curves passing through boundary points of a planar convex shape type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 124 year: '2017' ... --- _id: '1149' 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.' 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." author: - first_name: Tomoyuki full_name: Miyaji, Tomoyuki last_name: Miyaji - first_name: Pawel full_name: Pilarczyk, Pawel id: 3768D56A-F248-11E8-B48F-1D18A9856A87 last_name: Pilarczyk - first_name: Marcio full_name: Gameiro, Marcio last_name: Gameiro - first_name: Hiroshi full_name: Kokubu, Hiroshi last_name: Kokubu - first_name: Konstantin full_name: Mischaikow, Konstantin last_name: Mischaikow citation: ama: Miyaji T, Pilarczyk P, Gameiro M, Kokubu H, Mischaikow K. A study of rigorous ODE integrators for multi scale set oriented computations. Applied Numerical Mathematics. 2016;107:34-47. doi:10.1016/j.apnum.2016.04.005 apa: Miyaji, T., Pilarczyk, P., Gameiro, M., Kokubu, H., & Mischaikow, K. (2016). A study of rigorous ODE integrators for multi scale set oriented computations. Applied Numerical Mathematics. Elsevier. https://doi.org/10.1016/j.apnum.2016.04.005 chicago: Miyaji, Tomoyuki, Pawel Pilarczyk, Marcio Gameiro, Hiroshi Kokubu, and Konstantin Mischaikow. “A Study of Rigorous ODE Integrators for Multi Scale Set Oriented Computations.” Applied Numerical Mathematics. Elsevier, 2016. https://doi.org/10.1016/j.apnum.2016.04.005. 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. 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. 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. date_created: 2018-12-11T11:50:25Z date_published: 2016-09-01T00:00:00Z date_updated: 2021-01-12T06:48:38Z day: '01' department: - _id: HeEd doi: 10.1016/j.apnum.2016.04.005 ec_funded: 1 intvolume: ' 107' language: - iso: eng month: '09' oa_version: None page: 34 - 47 project: - _id: 255F06BE-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '622033' name: Persistent Homology - Images, Data and Maps publication: Applied Numerical Mathematics publication_status: published publisher: Elsevier publist_id: '6209' quality_controlled: '1' scopus_import: 1 status: public title: A study of rigorous ODE integrators for multi scale set oriented computations type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 107 year: '2016' ... --- _id: '1216' abstract: - lang: eng 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.' 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" author: - first_name: Jens full_name: Kasten, Jens last_name: Kasten - first_name: Jan full_name: Reininghaus, Jan id: 4505473A-F248-11E8-B48F-1D18A9856A87 last_name: Reininghaus - first_name: Ingrid full_name: Hotz, Ingrid last_name: Hotz - first_name: Hans full_name: Hege, Hans last_name: Hege - first_name: Bernd full_name: Noack, Bernd last_name: Noack - first_name: Guillaume full_name: Daviller, Guillaume last_name: Daviller - first_name: Marek full_name: Morzyński, Marek last_name: Morzyński citation: 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. 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. 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. 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. short: J. Kasten, J. Reininghaus, I. Hotz, H. Hege, B. Noack, G. Daviller, M. Morzyński, Archives of Mechanics 68 (2016) 55–80. date_created: 2018-12-11T11:50:46Z date_published: 2016-01-01T00:00:00Z date_updated: 2021-01-12T06:49:09Z day: '01' department: - _id: HeEd intvolume: ' 68' issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: http://am.ippt.pan.pl/am/article/viewFile/v68p55/pdf month: '01' oa: 1 oa_version: Published Version page: 55 - 80 publication: Archives of Mechanics publication_status: published publisher: Polish Academy of Sciences Publishing House publist_id: '6118' quality_controlled: '1' scopus_import: 1 status: public title: Acceleration feature points of unsteady shear flows type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 68 year: '2016' ... --- _id: '1222' 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. 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. author: - first_name: Oleg full_name: Musin, Oleg last_name: Musin - first_name: Anton full_name: Nikitenko, Anton id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87 last_name: Nikitenko citation: 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 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 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. 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. ista: Musin O, Nikitenko A. 2016. Optimal packings of congruent circles on a square flat torus. Discrete & Computational Geometry. 55(1), 1–20. 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. date_created: 2018-12-11T11:50:48Z date_published: 2016-01-01T00:00:00Z date_updated: 2021-01-12T06:49:11Z day: '01' department: - _id: HeEd doi: 10.1007/s00454-015-9742-6 intvolume: ' 55' issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1212.0649 month: '01' oa: 1 oa_version: Preprint page: 1 - 20 publication: Discrete & Computational Geometry publication_status: published publisher: Springer publist_id: '6111' quality_controlled: '1' scopus_import: 1 status: public title: Optimal packings of congruent circles on a square flat torus type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 55 year: '2016' ... --- _id: '1237' 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.' 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.). alternative_title: - LNCS author: - first_name: Marek full_name: Krcál, Marek id: 33E21118-F248-11E8-B48F-1D18A9856A87 last_name: Krcál - first_name: Pawel full_name: Pilarczyk, Pawel id: 3768D56A-F248-11E8-B48F-1D18A9856A87 last_name: Pilarczyk citation: 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' 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' 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. 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.' ista: 'Krcál M, Pilarczyk P. 2016. Computation of cubical Steenrod squares. CTIC: Computational Topology in Image Context, LNCS, vol. 9667, 140–151.' mla: Krcál, Marek, and Pawel Pilarczyk. Computation of Cubical Steenrod Squares. Vol. 9667, Springer, 2016, pp. 140–51, doi:10.1007/978-3-319-39441-1_13. short: M. Krcál, P. Pilarczyk, in:, Springer, 2016, pp. 140–151. conference: end_date: 2016-06-17 location: Marseille, France name: 'CTIC: Computational Topology in Image Context' start_date: 2016-06-15 date_created: 2018-12-11T11:50:52Z date_published: 2016-06-02T00:00:00Z date_updated: 2021-01-12T06:49:18Z day: '02' department: - _id: UlWa - _id: HeEd doi: 10.1007/978-3-319-39441-1_13 ec_funded: 1 intvolume: ' 9667' language: - iso: eng month: '06' oa_version: None page: 140 - 151 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme - _id: 255F06BE-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '622033' name: Persistent Homology - Images, Data and Maps publication_status: published publisher: Springer publist_id: '6096' quality_controlled: '1' scopus_import: 1 status: public title: Computation of cubical Steenrod squares type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 9667 year: '2016' ... --- _id: '1252' abstract: - lang: eng text: We study the homomorphism induced in homology by a closed correspondence between topological spaces, using projections from the graph of the correspondence to its domain and codomain. We provide assumptions under which the homomorphism induced by an outer approximation of a continuous map coincides with the homomorphism induced in homology by the map. In contrast to more classical results we do not require that the projection to the domain have acyclic preimages. Moreover, we show that it is possible to retrieve correct homological information from a correspondence even if some data is missing or perturbed. Finally, we describe an application to combinatorial maps that are either outer approximations of continuous maps or reconstructions of such maps from a finite set of data points. 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." article_processing_charge: No article_type: original 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 - first_name: Pawel full_name: Pilarczyk, Pawel id: 3768D56A-F248-11E8-B48F-1D18A9856A87 last_name: Pilarczyk citation: 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 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 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. 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. 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. 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. short: S. Harker, H. Kokubu, K. Mischaikow, P. Pilarczyk, Proceedings of the American Mathematical Society 144 (2016) 1787–1801. date_created: 2018-12-11T11:50:57Z date_published: 2016-04-01T00:00:00Z date_updated: 2022-05-24T09:35:58Z day: '01' department: - _id: HeEd doi: 10.1090/proc/12812 ec_funded: 1 external_id: arxiv: - '1411.7563' intvolume: ' 144' issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1411.7563 month: '04' oa: 1 oa_version: Preprint page: 1787 - 1801 project: - _id: 255F06BE-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '622033' name: Persistent Homology - Images, Data and Maps publication: Proceedings of the American Mathematical Society publication_identifier: issn: - 1088-6826 publication_status: published publisher: American Mathematical Society publist_id: '6075' quality_controlled: '1' scopus_import: '1' status: public title: Inducing a map on homology from a correspondence type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 144 year: '2016' ... --- _id: '1254' abstract: - lang: eng 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/. 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." author: - first_name: Ali full_name: Golmakani, Ali last_name: Golmakani - first_name: Stefano full_name: Luzzatto, Stefano last_name: Luzzatto - first_name: Pawel full_name: Pilarczyk, Pawel id: 3768D56A-F248-11E8-B48F-1D18A9856A87 last_name: Pilarczyk citation: 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 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. 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. 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. short: A. Golmakani, S. Luzzatto, P. Pilarczyk, Experimental Mathematics 25 (2016) 116–124. date_created: 2018-12-11T11:50:58Z date_published: 2016-04-02T00:00:00Z date_updated: 2021-01-12T06:49:25Z day: '02' department: - _id: HeEd doi: 10.1080/10586458.2015.1048011 ec_funded: 1 intvolume: ' 25' issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1504.00116 month: '04' oa: 1 oa_version: Preprint page: 116 - 124 project: - _id: 255F06BE-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '622033' name: Persistent Homology - Images, Data and Maps publication: Experimental Mathematics publication_status: published publisher: Taylor and Francis publist_id: '6071' quality_controlled: '1' scopus_import: 1 status: public title: Uniform expansivity outside a critical neighborhood in the quadratic family type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 25 year: '2016' ... --- _id: '1272' abstract: - lang: eng text: We study different means to extend offsetting based on skeletal structures beyond the well-known constant-radius and mitered offsets supported by Voronoi diagrams and straight skeletons, for which the orthogonal distance of offset elements to their respective input elements is constant and uniform over all input elements. Our main contribution is a new geometric structure, called variable-radius Voronoi diagram, which supports the computation of variable-radius offsets, i.e., offsets whose distance to the input is allowed to vary along the input. We discuss properties of this structure and sketch a prototype implementation that supports the computation of variable-radius offsets based on this new variant of Voronoi diagrams. acknowledgement: 'This work was supported by Austrian Science Fund (FWF): P25816-N15.' author: - first_name: Martin full_name: Held, Martin last_name: Held - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Peter full_name: Palfrader, Peter last_name: Palfrader citation: 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 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. 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. 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. short: M. Held, S. Huber, P. Palfrader, Computer-Aided Design and Applications 13 (2016) 712–721. date_created: 2018-12-11T11:51:04Z date_published: 2016-09-02T00:00:00Z date_updated: 2021-01-12T06:49:32Z day: '02' ddc: - '004' - '516' department: - _id: HeEd doi: 10.1080/16864360.2016.1150718 file: - access_level: open_access checksum: c746f3a48edb62b588d92ea5d0fd2c0e content_type: application/pdf creator: system date_created: 2018-12-12T10:16:20Z date_updated: 2020-07-14T12:44:42Z file_id: '5206' file_name: IST-2016-694-v1+1_Generalized_offsetting_of_planar_structures_using_skeletons.pdf file_size: 1678369 relation: main_file file_date_updated: 2020-07-14T12:44:42Z has_accepted_license: '1' intvolume: ' 13' issue: '5' language: - iso: eng month: '09' oa: 1 oa_version: Published Version page: 712 - 721 publication: Computer-Aided Design and Applications publication_status: published publisher: Taylor and Francis publist_id: '6048' pubrep_id: '694' quality_controlled: '1' scopus_import: 1 status: public title: Generalized offsetting of planar structures using skeletons tmp: image: /images/cc_by_nc_nd.png legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) short: CC BY-NC-ND (4.0) type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 13 year: '2016' ... --- _id: '1295' abstract: - lang: eng text: Voronoi diagrams and Delaunay triangulations have been extensively used to represent and compute geometric features of point configurations. We introduce a generalization to poset diagrams and poset complexes, which contain order-k and degree-k Voronoi diagrams and their duals as special cases. Extending a result of Aurenhammer from 1990, we show how to construct poset diagrams as weighted Voronoi diagrams of average balls. acknowledgement: This work is partially supported by the Toposys project FP7-ICT-318493-STREP, and by ESF under the ACAT Research Network Programme. author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Mabel full_name: Iglesias Ham, Mabel id: 41B58C0C-F248-11E8-B48F-1D18A9856A87 last_name: Iglesias Ham citation: ama: 'Edelsbrunner H, Iglesias Ham M. Multiple covers with balls II: Weighted averages. Electronic Notes in Discrete Mathematics. 2016;54:169-174. doi:10.1016/j.endm.2016.09.030' apa: 'Edelsbrunner, H., & Iglesias Ham, M. (2016). Multiple covers with balls II: Weighted averages. Electronic Notes in Discrete Mathematics. Elsevier. https://doi.org/10.1016/j.endm.2016.09.030' chicago: 'Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls II: Weighted Averages.” Electronic Notes in Discrete Mathematics. Elsevier, 2016. https://doi.org/10.1016/j.endm.2016.09.030.' ieee: 'H. Edelsbrunner and M. Iglesias Ham, “Multiple covers with balls II: Weighted averages,” Electronic Notes in Discrete Mathematics, vol. 54. Elsevier, pp. 169–174, 2016.' ista: 'Edelsbrunner H, Iglesias Ham M. 2016. Multiple covers with balls II: Weighted averages. Electronic Notes in Discrete Mathematics. 54, 169–174.' mla: 'Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls II: Weighted Averages.” Electronic Notes in Discrete Mathematics, vol. 54, Elsevier, 2016, pp. 169–74, doi:10.1016/j.endm.2016.09.030.' short: H. Edelsbrunner, M. Iglesias Ham, Electronic Notes in Discrete Mathematics 54 (2016) 169–174. date_created: 2018-12-11T11:51:12Z date_published: 2016-10-01T00:00:00Z date_updated: 2021-01-12T06:49:41Z day: '01' department: - _id: HeEd doi: 10.1016/j.endm.2016.09.030 ec_funded: 1 intvolume: ' 54' language: - iso: eng month: '10' oa_version: None page: 169 - 174 project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems publication: Electronic Notes in Discrete Mathematics publication_status: published publisher: Elsevier publist_id: '5976' quality_controlled: '1' scopus_import: 1 status: public title: 'Multiple covers with balls II: Weighted averages' type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 54 year: '2016' ... --- _id: '1292' abstract: - lang: eng text: We give explicit formulas and algorithms for the computation of the Thurston–Bennequin invariant of a nullhomologous Legendrian knot on a page of a contact open book and on Heegaard surfaces in convex position. Furthermore, we extend the results to rationally nullhomologous knots in arbitrary 3-manifolds. acknowledgement: "The authors are veryg rateful to Hansj ̈org Geiges \r\nfor fruitful discussions and advice and Christian Evers for helpful remarks on a draft version." author: - first_name: Sebastian full_name: Durst, Sebastian last_name: Durst - first_name: Marc full_name: Kegel, Marc last_name: Kegel - first_name: Mirko D full_name: Klukas, Mirko D id: 34927512-F248-11E8-B48F-1D18A9856A87 last_name: Klukas citation: ama: Durst S, Kegel M, Klukas MD. Computing the Thurston–Bennequin invariant in open books. Acta Mathematica Hungarica. 2016;150(2):441-455. doi:10.1007/s10474-016-0648-4 apa: Durst, S., Kegel, M., & Klukas, M. D. (2016). Computing the Thurston–Bennequin invariant in open books. Acta Mathematica Hungarica. Springer. https://doi.org/10.1007/s10474-016-0648-4 chicago: Durst, Sebastian, Marc Kegel, and Mirko D Klukas. “Computing the Thurston–Bennequin Invariant in Open Books.” Acta Mathematica Hungarica. Springer, 2016. https://doi.org/10.1007/s10474-016-0648-4. ieee: S. Durst, M. Kegel, and M. D. Klukas, “Computing the Thurston–Bennequin invariant in open books,” Acta Mathematica Hungarica, vol. 150, no. 2. Springer, pp. 441–455, 2016. ista: Durst S, Kegel M, Klukas MD. 2016. Computing the Thurston–Bennequin invariant in open books. Acta Mathematica Hungarica. 150(2), 441–455. mla: Durst, Sebastian, et al. “Computing the Thurston–Bennequin Invariant in Open Books.” Acta Mathematica Hungarica, vol. 150, no. 2, Springer, 2016, pp. 441–55, doi:10.1007/s10474-016-0648-4. short: S. Durst, M. Kegel, M.D. Klukas, Acta Mathematica Hungarica 150 (2016) 441–455. date_created: 2018-12-11T11:51:11Z date_published: 2016-12-01T00:00:00Z date_updated: 2021-01-12T06:49:40Z day: '01' department: - _id: HeEd doi: 10.1007/s10474-016-0648-4 intvolume: ' 150' issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1605.00794 month: '12' oa: 1 oa_version: Preprint page: 441 - 455 publication: Acta Mathematica Hungarica publication_status: published publisher: Springer publist_id: '6023' quality_controlled: '1' scopus_import: 1 status: public title: Computing the Thurston–Bennequin invariant in open books type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 150 year: '2016' ... --- _id: '1330' abstract: - lang: eng text: In this paper we investigate the existence of closed billiard trajectories in not necessarily smooth convex bodies. In particular, we show that if a body K ⊂ Rd has the property that the tangent cone of every non-smooth point q ∉ ∂K is acute (in a certain sense), then there is a closed billiard trajectory in K. acknowledgement: Supported by People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement n°[291734]. Supported by the Russian Foundation for Basic Research grant 15-31-20403 (mol a ved), by the Russian Foundation for Basic Research grant 15-01-99563 A, in part by the Moebius Contest Foundation for Young Scientists, and in part by the Simons Foundation. author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Alexey full_name: Balitskiy, Alexey last_name: Balitskiy citation: ama: Akopyan A, Balitskiy A. Billiards in convex bodies with acute angles. Israel Journal of Mathematics. 2016;216(2):833-845. doi:10.1007/s11856-016-1429-z apa: Akopyan, A., & Balitskiy, A. (2016). Billiards in convex bodies with acute angles. Israel Journal of Mathematics. Springer. https://doi.org/10.1007/s11856-016-1429-z chicago: Akopyan, Arseniy, and Alexey Balitskiy. “Billiards in Convex Bodies with Acute Angles.” Israel Journal of Mathematics. Springer, 2016. https://doi.org/10.1007/s11856-016-1429-z. ieee: A. Akopyan and A. Balitskiy, “Billiards in convex bodies with acute angles,” Israel Journal of Mathematics, vol. 216, no. 2. Springer, pp. 833–845, 2016. ista: Akopyan A, Balitskiy A. 2016. Billiards in convex bodies with acute angles. Israel Journal of Mathematics. 216(2), 833–845. mla: Akopyan, Arseniy, and Alexey Balitskiy. “Billiards in Convex Bodies with Acute Angles.” Israel Journal of Mathematics, vol. 216, no. 2, Springer, 2016, pp. 833–45, doi:10.1007/s11856-016-1429-z. short: A. Akopyan, A. Balitskiy, Israel Journal of Mathematics 216 (2016) 833–845. date_created: 2018-12-11T11:51:24Z date_published: 2016-10-15T00:00:00Z date_updated: 2021-01-12T06:49:56Z day: '15' department: - _id: HeEd doi: 10.1007/s11856-016-1429-z ec_funded: 1 intvolume: ' 216' issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1506.06014 month: '10' oa: 1 oa_version: Preprint page: 833 - 845 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Israel Journal of Mathematics publication_status: published publisher: Springer publist_id: '5938' quality_controlled: '1' scopus_import: 1 status: public title: Billiards in convex bodies with acute angles type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 216 year: '2016' ... --- _id: '1360' abstract: - lang: eng text: 'We apply the technique of Károly Bezdek and Daniel Bezdek to study billiard trajectories in convex bodies, when the length is measured with a (possibly asymmetric) norm. We prove a lower bound for the length of the shortest closed billiard trajectory, related to the non-symmetric Mahler problem. With this technique we are able to give short and elementary proofs to some known results. ' acknowledgement: The first and third authors were supported by the Dynasty Foundation. The first, second and third authors were supported by the Russian Foundation for Basic Re- search grant 15-31-20403 (mol a ved). article_processing_charge: No author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Alexey full_name: Balitskiy, Alexey last_name: Balitskiy - first_name: Roman full_name: Karasev, Roman last_name: Karasev - first_name: Anastasia full_name: Sharipova, Anastasia last_name: Sharipova citation: ama: Akopyan A, Balitskiy A, Karasev R, Sharipova A. Elementary approach to closed billiard trajectories in asymmetric normed spaces. Proceedings of the American Mathematical Society. 2016;144(10):4501-4513. doi:10.1090/proc/13062 apa: Akopyan, A., Balitskiy, A., Karasev, R., & Sharipova, A. (2016). Elementary approach to closed billiard trajectories in asymmetric normed spaces. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/13062 chicago: Akopyan, Arseniy, Alexey Balitskiy, Roman Karasev, and Anastasia Sharipova. “Elementary Approach to Closed Billiard Trajectories in Asymmetric Normed Spaces.” Proceedings of the American Mathematical Society. American Mathematical Society, 2016. https://doi.org/10.1090/proc/13062. ieee: A. Akopyan, A. Balitskiy, R. Karasev, and A. Sharipova, “Elementary approach to closed billiard trajectories in asymmetric normed spaces,” Proceedings of the American Mathematical Society, vol. 144, no. 10. American Mathematical Society, pp. 4501–4513, 2016. ista: Akopyan A, Balitskiy A, Karasev R, Sharipova A. 2016. Elementary approach to closed billiard trajectories in asymmetric normed spaces. Proceedings of the American Mathematical Society. 144(10), 4501–4513. mla: Akopyan, Arseniy, et al. “Elementary Approach to Closed Billiard Trajectories in Asymmetric Normed Spaces.” Proceedings of the American Mathematical Society, vol. 144, no. 10, American Mathematical Society, 2016, pp. 4501–13, doi:10.1090/proc/13062. short: A. Akopyan, A. Balitskiy, R. Karasev, A. Sharipova, Proceedings of the American Mathematical Society 144 (2016) 4501–4513. date_created: 2018-12-11T11:51:34Z date_published: 2016-10-01T00:00:00Z date_updated: 2021-01-12T06:50:09Z day: '01' department: - _id: HeEd doi: 10.1090/proc/13062 ec_funded: 1 intvolume: ' 144' issue: '10' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1401.0442 month: '10' oa: 1 oa_version: Preprint page: 4501 - 4513 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Proceedings of the American Mathematical Society publication_status: published publisher: American Mathematical Society publist_id: '5885' quality_controlled: '1' scopus_import: 1 status: public title: Elementary approach to closed billiard trajectories in asymmetric normed spaces type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 144 year: '2016' ... --- _id: '1408' abstract: - lang: eng text: 'The concept of well group in a special but important case captures homological properties of the zero set of a continuous map (Formula presented.) on a compact space K that are invariant with respect to perturbations of f. The perturbations are arbitrary continuous maps within (Formula presented.) distance r from f for a given (Formula presented.). The main drawback of the approach is that the computability of well groups was shown only when (Formula presented.) or (Formula presented.). Our contribution to the theory of well groups is twofold: on the one hand we improve on the computability issue, but on the other hand we present a range of examples where the well groups are incomplete invariants, that is, fail to capture certain important robust properties of the zero set. For the first part, we identify a computable subgroup of the well group that is obtained by cap product with the pullback of the orientation of (Formula presented.) by f. In other words, well groups can be algorithmically approximated from below. When f is smooth and (Formula presented.), our approximation of the (Formula presented.)th well group is exact. For the second part, we find examples of maps (Formula presented.) with all well groups isomorphic but whose perturbations have different zero sets. We discuss on a possible replacement of the well groups of vector valued maps by an invariant of a better descriptive power and computability status.' acknowledgement: 'Open access funding provided by Institute of Science and Technology (IST Austria). ' article_processing_charge: Yes (via OA deal) author: - first_name: Peter full_name: Franek, Peter id: 473294AE-F248-11E8-B48F-1D18A9856A87 last_name: Franek - first_name: Marek full_name: Krcál, Marek id: 33E21118-F248-11E8-B48F-1D18A9856A87 last_name: Krcál citation: ama: Franek P, Krcál M. On computability and triviality of well groups. Discrete & Computational Geometry. 2016;56(1):126-164. doi:10.1007/s00454-016-9794-2 apa: Franek, P., & Krcál, M. (2016). On computability and triviality of well groups. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-016-9794-2 chicago: Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well Groups.” Discrete & Computational Geometry. Springer, 2016. https://doi.org/10.1007/s00454-016-9794-2. ieee: P. Franek and M. Krcál, “On computability and triviality of well groups,” Discrete & Computational Geometry, vol. 56, no. 1. Springer, pp. 126–164, 2016. ista: Franek P, Krcál M. 2016. On computability and triviality of well groups. Discrete & Computational Geometry. 56(1), 126–164. mla: Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well Groups.” Discrete & Computational Geometry, vol. 56, no. 1, Springer, 2016, pp. 126–64, doi:10.1007/s00454-016-9794-2. short: P. Franek, M. Krcál, Discrete & Computational Geometry 56 (2016) 126–164. date_created: 2018-12-11T11:51:51Z date_published: 2016-07-01T00:00:00Z date_updated: 2023-02-23T10:02:11Z day: '01' ddc: - '510' department: - _id: UlWa - _id: HeEd doi: 10.1007/s00454-016-9794-2 ec_funded: 1 file: - access_level: open_access checksum: e0da023abf6b72abd8c6a8c76740d53c content_type: application/pdf creator: system date_created: 2018-12-12T10:10:55Z date_updated: 2020-07-14T12:44:53Z file_id: '4846' file_name: IST-2016-614-v1+1_s00454-016-9794-2.pdf file_size: 905303 relation: main_file file_date_updated: 2020-07-14T12:44:53Z has_accepted_license: '1' intvolume: ' 56' issue: '1' language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: 126 - 164 project: - _id: 25F8B9BC-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: M01980 name: Robust invariants of Nonlinear Systems - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Discrete & Computational Geometry publication_status: published publisher: Springer publist_id: '5799' pubrep_id: '614' quality_controlled: '1' related_material: record: - id: '1510' relation: earlier_version status: public scopus_import: 1 status: public title: On computability and triviality of well groups tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 56 year: '2016' ... --- _id: '1289' abstract: - lang: eng text: 'Aiming at the automatic diagnosis of tumors using narrow band imaging (NBI) magnifying endoscopic (ME) images of the stomach, we combine methods from image processing, topology, geometry, and machine learning to classify patterns into three classes: oval, tubular and irregular. Training the algorithm on a small number of images of each type, we achieve a high rate of correct classifications. The analysis of the learning algorithm reveals that a handful of geometric and topological features are responsible for the overwhelming majority of decisions.' article_processing_charge: No author: - first_name: Olga full_name: Dunaeva, Olga last_name: Dunaeva - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Anton full_name: Lukyanov, Anton last_name: Lukyanov - first_name: Michael full_name: Machin, Michael last_name: Machin - first_name: Daria full_name: Malkova, Daria last_name: Malkova - first_name: Roman full_name: Kuvaev, Roman last_name: Kuvaev - first_name: Sergey full_name: Kashin, Sergey last_name: Kashin citation: ama: Dunaeva O, Edelsbrunner H, Lukyanov A, et al. The classification of endoscopy images with persistent homology. Pattern Recognition Letters. 2016;83(1):13-22. doi:10.1016/j.patrec.2015.12.012 apa: Dunaeva, O., Edelsbrunner, H., Lukyanov, A., Machin, M., Malkova, D., Kuvaev, R., & Kashin, S. (2016). The classification of endoscopy images with persistent homology. Pattern Recognition Letters. Elsevier. https://doi.org/10.1016/j.patrec.2015.12.012 chicago: Dunaeva, Olga, Herbert Edelsbrunner, Anton Lukyanov, Michael Machin, Daria Malkova, Roman Kuvaev, and Sergey Kashin. “The Classification of Endoscopy Images with Persistent Homology.” Pattern Recognition Letters. Elsevier, 2016. https://doi.org/10.1016/j.patrec.2015.12.012. ieee: O. Dunaeva et al., “The classification of endoscopy images with persistent homology,” Pattern Recognition Letters, vol. 83, no. 1. Elsevier, pp. 13–22, 2016. ista: Dunaeva O, Edelsbrunner H, Lukyanov A, Machin M, Malkova D, Kuvaev R, Kashin S. 2016. The classification of endoscopy images with persistent homology. Pattern Recognition Letters. 83(1), 13–22. mla: Dunaeva, Olga, et al. “The Classification of Endoscopy Images with Persistent Homology.” Pattern Recognition Letters, vol. 83, no. 1, Elsevier, 2016, pp. 13–22, doi:10.1016/j.patrec.2015.12.012. short: O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, D. Malkova, R. Kuvaev, S. Kashin, Pattern Recognition Letters 83 (2016) 13–22. date_created: 2018-12-11T11:51:10Z date_published: 2016-11-01T00:00:00Z date_updated: 2023-02-23T10:04:40Z day: '01' ddc: - '004' - '514' department: - _id: HeEd doi: 10.1016/j.patrec.2015.12.012 file: - access_level: open_access checksum: 33458bbb8c32a339e1adeca6d5a1112d content_type: application/pdf creator: dernst date_created: 2019-04-17T07:55:51Z date_updated: 2020-07-14T12:44:42Z file_id: '6334' file_name: 2016-Edelsbrunner_The_classification.pdf file_size: 1921113 relation: main_file file_date_updated: 2020-07-14T12:44:42Z has_accepted_license: '1' intvolume: ' 83' issue: '1' language: - iso: eng month: '11' oa: 1 oa_version: Submitted Version page: 13 - 22 publication: Pattern Recognition Letters publication_status: published publisher: Elsevier publist_id: '6027' pubrep_id: '975' quality_controlled: '1' related_material: record: - id: '1568' relation: earlier_version status: public scopus_import: 1 status: public title: The classification of endoscopy images with persistent homology tmp: image: /images/cc_by_nc_nd.png legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) short: CC BY-NC-ND (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 83 year: '2016' ... --- _id: '1617' abstract: - lang: eng text: 'We study the discrepancy of jittered sampling sets: such a set P⊂ [0,1]d is generated for fixed m∈ℕ by partitioning [0,1]d into md axis aligned cubes of equal measure and placing a random point inside each of the N=md cubes. We prove that, for N sufficiently large, 1/10 d/N1/2+1/2d ≤EDN∗(P)≤ √d(log N) 1/2/N1/2+1/2d, where the upper bound with an unspecified constant Cd was proven earlier by Beck. Our proof makes crucial use of the sharp Dvoretzky-Kiefer-Wolfowitz inequality and a suitably taylored Bernstein inequality; we have reasons to believe that the upper bound has the sharp scaling in N. Additional heuristics suggest that jittered sampling should be able to improve known bounds on the inverse of the star-discrepancy in the regime N≳dd. We also prove a partition principle showing that every partition of [0,1]d combined with a jittered sampling construction gives rise to a set whose expected squared L2-discrepancy is smaller than that of purely random points.' acknowledgement: We are grateful to the referee whose suggestions greatly improved the quality and clarity of the exposition. author: - first_name: Florian full_name: Pausinger, Florian id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87 last_name: Pausinger orcid: 0000-0002-8379-3768 - first_name: Stefan full_name: Steinerberger, Stefan last_name: Steinerberger citation: ama: Pausinger F, Steinerberger S. On the discrepancy of jittered sampling. Journal of Complexity. 2016;33:199-216. doi:10.1016/j.jco.2015.11.003 apa: Pausinger, F., & Steinerberger, S. (2016). On the discrepancy of jittered sampling. Journal of Complexity. Academic Press. https://doi.org/10.1016/j.jco.2015.11.003 chicago: Pausinger, Florian, and Stefan Steinerberger. “On the Discrepancy of Jittered Sampling.” Journal of Complexity. Academic Press, 2016. https://doi.org/10.1016/j.jco.2015.11.003. ieee: F. Pausinger and S. Steinerberger, “On the discrepancy of jittered sampling,” Journal of Complexity, vol. 33. Academic Press, pp. 199–216, 2016. ista: Pausinger F, Steinerberger S. 2016. On the discrepancy of jittered sampling. Journal of Complexity. 33, 199–216. mla: Pausinger, Florian, and Stefan Steinerberger. “On the Discrepancy of Jittered Sampling.” Journal of Complexity, vol. 33, Academic Press, 2016, pp. 199–216, doi:10.1016/j.jco.2015.11.003. short: F. Pausinger, S. Steinerberger, Journal of Complexity 33 (2016) 199–216. date_created: 2018-12-11T11:53:03Z date_published: 2016-04-01T00:00:00Z date_updated: 2021-01-12T06:52:02Z day: '01' department: - _id: HeEd doi: 10.1016/j.jco.2015.11.003 intvolume: ' 33' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1510.00251 month: '04' oa: 1 oa_version: Submitted Version page: 199 - 216 publication: Journal of Complexity publication_status: published publisher: Academic Press publist_id: '5549' quality_controlled: '1' scopus_import: 1 status: public title: On the discrepancy of jittered sampling type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 33 year: '2016' ... --- _id: '5806' abstract: - lang: eng text: Although the concept of functional plane for naive plane is studied and reported in the literature in great detail, no similar study is yet found for naive sphere. This article exposes the first study in this line, opening up further prospects of analyzing the topological properties of sphere in the discrete space. We show that each quadraginta octant Q of a naive sphere forms a bijection with its projected pixel set on a unique coordinate plane, which thereby serves as the functional plane of Q, and hence gives rise to merely mono-jumps during back projection. The other two coordinate planes serve as para-functional and dia-functional planes for Q, as the former is ‘mono-jumping’ but not bijective, whereas the latter holds neither of the two. Owing to this, the quadraginta octants form symmetry groups and subgroups with equivalent jump conditions. We also show a potential application in generating a special class of discrete 3D circles based on back projection and jump bridging by Steiner voxels. A circle in this class possesses 4-symmetry, uniqueness, and bounded distance from the underlying real sphere and real plane. alternative_title: - LNCS article_processing_charge: No author: - first_name: Ranita full_name: Biswas, Ranita id: 3C2B033E-F248-11E8-B48F-1D18A9856A87 last_name: Biswas orcid: 0000-0002-5372-7890 - first_name: Partha full_name: Bhowmick, Partha last_name: Bhowmick citation: ama: 'Biswas R, Bhowmick P. On functionality of quadraginta octants of naive sphere with application to circle drawing. In: Discrete Geometry for Computer Imagery. Vol 9647. Cham: Springer Nature; 2016:256-267. doi:10.1007/978-3-319-32360-2_20' apa: 'Biswas, R., & Bhowmick, P. (2016). On functionality of quadraginta octants of naive sphere with application to circle drawing. In Discrete Geometry for Computer Imagery (Vol. 9647, pp. 256–267). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-32360-2_20' chicago: 'Biswas, Ranita, and Partha Bhowmick. “On Functionality of Quadraginta Octants of Naive Sphere with Application to Circle Drawing.” In Discrete Geometry for Computer Imagery, 9647:256–67. Cham: Springer Nature, 2016. https://doi.org/10.1007/978-3-319-32360-2_20.' ieee: R. Biswas and P. Bhowmick, “On functionality of quadraginta octants of naive sphere with application to circle drawing,” in Discrete Geometry for Computer Imagery, Nantes, France, 2016, vol. 9647, pp. 256–267. ista: 'Biswas R, Bhowmick P. 2016. On functionality of quadraginta octants of naive sphere with application to circle drawing. Discrete Geometry for Computer Imagery. DGCI: International Conference on Discrete Geometry for Computer Imagery, LNCS, vol. 9647, 256–267.' mla: Biswas, Ranita, and Partha Bhowmick. “On Functionality of Quadraginta Octants of Naive Sphere with Application to Circle Drawing.” Discrete Geometry for Computer Imagery, vol. 9647, Springer Nature, 2016, pp. 256–67, doi:10.1007/978-3-319-32360-2_20. short: R. Biswas, P. Bhowmick, in:, Discrete Geometry for Computer Imagery, Springer Nature, Cham, 2016, pp. 256–267. conference: end_date: 2016-04-20 location: Nantes, France name: 'DGCI: International Conference on Discrete Geometry for Computer Imagery' start_date: 2016-04-18 date_created: 2019-01-08T20:44:37Z date_published: 2016-04-09T00:00:00Z date_updated: 2022-01-28T08:10:11Z day: '09' department: - _id: HeEd doi: 10.1007/978-3-319-32360-2_20 extern: '1' intvolume: ' 9647' language: - iso: eng month: '04' oa_version: None page: 256-267 place: Cham publication: Discrete Geometry for Computer Imagery publication_identifier: eisbn: - 978-3-319-32360-2 isbn: - 978-3-319-32359-6 issn: - 0302-9743 - 1611-3349 publication_status: published publisher: Springer Nature quality_controlled: '1' status: public title: On functionality of quadraginta octants of naive sphere with application to circle drawing type: conference user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 volume: 9647 year: '2016' ... --- _id: '5805' abstract: - lang: eng text: Discretization of sphere in the integer space follows a particular discretization scheme, which, in principle, conforms to some topological model. This eventually gives rise to interesting topological properties of a discrete spherical surface, which need to be investigated for its analytical characterization. This paper presents some novel results on the local topological properties of the naive model of discrete sphere. They follow from the bijection of each quadraginta octant of naive sphere with its projection map called f -map on the corresponding functional plane and from the characterization of certain jumps in the f-map. As an application, we have shown how these properties can be used in designing an efficient reconstruction algorithm for a naive spherical surface from an input voxel set when it is sparse or noisy. alternative_title: - LNCS article_processing_charge: No author: - first_name: Nabhasmita full_name: Sen, Nabhasmita last_name: Sen - first_name: Ranita full_name: Biswas, Ranita id: 3C2B033E-F248-11E8-B48F-1D18A9856A87 last_name: Biswas orcid: 0000-0002-5372-7890 - first_name: Partha full_name: Bhowmick, Partha last_name: Bhowmick citation: ama: 'Sen N, Biswas R, Bhowmick P. On some local topological properties of naive discrete sphere. In: Computational Topology in Image Context. Vol 9667. Cham: Springer Nature; 2016:253-264. doi:10.1007/978-3-319-39441-1_23' apa: 'Sen, N., Biswas, R., & Bhowmick, P. (2016). On some local topological properties of naive discrete sphere. In Computational Topology in Image Context (Vol. 9667, pp. 253–264). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-39441-1_23' chicago: 'Sen, Nabhasmita, Ranita Biswas, and Partha Bhowmick. “On Some Local Topological Properties of Naive Discrete Sphere.” In Computational Topology in Image Context, 9667:253–64. Cham: Springer Nature, 2016. https://doi.org/10.1007/978-3-319-39441-1_23.' ieee: 'N. Sen, R. Biswas, and P. Bhowmick, “On some local topological properties of naive discrete sphere,” in Computational Topology in Image Context, vol. 9667, Cham: Springer Nature, 2016, pp. 253–264.' ista: 'Sen N, Biswas R, Bhowmick P. 2016.On some local topological properties of naive discrete sphere. In: Computational Topology in Image Context. LNCS, vol. 9667, 253–264.' mla: Sen, Nabhasmita, et al. “On Some Local Topological Properties of Naive Discrete Sphere.” Computational Topology in Image Context, vol. 9667, Springer Nature, 2016, pp. 253–64, doi:10.1007/978-3-319-39441-1_23. short: N. Sen, R. Biswas, P. Bhowmick, in:, Computational Topology in Image Context, Springer Nature, Cham, 2016, pp. 253–264. conference: end_date: 2016-06-17 location: Marseille, France name: 'CTIC: Computational Topology in Image Context' start_date: 2016-06-15 date_created: 2019-01-08T20:44:24Z date_published: 2016-06-02T00:00:00Z date_updated: 2022-01-28T08:01:22Z day: '02' department: - _id: HeEd doi: 10.1007/978-3-319-39441-1_23 extern: '1' intvolume: ' 9667' language: - iso: eng month: '06' oa_version: None page: 253-264 place: Cham publication: Computational Topology in Image Context publication_identifier: eisbn: - 978-3-319-39441-1 eissn: - 1611-3349 isbn: - 978-3-319-39440-4 issn: - 0302-9743 publication_status: published publisher: Springer Nature quality_controlled: '1' status: public title: On some local topological properties of naive discrete sphere type: book_chapter user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 volume: 9667 year: '2016' ... --- _id: '5809' abstract: - lang: eng text: A discrete spherical circle is a topologically well-connected 3D circle in the integer space, which belongs to a discrete sphere as well as a discrete plane. It is one of the most important 3D geometric primitives, but has not possibly yet been studied up to its merit. This paper is a maiden exposition of some of its elementary properties, which indicates a sense of its profound theoretical prospects in the framework of digital geometry. We have shown how different types of discretization can lead to forbidden and admissible classes, when one attempts to define the discretization of a spherical circle in terms of intersection between a discrete sphere and a discrete plane. Several fundamental theoretical results have been presented, the algorithm for construction of discrete spherical circles has been discussed, and some test results have been furnished to demonstrate its practicality and usefulness. article_processing_charge: No author: - first_name: Ranita full_name: Biswas, Ranita id: 3C2B033E-F248-11E8-B48F-1D18A9856A87 last_name: Biswas orcid: 0000-0002-5372-7890 - first_name: Partha full_name: Bhowmick, Partha last_name: Bhowmick - first_name: Valentin E. full_name: Brimkov, Valentin E. last_name: Brimkov citation: ama: 'Biswas R, Bhowmick P, Brimkov VE. On the connectivity and smoothness of discrete spherical circles. In: Combinatorial Image Analysis. Vol 9448. Cham: Springer Nature; 2016:86-100. doi:10.1007/978-3-319-26145-4_7' apa: 'Biswas, R., Bhowmick, P., & Brimkov, V. E. (2016). On the connectivity and smoothness of discrete spherical circles. In Combinatorial image analysis (Vol. 9448, pp. 86–100). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-26145-4_7' chicago: 'Biswas, Ranita, Partha Bhowmick, and Valentin E. Brimkov. “On the Connectivity and Smoothness of Discrete Spherical Circles.” In Combinatorial Image Analysis, 9448:86–100. Cham: Springer Nature, 2016. https://doi.org/10.1007/978-3-319-26145-4_7.' ieee: 'R. Biswas, P. Bhowmick, and V. E. Brimkov, “On the connectivity and smoothness of discrete spherical circles,” in Combinatorial image analysis, vol. 9448, Cham: Springer Nature, 2016, pp. 86–100.' ista: 'Biswas R, Bhowmick P, Brimkov VE. 2016.On the connectivity and smoothness of discrete spherical circles. In: Combinatorial image analysis. vol. 9448, 86–100.' mla: Biswas, Ranita, et al. “On the Connectivity and Smoothness of Discrete Spherical Circles.” Combinatorial Image Analysis, vol. 9448, Springer Nature, 2016, pp. 86–100, doi:10.1007/978-3-319-26145-4_7. short: R. Biswas, P. Bhowmick, V.E. Brimkov, in:, Combinatorial Image Analysis, Springer Nature, Cham, 2016, pp. 86–100. conference: end_date: 2015-11-27 location: Kolkata, India name: 'IWCIA: International Workshop on Combinatorial Image Analysis' start_date: 2015-11-24 date_created: 2019-01-08T20:45:19Z date_published: 2016-01-06T00:00:00Z date_updated: 2022-01-28T08:13:03Z day: '06' department: - _id: HeEd doi: 10.1007/978-3-319-26145-4_7 extern: '1' intvolume: ' 9448' language: - iso: eng month: '01' oa_version: None page: 86-100 place: Cham publication: Combinatorial image analysis publication_identifier: eisbn: - 978-3-319-26145-4 eissn: - 1611-3349 isbn: - 978-3-319-26144-7 issn: - 0302-9743 publication_status: published publisher: Springer Nature quality_controlled: '1' status: public title: On the connectivity and smoothness of discrete spherical circles type: book_chapter user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 volume: 9448 year: '2016' ... --- _id: '1662' abstract: - lang: eng text: We introduce a modification of the classic notion of intrinsic volume using persistence moments of height functions. Evaluating the modified first intrinsic volume on digital approximations of a compact body with smoothly embedded boundary in Rn, we prove convergence to the first intrinsic volume of the body as the resolution of the approximation improves. We have weaker results for the other modified intrinsic volumes, proving they converge to the corresponding intrinsic volumes of the n-dimensional unit ball. acknowledgement: "This research is partially supported by the Toposys project FP7-ICT-318493-STREP, and by ESF under the ACAT Research Network Programme.\r\nBoth authors thank Anne Marie Svane for her comments on an early version of this paper. The second author wishes to thank Eva B. Vedel Jensen and Markus Kiderlen from Aarhus University for enlightening discussions and their kind hospitality during a visit of their department in 2014." author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Florian full_name: Pausinger, Florian id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87 last_name: Pausinger orcid: 0000-0002-8379-3768 citation: ama: Edelsbrunner H, Pausinger F. Approximation and convergence of the intrinsic volume. Advances in Mathematics. 2016;287:674-703. doi:10.1016/j.aim.2015.10.004 apa: Edelsbrunner, H., & Pausinger, F. (2016). Approximation and convergence of the intrinsic volume. Advances in Mathematics. Academic Press. https://doi.org/10.1016/j.aim.2015.10.004 chicago: Edelsbrunner, Herbert, and Florian Pausinger. “Approximation and Convergence of the Intrinsic Volume.” Advances in Mathematics. Academic Press, 2016. https://doi.org/10.1016/j.aim.2015.10.004. ieee: H. Edelsbrunner and F. Pausinger, “Approximation and convergence of the intrinsic volume,” Advances in Mathematics, vol. 287. Academic Press, pp. 674–703, 2016. ista: Edelsbrunner H, Pausinger F. 2016. Approximation and convergence of the intrinsic volume. Advances in Mathematics. 287, 674–703. mla: Edelsbrunner, Herbert, and Florian Pausinger. “Approximation and Convergence of the Intrinsic Volume.” Advances in Mathematics, vol. 287, Academic Press, 2016, pp. 674–703, doi:10.1016/j.aim.2015.10.004. short: H. Edelsbrunner, F. Pausinger, Advances in Mathematics 287 (2016) 674–703. date_created: 2018-12-11T11:53:20Z date_published: 2016-01-10T00:00:00Z date_updated: 2023-09-07T11:41:25Z day: '10' ddc: - '004' department: - _id: HeEd doi: 10.1016/j.aim.2015.10.004 ec_funded: 1 file: - access_level: open_access checksum: f8869ec110c35c852ef6a37425374af7 content_type: application/pdf creator: system date_created: 2018-12-12T10:12:10Z date_updated: 2020-07-14T12:45:10Z file_id: '4928' file_name: IST-2017-774-v1+1_2016-J-03-FirstIntVolume.pdf file_size: 248985 relation: main_file file_date_updated: 2020-07-14T12:45:10Z has_accepted_license: '1' intvolume: ' 287' language: - iso: eng month: '01' oa: 1 oa_version: Published Version page: 674 - 703 project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems publication: Advances in Mathematics publication_status: published publisher: Academic Press publist_id: '5488' pubrep_id: '774' quality_controlled: '1' related_material: record: - id: '1399' relation: dissertation_contains status: public scopus_import: 1 status: public title: Approximation and convergence of the intrinsic volume tmp: image: /images/cc_by_nc_nd.png legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) short: CC BY-NC-ND (4.0) type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 287 year: '2016' ... --- _id: '1424' abstract: - lang: eng text: We consider the problem of statistical computations with persistence diagrams, a summary representation of topological features in data. These diagrams encode persistent homology, a widely used invariant in topological data analysis. While several avenues towards a statistical treatment of the diagrams have been explored recently, we follow an alternative route that is motivated by the success of methods based on the embedding of probability measures into reproducing kernel Hilbert spaces. In fact, a positive definite kernel on persistence diagrams has recently been proposed, connecting persistent homology to popular kernel-based learning techniques such as support vector machines. However, important properties of that kernel enabling a principled use in the context of probability measure embeddings remain to be explored. Our contribution is to close this gap by proving universality of a variant of the original kernel, and to demonstrate its effective use in twosample hypothesis testing on synthetic as well as real-world data. acknowledgement: This work was partially supported by the Austrian Science FUnd, project no. KLI 00012. alternative_title: - Advances in Neural Information Processing Systems author: - first_name: Roland full_name: Kwitt, Roland last_name: Kwitt - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Marc full_name: Niethammer, Marc last_name: Niethammer - first_name: Weili full_name: Lin, Weili last_name: Lin - first_name: Ulrich full_name: Bauer, Ulrich id: 2ADD483A-F248-11E8-B48F-1D18A9856A87 last_name: Bauer orcid: 0000-0002-9683-0724 citation: ama: 'Kwitt R, Huber S, Niethammer M, Lin W, Bauer U. Statistical topological data analysis-A kernel perspective. In: Vol 28. Neural Information Processing Systems; 2015:3070-3078.' apa: 'Kwitt, R., Huber, S., Niethammer, M., Lin, W., & Bauer, U. (2015). Statistical topological data analysis-A kernel perspective (Vol. 28, pp. 3070–3078). Presented at the NIPS: Neural Information Processing Systems, Montreal, Canada: Neural Information Processing Systems.' chicago: Kwitt, Roland, Stefan Huber, Marc Niethammer, Weili Lin, and Ulrich Bauer. “Statistical Topological Data Analysis-A Kernel Perspective,” 28:3070–78. Neural Information Processing Systems, 2015. ieee: 'R. Kwitt, S. Huber, M. Niethammer, W. Lin, and U. Bauer, “Statistical topological data analysis-A kernel perspective,” presented at the NIPS: Neural Information Processing Systems, Montreal, Canada, 2015, vol. 28, pp. 3070–3078.' ista: 'Kwitt R, Huber S, Niethammer M, Lin W, Bauer U. 2015. Statistical topological data analysis-A kernel perspective. NIPS: Neural Information Processing Systems, Advances in Neural Information Processing Systems, vol. 28, 3070–3078.' mla: Kwitt, Roland, et al. Statistical Topological Data Analysis-A Kernel Perspective. Vol. 28, Neural Information Processing Systems, 2015, pp. 3070–78. short: R. Kwitt, S. Huber, M. Niethammer, W. Lin, U. Bauer, in:, Neural Information Processing Systems, 2015, pp. 3070–3078. conference: end_date: 2015-12-12 location: Montreal, Canada name: 'NIPS: Neural Information Processing Systems' start_date: 2015-12-07 date_created: 2018-12-11T11:51:56Z date_published: 2015-12-01T00:00:00Z date_updated: 2021-01-12T06:50:38Z day: '01' department: - _id: HeEd intvolume: ' 28' language: - iso: eng main_file_link: - open_access: '1' url: https://papers.nips.cc/paper/5887-statistical-topological-data-analysis-a-kernel-perspective month: '12' oa: 1 oa_version: Submitted Version page: 3070 - 3078 publication_status: published publisher: Neural Information Processing Systems publist_id: '5782' quality_controlled: '1' status: public title: Statistical topological data analysis-A kernel perspective type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 28 year: '2015' ... --- _id: '1483' abstract: - lang: eng text: Topological data analysis offers a rich source of valuable information to study vision problems. Yet, so far we lack a theoretically sound connection to popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In this work, we establish such a connection by designing a multi-scale kernel for persistence diagrams, a stable summary representation of topological features in data. We show that this kernel is positive definite and prove its stability with respect to the 1-Wasserstein distance. Experiments on two benchmark datasets for 3D shape classification/retrieval and texture recognition show considerable performance gains of the proposed method compared to an alternative approach that is based on the recently introduced persistence landscapes. author: - first_name: Jan full_name: Reininghaus, Jan id: 4505473A-F248-11E8-B48F-1D18A9856A87 last_name: Reininghaus - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Ulrich full_name: Bauer, Ulrich id: 2ADD483A-F248-11E8-B48F-1D18A9856A87 last_name: Bauer orcid: 0000-0002-9683-0724 - first_name: Roland full_name: Kwitt, Roland last_name: Kwitt citation: ama: 'Reininghaus J, Huber S, Bauer U, Kwitt R. A stable multi-scale kernel for topological machine learning. In: IEEE; 2015:4741-4748. doi:10.1109/CVPR.2015.7299106' apa: 'Reininghaus, J., Huber, S., Bauer, U., & Kwitt, R. (2015). A stable multi-scale kernel for topological machine learning (pp. 4741–4748). Presented at the CVPR: Computer Vision and Pattern Recognition, Boston, MA, USA: IEEE. https://doi.org/10.1109/CVPR.2015.7299106' chicago: Reininghaus, Jan, Stefan Huber, Ulrich Bauer, and Roland Kwitt. “A Stable Multi-Scale Kernel for Topological Machine Learning,” 4741–48. IEEE, 2015. https://doi.org/10.1109/CVPR.2015.7299106. ieee: 'J. Reininghaus, S. Huber, U. Bauer, and R. Kwitt, “A stable multi-scale kernel for topological machine learning,” presented at the CVPR: Computer Vision and Pattern Recognition, Boston, MA, USA, 2015, pp. 4741–4748.' ista: 'Reininghaus J, Huber S, Bauer U, Kwitt R. 2015. A stable multi-scale kernel for topological machine learning. CVPR: Computer Vision and Pattern Recognition, 4741–4748.' mla: Reininghaus, Jan, et al. A Stable Multi-Scale Kernel for Topological Machine Learning. IEEE, 2015, pp. 4741–48, doi:10.1109/CVPR.2015.7299106. short: J. Reininghaus, S. Huber, U. Bauer, R. Kwitt, in:, IEEE, 2015, pp. 4741–4748. conference: end_date: 2015-06-12 location: Boston, MA, USA name: 'CVPR: Computer Vision and Pattern Recognition' start_date: 2015-06-07 date_created: 2018-12-11T11:52:17Z date_published: 2015-10-14T00:00:00Z date_updated: 2021-01-12T06:51:03Z day: '14' department: - _id: HeEd doi: 10.1109/CVPR.2015.7299106 language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1412.6821 month: '10' oa: 1 oa_version: Preprint page: 4741 - 4748 publication_identifier: eisbn: - '978-1-4673-6964-0 ' publication_status: published publisher: IEEE publist_id: '5709' scopus_import: 1 status: public title: A stable multi-scale kernel for topological machine learning type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2015' ... --- _id: '1495' abstract: - lang: eng text: 'Motivated by biological questions, we study configurations of equal-sized disks in the Euclidean plane that neither pack nor cover. Measuring the quality by the probability that a random point lies in exactly one disk, we show that the regular hexagonal grid gives the maximum among lattice configurations. ' author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Mabel full_name: Iglesias Ham, Mabel id: 41B58C0C-F248-11E8-B48F-1D18A9856A87 last_name: Iglesias Ham - first_name: Vitaliy full_name: Kurlin, Vitaliy last_name: Kurlin citation: ama: 'Edelsbrunner H, Iglesias Ham M, Kurlin V. Relaxed disk packing. In: Proceedings of the 27th Canadian Conference on Computational Geometry. Vol 2015-August. Queen’s University; 2015:128-135.' apa: 'Edelsbrunner, H., Iglesias Ham, M., & Kurlin, V. (2015). Relaxed disk packing. In Proceedings of the 27th Canadian Conference on Computational Geometry (Vol. 2015–August, pp. 128–135). Ontario, Canada: Queen’s University.' chicago: Edelsbrunner, Herbert, Mabel Iglesias Ham, and Vitaliy Kurlin. “Relaxed Disk Packing.” In Proceedings of the 27th Canadian Conference on Computational Geometry, 2015–August:128–35. Queen’s University, 2015. ieee: H. Edelsbrunner, M. Iglesias Ham, and V. Kurlin, “Relaxed disk packing,” in Proceedings of the 27th Canadian Conference on Computational Geometry, Ontario, Canada, 2015, vol. 2015–August, pp. 128–135. ista: 'Edelsbrunner H, Iglesias Ham M, Kurlin V. 2015. Relaxed disk packing. Proceedings of the 27th Canadian Conference on Computational Geometry. CCCG: Canadian Conference on Computational Geometry vol. 2015–August, 128–135.' mla: Edelsbrunner, Herbert, et al. “Relaxed Disk Packing.” Proceedings of the 27th Canadian Conference on Computational Geometry, vol. 2015–August, Queen’s University, 2015, pp. 128–35. short: H. Edelsbrunner, M. Iglesias Ham, V. Kurlin, in:, Proceedings of the 27th Canadian Conference on Computational Geometry, Queen’s University, 2015, pp. 128–135. conference: end_date: 2015-08-12 location: Ontario, Canada name: 'CCCG: Canadian Conference on Computational Geometry' start_date: 2015-08-10 date_created: 2018-12-11T11:52:21Z date_published: 2015-08-01T00:00:00Z date_updated: 2021-01-12T06:51:09Z day: '01' department: - _id: HeEd ec_funded: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1505.03402 month: '08' oa: 1 oa_version: Submitted Version page: 128-135 project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems publication: Proceedings of the 27th Canadian Conference on Computational Geometry publication_status: published publisher: Queen's University publist_id: '5684' quality_controlled: '1' scopus_import: 1 status: public title: Relaxed disk packing type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 2015-August year: '2015' ... --- _id: '1510' abstract: - lang: eng text: 'The concept of well group in a special but important case captures homological properties of the zero set of a continuous map f from K to R^n on a compact space K that are invariant with respect to perturbations of f. The perturbations are arbitrary continuous maps within L_infty distance r from f for a given r > 0. The main drawback of the approach is that the computability of well groups was shown only when dim K = n or n = 1. Our contribution to the theory of well groups is twofold: on the one hand we improve on the computability issue, but on the other hand we present a range of examples where the well groups are incomplete invariants, that is, fail to capture certain important robust properties of the zero set. For the first part, we identify a computable subgroup of the well group that is obtained by cap product with the pullback of the orientation of R^n by f. In other words, well groups can be algorithmically approximated from below. When f is smooth and dim K < 2n-2, our approximation of the (dim K-n)th well group is exact. For the second part, we find examples of maps f, f'' from K to R^n with all well groups isomorphic but whose perturbations have different zero sets. We discuss on a possible replacement of the well groups of vector valued maps by an invariant of a better descriptive power and computability status. ' alternative_title: - LIPIcs author: - first_name: Peter full_name: Franek, Peter id: 473294AE-F248-11E8-B48F-1D18A9856A87 last_name: Franek - first_name: Marek full_name: Krcál, Marek id: 33E21118-F248-11E8-B48F-1D18A9856A87 last_name: Krcál citation: ama: 'Franek P, Krcál M. On computability and triviality of well groups. In: Vol 34. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2015:842-856. doi:10.4230/LIPIcs.SOCG.2015.842' apa: 'Franek, P., & Krcál, M. (2015). On computability and triviality of well groups (Vol. 34, pp. 842–856). Presented at the SoCG: Symposium on Computational Geometry, Eindhoven, Netherlands: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SOCG.2015.842' chicago: Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well Groups,” 34:842–56. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015. https://doi.org/10.4230/LIPIcs.SOCG.2015.842. ieee: 'P. Franek and M. Krcál, “On computability and triviality of well groups,” presented at the SoCG: Symposium on Computational Geometry, Eindhoven, Netherlands, 2015, vol. 34, pp. 842–856.' ista: 'Franek P, Krcál M. 2015. On computability and triviality of well groups. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 34, 842–856.' mla: Franek, Peter, and Marek Krcál. On Computability and Triviality of Well Groups. Vol. 34, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015, pp. 842–56, doi:10.4230/LIPIcs.SOCG.2015.842. short: P. Franek, M. Krcál, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015, pp. 842–856. conference: end_date: 2015-06-25 location: Eindhoven, Netherlands name: 'SoCG: Symposium on Computational Geometry' start_date: 2015-06-22 date_created: 2018-12-11T11:52:26Z date_published: 2015-06-11T00:00:00Z date_updated: 2023-02-21T17:02:57Z day: '11' ddc: - '510' department: - _id: UlWa - _id: HeEd doi: 10.4230/LIPIcs.SOCG.2015.842 ec_funded: 1 file: - access_level: open_access checksum: 49eb5021caafaabe5356c65b9c5f8c9c content_type: application/pdf creator: system date_created: 2018-12-12T10:13:19Z date_updated: 2020-07-14T12:44:59Z file_id: '5001' file_name: IST-2016-503-v1+1_32.pdf file_size: 623563 relation: main_file file_date_updated: 2020-07-14T12:44:59Z has_accepted_license: '1' intvolume: ' 34' language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: 842 - 856 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik publist_id: '5667' pubrep_id: '503' quality_controlled: '1' related_material: record: - id: '1408' relation: later_version status: public scopus_import: 1 status: public title: On computability and triviality of well groups tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 34 year: '2015' ... --- _id: '1531' abstract: - lang: eng text: The Heat Kernel Signature (HKS) is a scalar quantity which is derived from the heat kernel of a given shape. Due to its robustness, isometry invariance, and multiscale nature, it has been successfully applied in many geometric applications. From a more general point of view, the HKS can be considered as a descriptor of the metric of a Riemannian manifold. Given a symmetric positive definite tensor field we may interpret it as the metric of some Riemannian manifold and thereby apply the HKS to visualize and analyze the given tensor data. In this paper, we propose a generalization of this approach that enables the treatment of indefinite tensor fields, like the stress tensor, by interpreting them as a generator of a positive definite tensor field. To investigate the usefulness of this approach we consider the stress tensor from the two-point-load model example and from a mechanical work piece. alternative_title: - Mathematics and Visualization article_processing_charge: No author: - first_name: Valentin full_name: Zobel, Valentin last_name: Zobel - first_name: Jan full_name: Reininghaus, Jan id: 4505473A-F248-11E8-B48F-1D18A9856A87 last_name: Reininghaus - first_name: Ingrid full_name: Hotz, Ingrid last_name: Hotz citation: ama: 'Zobel V, Reininghaus J, Hotz I. Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature. In: Hotz I, Schultz T, eds. Visualization and Processing of Higher Order Descriptors for Multi-Valued Data. Vol 40. 1st ed. Springer; 2015:257-267. doi:10.1007/978-3-319-15090-1_13' apa: Zobel, V., Reininghaus, J., & Hotz, I. (2015). Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature. In I. Hotz & T. Schultz (Eds.), Visualization and Processing of Higher Order Descriptors for Multi-Valued Data (1st ed., Vol. 40, pp. 257–267). Springer. https://doi.org/10.1007/978-3-319-15090-1_13 chicago: Zobel, Valentin, Jan Reininghaus, and Ingrid Hotz. “Visualizing Symmetric Indefinite 2D Tensor Fields Using The Heat Kernel Signature.” In Visualization and Processing of Higher Order Descriptors for Multi-Valued Data, edited by Ingrid Hotz and Thomas Schultz, 1st ed., 40:257–67. Springer, 2015. https://doi.org/10.1007/978-3-319-15090-1_13. ieee: V. Zobel, J. Reininghaus, and I. Hotz, “Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature,” in Visualization and Processing of Higher Order Descriptors for Multi-Valued Data, 1st ed., vol. 40, I. Hotz and T. Schultz, Eds. Springer, 2015, pp. 257–267. ista: 'Zobel V, Reininghaus J, Hotz I. 2015.Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature. In: Visualization and Processing of Higher Order Descriptors for Multi-Valued Data. Mathematics and Visualization, vol. 40, 257–267.' mla: Zobel, Valentin, et al. “Visualizing Symmetric Indefinite 2D Tensor Fields Using The Heat Kernel Signature.” Visualization and Processing of Higher Order Descriptors for Multi-Valued Data, edited by Ingrid Hotz and Thomas Schultz, 1st ed., vol. 40, Springer, 2015, pp. 257–67, doi:10.1007/978-3-319-15090-1_13. short: V. Zobel, J. Reininghaus, I. Hotz, in:, I. Hotz, T. Schultz (Eds.), Visualization and Processing of Higher Order Descriptors for Multi-Valued Data, 1st ed., Springer, 2015, pp. 257–267. date_created: 2018-12-11T11:52:33Z date_published: 2015-01-01T00:00:00Z date_updated: 2022-06-10T09:50:14Z day: '01' department: - _id: HeEd doi: 10.1007/978-3-319-15090-1_13 edition: '1' editor: - first_name: Ingrid full_name: Hotz, Ingrid last_name: Hotz - first_name: Thomas full_name: Schultz, Thomas last_name: Schultz intvolume: ' 40' language: - iso: eng month: '01' oa_version: None page: 257 - 267 publication: Visualization and Processing of Higher Order Descriptors for Multi-Valued Data publication_identifier: isbn: - 978-3-319-15089-5 publication_status: published publisher: Springer publist_id: '5640' quality_controlled: '1' scopus_import: '1' status: public title: Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature type: book_chapter user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 40 year: '2015' ... --- _id: '1555' abstract: - lang: eng text: We show that incorporating spatial dispersal of individuals into a simple vaccination epidemic model may give rise to a model that exhibits rich dynamical behavior. Using an SIVS (susceptible-infected-vaccinated-susceptible) model as a basis, we describe the spread of an infectious disease in a population split into two regions. In each subpopulation, both forward and backward bifurcations can occur. This implies that for disconnected regions the two-patch system may admit several steady states. We consider traveling between the regions and investigate the impact of spatial dispersal of individuals on the model dynamics. We establish conditions for the existence of multiple nontrivial steady states in the system, and we study the structure of the equilibria. The mathematical analysis reveals an unusually rich dynamical behavior, not normally found in the simple epidemic models. In addition to the disease-free equilibrium, eight endemic equilibria emerge from backward transcritical and saddle-node bifurcation points, forming an interesting bifurcation diagram. Stability of steady states, their bifurcations, and the global dynamics are investigated with analytical tools, numerical simulations, and rigorous set-oriented numerical computations. acknowledgement: Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria (pawel.pilarczyk@ist.ac.at). This author’s work was partially supported by the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement 622033, by Fundo Europeu de Desenvolvimento Regional (FEDER) through COMPETE—Programa Operacional Factores de Competitividade (POFC), by the Portuguese national funds through Funda ̧caoparaaCiˆencia e a Tecnologia (FCT) in the framework of the research project FCOMP-01-0124-FEDER-010645 (ref. FCT PTDC/MAT/098871/2008), and by European Research Council through StG 259559 in the framework of the EPIDELAY project. article_processing_charge: No article_type: original author: - first_name: Diána full_name: Knipl, Diána last_name: Knipl - first_name: Pawel full_name: Pilarczyk, Pawel id: 3768D56A-F248-11E8-B48F-1D18A9856A87 last_name: Pilarczyk - first_name: Gergely full_name: Röst, Gergely last_name: Röst citation: ama: Knipl D, Pilarczyk P, Röst G. Rich bifurcation structure in a two patch vaccination model. SIAM Journal on Applied Dynamical Systems. 2015;14(2):980-1017. doi:10.1137/140993934 apa: Knipl, D., Pilarczyk, P., & Röst, G. (2015). Rich bifurcation structure in a two patch vaccination model. SIAM Journal on Applied Dynamical Systems. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/140993934 chicago: Knipl, Diána, Pawel Pilarczyk, and Gergely Röst. “Rich Bifurcation Structure in a Two Patch Vaccination Model.” SIAM Journal on Applied Dynamical Systems. Society for Industrial and Applied Mathematics , 2015. https://doi.org/10.1137/140993934. ieee: D. Knipl, P. Pilarczyk, and G. Röst, “Rich bifurcation structure in a two patch vaccination model,” SIAM Journal on Applied Dynamical Systems, vol. 14, no. 2. Society for Industrial and Applied Mathematics , pp. 980–1017, 2015. ista: Knipl D, Pilarczyk P, Röst G. 2015. Rich bifurcation structure in a two patch vaccination model. SIAM Journal on Applied Dynamical Systems. 14(2), 980–1017. mla: Knipl, Diána, et al. “Rich Bifurcation Structure in a Two Patch Vaccination Model.” SIAM Journal on Applied Dynamical Systems, vol. 14, no. 2, Society for Industrial and Applied Mathematics , 2015, pp. 980–1017, doi:10.1137/140993934. short: D. Knipl, P. Pilarczyk, G. Röst, SIAM Journal on Applied Dynamical Systems 14 (2015) 980–1017. date_created: 2018-12-11T11:52:42Z date_published: 2015-01-01T00:00:00Z date_updated: 2021-01-12T06:51:34Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.1137/140993934 ec_funded: 1 intvolume: ' 14' issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: http://discovery.ucl.ac.uk/1473750/1/99393.pdf month: '01' oa: 1 oa_version: Published Version page: 980 - 1017 project: - _id: 255F06BE-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '622033' name: Persistent Homology - Images, Data and Maps publication: SIAM Journal on Applied Dynamical Systems publication_identifier: eissn: - 1536-0040 publication_status: published publisher: 'Society for Industrial and Applied Mathematics ' publist_id: '5616' quality_controlled: '1' scopus_import: 1 status: public title: Rich bifurcation structure in a two patch vaccination model type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 14 year: '2015' ... --- _id: '1568' abstract: - lang: eng text: Aiming at the automatic diagnosis of tumors from narrow band imaging (NBI) magnifying endoscopy (ME) images of the stomach, we combine methods from image processing, computational topology, and machine learning to classify patterns into normal, tubular, vessel. Training the algorithm on a small number of images of each type, we achieve a high rate of correct classifications. The analysis of the learning algorithm reveals that a handful of geometric and topological features are responsible for the overwhelming majority of decisions. acknowledgement: This research is supported by the project No. 477 of P.G. Demidov Yaroslavl State University within State Assignment for Research. author: - first_name: Olga full_name: Dunaeva, Olga last_name: Dunaeva - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Anton full_name: Lukyanov, Anton last_name: Lukyanov - first_name: Michael full_name: Machin, Michael last_name: Machin - first_name: Daria full_name: Malkova, Daria last_name: Malkova citation: ama: 'Dunaeva O, Edelsbrunner H, Lukyanov A, Machin M, Malkova D. The classification of endoscopy images with persistent homology. In: Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing. IEEE; 2015:7034731. doi:10.1109/SYNASC.2014.81' apa: 'Dunaeva, O., Edelsbrunner, H., Lukyanov, A., Machin, M., & Malkova, D. (2015). The classification of endoscopy images with persistent homology. In Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (p. 7034731). Timisoara, Romania: IEEE. https://doi.org/10.1109/SYNASC.2014.81' chicago: Dunaeva, Olga, Herbert Edelsbrunner, Anton Lukyanov, Michael Machin, and Daria Malkova. “The Classification of Endoscopy Images with Persistent Homology.” In Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, 7034731. IEEE, 2015. https://doi.org/10.1109/SYNASC.2014.81. ieee: O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, and D. Malkova, “The classification of endoscopy images with persistent homology,” in Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, Timisoara, Romania, 2015, p. 7034731. ista: 'Dunaeva O, Edelsbrunner H, Lukyanov A, Machin M, Malkova D. 2015. The classification of endoscopy images with persistent homology. Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing. SYNASC: Symbolic and Numeric Algorithms for Scientific Computing, 7034731.' mla: Dunaeva, Olga, et al. “The Classification of Endoscopy Images with Persistent Homology.” Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, IEEE, 2015, p. 7034731, doi:10.1109/SYNASC.2014.81. short: O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, D. Malkova, in:, Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, IEEE, 2015, p. 7034731. conference: end_date: 2014-09-25 location: Timisoara, Romania name: 'SYNASC: Symbolic and Numeric Algorithms for Scientific Computing' start_date: 2014-09-22 date_created: 2018-12-11T11:52:46Z date_published: 2015-02-05T00:00:00Z date_updated: 2023-02-21T16:57:29Z day: '05' department: - _id: HeEd doi: 10.1109/SYNASC.2014.81 language: - iso: eng month: '02' oa_version: None page: '7034731' publication: Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing publication_status: published publisher: IEEE publist_id: '5603' quality_controlled: '1' related_material: record: - id: '1289' relation: later_version status: public scopus_import: 1 status: public title: The classification of endoscopy images with persistent homology type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 year: '2015' ... --- _id: '1567' abstract: - lang: eng text: My personal journey to the fascinating world of geometric forms started more than 30 years ago with the invention of alpha shapes in the plane. It took about 10 years before we generalized the concept to higher dimensions, we produced working software with a graphics interface for the three-dimensional case. At the same time, we added homology to the computations. Needless to say that this foreshadowed the inception of persistent homology, because it suggested the study of filtrations to capture the scale of a shape or data set. Importantly, this method has fast algorithms. The arguably most useful result on persistent homology is the stability of its diagrams under perturbations. alternative_title: - LNCS article_processing_charge: No author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 citation: ama: 'Edelsbrunner H. Shape, homology, persistence, and stability. In: 23rd International Symposium. Vol 9411. Springer Nature; 2015.' apa: 'Edelsbrunner, H. (2015). Shape, homology, persistence, and stability. In 23rd International Symposium (Vol. 9411). Los Angeles, CA, United States: Springer Nature.' chicago: Edelsbrunner, Herbert. “Shape, Homology, Persistence, and Stability.” In 23rd International Symposium, Vol. 9411. Springer Nature, 2015. ieee: H. Edelsbrunner, “Shape, homology, persistence, and stability,” in 23rd International Symposium, Los Angeles, CA, United States, 2015, vol. 9411. ista: 'Edelsbrunner H. 2015. Shape, homology, persistence, and stability. 23rd International Symposium. GD: Graph Drawing and Network Visualization, LNCS, vol. 9411.' mla: Edelsbrunner, Herbert. “Shape, Homology, Persistence, and Stability.” 23rd International Symposium, vol. 9411, Springer Nature, 2015. short: H. Edelsbrunner, in:, 23rd International Symposium, Springer Nature, 2015. conference: end_date: 2015-09-26 location: Los Angeles, CA, United States name: 'GD: Graph Drawing and Network Visualization' start_date: 2015-09-24 date_created: 2018-12-11T11:52:46Z date_published: 2015-01-01T00:00:00Z date_updated: 2022-01-28T08:25:00Z day: '01' department: - _id: HeEd intvolume: ' 9411' language: - iso: eng month: '01' oa_version: None publication: 23rd International Symposium publication_status: published publisher: Springer Nature publist_id: '5604' quality_controlled: '1' scopus_import: '1' status: public title: Shape, homology, persistence, and stability type: conference user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 volume: 9411 year: '2015' ... --- _id: '1563' abstract: - lang: eng text: For a given self-map $f$ of $M$, a closed smooth connected and simply-connected manifold of dimension $m\geq 4$, we provide an algorithm for estimating the values of the topological invariant $D^m_r[f]$, which equals the minimal number of $r$-periodic points in the smooth homotopy class of $f$. Our results are based on the combinatorial scheme for computing $D^m_r[f]$ introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013), 63-84]. An open-source implementation of the algorithm programmed in C++ is publicly available at {\tt http://www.pawelpilarczyk.com/combtop/}. author: - first_name: Grzegorz full_name: Graff, Grzegorz last_name: Graff - first_name: Pawel full_name: Pilarczyk, Pawel id: 3768D56A-F248-11E8-B48F-1D18A9856A87 last_name: Pilarczyk citation: ama: Graff G, Pilarczyk P. An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds. Topological Methods in Nonlinear Analysis. 2015;45(1):273-286. doi:10.12775/TMNA.2015.014 apa: Graff, G., & Pilarczyk, P. (2015). An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds. Topological Methods in Nonlinear Analysis. Juliusz Schauder Center for Nonlinear Studies. https://doi.org/10.12775/TMNA.2015.014 chicago: Graff, Grzegorz, and Pawel Pilarczyk. “An Algorithmic Approach to Estimating the Minimal Number of Periodic Points for Smooth Self-Maps of Simply-Connected Manifolds.” Topological Methods in Nonlinear Analysis. Juliusz Schauder Center for Nonlinear Studies, 2015. https://doi.org/10.12775/TMNA.2015.014. ieee: G. Graff and P. Pilarczyk, “An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds,” Topological Methods in Nonlinear Analysis, vol. 45, no. 1. Juliusz Schauder Center for Nonlinear Studies, pp. 273–286, 2015. ista: Graff G, Pilarczyk P. 2015. An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds. Topological Methods in Nonlinear Analysis. 45(1), 273–286. mla: Graff, Grzegorz, and Pawel Pilarczyk. “An Algorithmic Approach to Estimating the Minimal Number of Periodic Points for Smooth Self-Maps of Simply-Connected Manifolds.” Topological Methods in Nonlinear Analysis, vol. 45, no. 1, Juliusz Schauder Center for Nonlinear Studies, 2015, pp. 273–86, doi:10.12775/TMNA.2015.014. short: G. Graff, P. Pilarczyk, Topological Methods in Nonlinear Analysis 45 (2015) 273–286. date_created: 2018-12-11T11:52:44Z date_published: 2015-03-01T00:00:00Z date_updated: 2021-01-12T06:51:37Z day: '01' department: - _id: HeEd doi: 10.12775/TMNA.2015.014 intvolume: ' 45' issue: '1' language: - iso: eng month: '03' oa_version: None page: 273 - 286 publication: Topological Methods in Nonlinear Analysis publication_status: published publisher: Juliusz Schauder Center for Nonlinear Studies publist_id: '5608' quality_controlled: '1' scopus_import: 1 status: public title: An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 45 year: '2015' ... --- _id: '1578' abstract: - lang: eng text: We prove that the dual of the digital Voronoi diagram constructed by flooding the plane from the data points gives a geometrically and topologically correct dual triangulation. This provides the proof of correctness for recently developed GPU algorithms that outperform traditional CPU algorithms for constructing two-dimensional Delaunay triangulations. acknowledgement: "The research of the second author is partially supported by NSF under grant DBI-0820624 and by DARPA under grants HR011-05-1-0057 and HR0011-09-006\r\n" author: - first_name: Thanhtung full_name: Cao, Thanhtung last_name: Cao - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Tiowseng full_name: Tan, Tiowseng last_name: Tan citation: ama: Cao T, Edelsbrunner H, Tan T. Triangulations from topologically correct digital Voronoi diagrams. Computational Geometry. 2015;48(7):507-519. doi:10.1016/j.comgeo.2015.04.001 apa: Cao, T., Edelsbrunner, H., & Tan, T. (2015). Triangulations from topologically correct digital Voronoi diagrams. Computational Geometry. Elsevier. https://doi.org/10.1016/j.comgeo.2015.04.001 chicago: Cao, Thanhtung, Herbert Edelsbrunner, and Tiowseng Tan. “Triangulations from Topologically Correct Digital Voronoi Diagrams.” Computational Geometry. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2015.04.001. ieee: T. Cao, H. Edelsbrunner, and T. Tan, “Triangulations from topologically correct digital Voronoi diagrams,” Computational Geometry, vol. 48, no. 7. Elsevier, pp. 507–519, 2015. ista: Cao T, Edelsbrunner H, Tan T. 2015. Triangulations from topologically correct digital Voronoi diagrams. Computational Geometry. 48(7), 507–519. mla: Cao, Thanhtung, et al. “Triangulations from Topologically Correct Digital Voronoi Diagrams.” Computational Geometry, vol. 48, no. 7, Elsevier, 2015, pp. 507–19, doi:10.1016/j.comgeo.2015.04.001. short: T. Cao, H. Edelsbrunner, T. Tan, Computational Geometry 48 (2015) 507–519. date_created: 2018-12-11T11:52:49Z date_published: 2015-08-01T00:00:00Z date_updated: 2021-01-12T06:51:43Z day: '01' department: - _id: HeEd doi: 10.1016/j.comgeo.2015.04.001 intvolume: ' 48' issue: '7' language: - iso: eng month: '08' oa_version: None page: 507 - 519 publication: Computational Geometry publication_status: published publisher: Elsevier publist_id: '5593' quality_controlled: '1' scopus_import: 1 status: public title: Triangulations from topologically correct digital Voronoi diagrams type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 48 year: '2015' ... --- _id: '1584' abstract: - lang: eng text: We investigate weighted straight skeletons from a geometric, graph-theoretical, and combinatorial point of view. We start with a thorough definition and shed light on some ambiguity issues in the procedural definition. We investigate the geometry, combinatorics, and topology of faces and the roof model, and we discuss in which cases a weighted straight skeleton is connected. Finally, we show that the weighted straight skeleton of even a simple polygon may be non-planar and may contain cycles, and we discuss under which restrictions on the weights and/or the input polygon the weighted straight skeleton still behaves similar to its unweighted counterpart. In particular, we obtain a non-procedural description and a linear-time construction algorithm for the straight skeleton of strictly convex polygons with arbitrary weights. author: - first_name: Therese full_name: Biedl, Therese last_name: Biedl - first_name: Martin full_name: Held, Martin last_name: Held - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Dominik full_name: Kaaser, Dominik last_name: Kaaser - first_name: Peter full_name: Palfrader, Peter last_name: Palfrader citation: ama: 'Biedl T, Held M, Huber S, Kaaser D, Palfrader P. Reprint of: Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 2015;48(5):429-442. doi:10.1016/j.comgeo.2015.01.004' apa: 'Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). Reprint of: Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2015.01.004' chicago: 'Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader. “Reprint of: Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory and Applications. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2015.01.004.' ieee: 'T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “Reprint of: Weighted straight skeletons in the plane,” Computational Geometry: Theory and Applications, vol. 48, no. 5. Elsevier, pp. 429–442, 2015.' ista: 'Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. Reprint of: Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 48(5), 429–442.' mla: 'Biedl, Therese, et al. “Reprint of: Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory and Applications, vol. 48, no. 5, Elsevier, 2015, pp. 429–42, doi:10.1016/j.comgeo.2015.01.004.' short: 'T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Computational Geometry: Theory and Applications 48 (2015) 429–442.' date_created: 2018-12-11T11:52:51Z date_published: 2015-07-01T00:00:00Z date_updated: 2023-02-23T10:05:22Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1016/j.comgeo.2015.01.004 file: - access_level: open_access checksum: 5b33719a86f7f4c8e5dc62c1b6893f49 content_type: application/pdf creator: system date_created: 2018-12-12T10:17:36Z date_updated: 2020-07-14T12:45:03Z file_id: '5292' file_name: IST-2016-475-v1+1_1-s2.0-S092577211500005X-main.pdf file_size: 508379 relation: main_file file_date_updated: 2020-07-14T12:45:03Z has_accepted_license: '1' intvolume: ' 48' issue: '5' language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: 429 - 442 publication: 'Computational Geometry: Theory and Applications' publication_status: published publisher: Elsevier publist_id: '5587' pubrep_id: '475' quality_controlled: '1' related_material: record: - id: '1582' relation: other status: public scopus_import: 1 status: public title: 'Reprint of: Weighted straight skeletons in the plane' tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 48 year: '2015' ... --- _id: '1582' abstract: - lang: eng text: We investigate weighted straight skeletons from a geometric, graph-theoretical, and combinatorial point of view. We start with a thorough definition and shed light on some ambiguity issues in the procedural definition. We investigate the geometry, combinatorics, and topology of faces and the roof model, and we discuss in which cases a weighted straight skeleton is connected. Finally, we show that the weighted straight skeleton of even a simple polygon may be non-planar and may contain cycles, and we discuss under which restrictions on the weights and/or the input polygon the weighted straight skeleton still behaves similar to its unweighted counterpart. In particular, we obtain a non-procedural description and a linear-time construction algorithm for the straight skeleton of strictly convex polygons with arbitrary weights. author: - first_name: Therese full_name: Biedl, Therese last_name: Biedl - first_name: Martin full_name: Held, Martin last_name: Held - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Dominik full_name: Kaaser, Dominik last_name: Kaaser - first_name: Peter full_name: Palfrader, Peter last_name: Palfrader citation: ama: 'Biedl T, Held M, Huber S, Kaaser D, Palfrader P. Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 2015;48(2):120-133. doi:10.1016/j.comgeo.2014.08.006' apa: 'Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2014.08.006' chicago: 'Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader. “Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory and Applications. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2014.08.006.' ieee: 'T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “Weighted straight skeletons in the plane,” Computational Geometry: Theory and Applications, vol. 48, no. 2. Elsevier, pp. 120–133, 2015.' ista: 'Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 48(2), 120–133.' mla: 'Biedl, Therese, et al. “Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory and Applications, vol. 48, no. 2, Elsevier, 2015, pp. 120–33, doi:10.1016/j.comgeo.2014.08.006.' short: 'T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Computational Geometry: Theory and Applications 48 (2015) 120–133.' date_created: 2018-12-11T11:52:51Z date_published: 2015-02-01T00:00:00Z date_updated: 2023-02-23T10:05:27Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1016/j.comgeo.2014.08.006 file: - access_level: open_access checksum: c1ef67f6ec925e12f73a96b8fe285ab4 content_type: application/pdf creator: system date_created: 2018-12-12T10:16:28Z date_updated: 2020-07-14T12:45:02Z file_id: '5215' file_name: IST-2016-474-v1+1_1-s2.0-S0925772114000807-main.pdf file_size: 505987 relation: main_file file_date_updated: 2020-07-14T12:45:02Z has_accepted_license: '1' intvolume: ' 48' issue: '2' language: - iso: eng month: '02' oa: 1 oa_version: Published Version page: 120 - 133 publication: 'Computational Geometry: Theory and Applications' publication_status: published publisher: Elsevier publist_id: '5589' pubrep_id: '474' quality_controlled: '1' related_material: record: - id: '1584' relation: other status: public scopus_import: 1 status: public title: Weighted straight skeletons in the plane tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 48 year: '2015' ... --- _id: '1583' abstract: - lang: eng text: We study the characteristics of straight skeletons of monotone polygonal chains and use them to devise an algorithm for computing positively weighted straight skeletons of monotone polygons. Our algorithm runs in O(nlogn) time and O(n) space, where n denotes the number of vertices of the polygon. author: - first_name: Therese full_name: Biedl, Therese last_name: Biedl - first_name: Martin full_name: Held, Martin last_name: Held - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Dominik full_name: Kaaser, Dominik last_name: Kaaser - first_name: Peter full_name: Palfrader, Peter last_name: Palfrader citation: ama: Biedl T, Held M, Huber S, Kaaser D, Palfrader P. A simple algorithm for computing positively weighted straight skeletons of monotone polygons. Information Processing Letters. 2015;115(2):243-247. doi:10.1016/j.ipl.2014.09.021 apa: Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). A simple algorithm for computing positively weighted straight skeletons of monotone polygons. Information Processing Letters. Elsevier. https://doi.org/10.1016/j.ipl.2014.09.021 chicago: Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader. “A Simple Algorithm for Computing Positively Weighted Straight Skeletons of Monotone Polygons.” Information Processing Letters. Elsevier, 2015. https://doi.org/10.1016/j.ipl.2014.09.021. ieee: T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “A simple algorithm for computing positively weighted straight skeletons of monotone polygons,” Information Processing Letters, vol. 115, no. 2. Elsevier, pp. 243–247, 2015. ista: Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. A simple algorithm for computing positively weighted straight skeletons of monotone polygons. Information Processing Letters. 115(2), 243–247. mla: Biedl, Therese, et al. “A Simple Algorithm for Computing Positively Weighted Straight Skeletons of Monotone Polygons.” Information Processing Letters, vol. 115, no. 2, Elsevier, 2015, pp. 243–47, doi:10.1016/j.ipl.2014.09.021. short: T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Information Processing Letters 115 (2015) 243–247. date_created: 2018-12-11T11:52:51Z date_published: 2015-02-01T00:00:00Z date_updated: 2021-01-12T06:51:45Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1016/j.ipl.2014.09.021 file: - access_level: open_access checksum: 2779a648610c9b5c86d0b51a62816d23 content_type: application/pdf creator: system date_created: 2018-12-12T10:18:45Z date_updated: 2020-07-14T12:45:03Z file_id: '5367' file_name: IST-2016-473-v1+1_1-s2.0-S0020019014001987-main.pdf file_size: 270137 relation: main_file file_date_updated: 2020-07-14T12:45:03Z has_accepted_license: '1' intvolume: ' 115' issue: '2' language: - iso: eng month: '02' oa: 1 oa_version: Published Version page: 243 - 247 publication: Information Processing Letters publication_status: published publisher: Elsevier publist_id: '5588' pubrep_id: '473' quality_controlled: '1' scopus_import: 1 status: public title: A simple algorithm for computing positively weighted straight skeletons of monotone polygons tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 115 year: '2015' ... --- _id: '1590' abstract: - lang: eng text: 'The straight skeleton of a polygon is the geometric graph obtained by tracing the vertices during a mitered offsetting process. It is known that the straight skeleton of a simple polygon is a tree, and one can naturally derive directions on the edges of the tree from the propagation of the shrinking process. In this paper, we ask the reverse question: Given a tree with directed edges, can it be the straight skeleton of a polygon? And if so, can we find a suitable simple polygon? We answer these questions for all directed trees where the order of edges around each node is fixed.' alternative_title: - LNCS article_processing_charge: No author: - first_name: Oswin full_name: Aichholzer, Oswin last_name: Aichholzer - first_name: Therese full_name: Biedl, Therese last_name: Biedl - first_name: Thomas full_name: Hackl, Thomas last_name: Hackl - first_name: Martin full_name: Held, Martin last_name: Held - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Peter full_name: Palfrader, Peter last_name: Palfrader - first_name: Birgit full_name: Vogtenhuber, Birgit last_name: Vogtenhuber citation: ama: 'Aichholzer O, Biedl T, Hackl T, et al. Representing directed trees as straight skeletons. In: Graph Drawing and Network Visualization. Vol 9411. Springer Nature; 2015:335-347. doi:10.1007/978-3-319-27261-0_28' apa: 'Aichholzer, O., Biedl, T., Hackl, T., Held, M., Huber, S., Palfrader, P., & Vogtenhuber, B. (2015). Representing directed trees as straight skeletons. In Graph Drawing and Network Visualization (Vol. 9411, pp. 335–347). Los Angeles, CA, United States: Springer Nature. https://doi.org/10.1007/978-3-319-27261-0_28' chicago: Aichholzer, Oswin, Therese Biedl, Thomas Hackl, Martin Held, Stefan Huber, Peter Palfrader, and Birgit Vogtenhuber. “Representing Directed Trees as Straight Skeletons.” In Graph Drawing and Network Visualization, 9411:335–47. Springer Nature, 2015. https://doi.org/10.1007/978-3-319-27261-0_28. ieee: O. Aichholzer et al., “Representing directed trees as straight skeletons,” in Graph Drawing and Network Visualization, vol. 9411, Springer Nature, 2015, pp. 335–347. ista: 'Aichholzer O, Biedl T, Hackl T, Held M, Huber S, Palfrader P, Vogtenhuber B. 2015.Representing directed trees as straight skeletons. In: Graph Drawing and Network Visualization. LNCS, vol. 9411, 335–347.' mla: Aichholzer, Oswin, et al. “Representing Directed Trees as Straight Skeletons.” Graph Drawing and Network Visualization, vol. 9411, Springer Nature, 2015, pp. 335–47, doi:10.1007/978-3-319-27261-0_28. short: O. Aichholzer, T. Biedl, T. Hackl, M. Held, S. Huber, P. Palfrader, B. Vogtenhuber, in:, Graph Drawing and Network Visualization, Springer Nature, 2015, pp. 335–347. conference: end_date: 2015-09-26 location: Los Angeles, CA, United States name: 'GD: International Symposium on Graph Drawing' start_date: 2015-09-24 date_created: 2018-12-11T11:52:54Z date_published: 2015-11-27T00:00:00Z date_updated: 2022-01-28T09:10:37Z day: '27' department: - _id: HeEd doi: 10.1007/978-3-319-27261-0_28 intvolume: ' 9411' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1508.01076 month: '11' oa: 1 oa_version: Preprint page: 335 - 347 publication: Graph Drawing and Network Visualization publication_identifier: eisbn: - 978-3-319-27261-0 isbn: - 978-3-319-27260-3 publication_status: published publisher: Springer Nature publist_id: '5581' quality_controlled: '1' scopus_import: '1' status: public title: Representing directed trees as straight skeletons type: book_chapter user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 volume: 9411 year: '2015' ... --- _id: '1682' abstract: - lang: eng text: 'We study the problem of robust satisfiability of systems of nonlinear equations, namely, whether for a given continuous function f:K→ ℝn on a finite simplicial complex K and α > 0, it holds that each function g: K → ℝn such that ||g - f || ∞ < α, has a root in K. Via a reduction to the extension problem of maps into a sphere, we particularly show that this problem is decidable in polynomial time for every fixed n, assuming dimK ≤ 2n - 3. This is a substantial extension of previous computational applications of topological degree and related concepts in numerical and interval analysis. Via a reverse reduction, we prove that the problem is undecidable when dim K > 2n - 2, where the threshold comes from the stable range in homotopy theory. For the lucidity of our exposition, we focus on the setting when f is simplexwise linear. Such functions can approximate general continuous functions, and thus we get approximation schemes and undecidability of the robust satisfiability in other possible settings.' article_number: '26' author: - first_name: Peter full_name: Franek, Peter last_name: Franek - first_name: Marek full_name: Krcál, Marek id: 33E21118-F248-11E8-B48F-1D18A9856A87 last_name: Krcál citation: ama: Franek P, Krcál M. Robust satisfiability of systems of equations. Journal of the ACM. 2015;62(4). doi:10.1145/2751524 apa: Franek, P., & Krcál, M. (2015). Robust satisfiability of systems of equations. Journal of the ACM. ACM. https://doi.org/10.1145/2751524 chicago: Franek, Peter, and Marek Krcál. “Robust Satisfiability of Systems of Equations.” Journal of the ACM. ACM, 2015. https://doi.org/10.1145/2751524. ieee: P. Franek and M. Krcál, “Robust satisfiability of systems of equations,” Journal of the ACM, vol. 62, no. 4. ACM, 2015. ista: Franek P, Krcál M. 2015. Robust satisfiability of systems of equations. Journal of the ACM. 62(4), 26. mla: Franek, Peter, and Marek Krcál. “Robust Satisfiability of Systems of Equations.” Journal of the ACM, vol. 62, no. 4, 26, ACM, 2015, doi:10.1145/2751524. short: P. Franek, M. Krcál, Journal of the ACM 62 (2015). date_created: 2018-12-11T11:53:27Z date_published: 2015-08-01T00:00:00Z date_updated: 2021-01-12T06:52:30Z day: '01' department: - _id: UlWa - _id: HeEd doi: 10.1145/2751524 intvolume: ' 62' issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1402.0858 month: '08' oa: 1 oa_version: Preprint publication: Journal of the ACM publication_status: published publisher: ACM publist_id: '5466' quality_controlled: '1' scopus_import: 1 status: public title: Robust satisfiability of systems of equations type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 62 year: '2015' ... --- _id: '1710' abstract: - lang: eng text: 'We consider the hollow on the half-plane {(x, y) : y ≤ 0} ⊂ ℝ2 defined by a function u : (-1, 1) → ℝ, u(x) < 0, and a vertical flow of point particles incident on the hollow. It is assumed that u satisfies the so-called single impact condition (SIC): each incident particle is elastically reflected by graph(u) and goes away without hitting the graph of u anymore. We solve the problem: find the function u minimizing the force of resistance created by the flow. We show that the graph of the minimizer is formed by two arcs of parabolas symmetric to each other with respect to the y-axis. Assuming that the resistance of u ≡ 0 equals 1, we show that the minimal resistance equals π/2 - 2arctan(1/2) ≈ 0.6435. This result completes the previously obtained result [SIAM J. Math. Anal., 46 (2014), pp. 2730-2742] stating in particular that the minimal resistance of a hollow in higher dimensions equals 0.5. We additionally consider a similar problem of minimal resistance, where the hollow in the half-space {(x1,...,xd,y) : y ≤ 0} ⊂ ℝd+1 is defined by a radial function U satisfying the SIC, U(x) = u(|x|), with x = (x1,...,xd), u(ξ) < 0 for 0 ≤ ξ < 1, and u(ξ) = 0 for ξ ≥ 1, and the flow is parallel to the y-axis. The minimal resistance is greater than 0.5 (and coincides with 0.6435 when d = 1) and converges to 0.5 as d → ∞.' author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Alexander full_name: Plakhov, Alexander last_name: Plakhov citation: ama: Akopyan A, Plakhov A. Minimal resistance of curves under the single impact assumption. Society for Industrial and Applied Mathematics. 2015;47(4):2754-2769. doi:10.1137/140993843 apa: Akopyan, A., & Plakhov, A. (2015). Minimal resistance of curves under the single impact assumption. Society for Industrial and Applied Mathematics. SIAM. https://doi.org/10.1137/140993843 chicago: Akopyan, Arseniy, and Alexander Plakhov. “Minimal Resistance of Curves under the Single Impact Assumption.” Society for Industrial and Applied Mathematics. SIAM, 2015. https://doi.org/10.1137/140993843. ieee: A. Akopyan and A. Plakhov, “Minimal resistance of curves under the single impact assumption,” Society for Industrial and Applied Mathematics, vol. 47, no. 4. SIAM, pp. 2754–2769, 2015. ista: Akopyan A, Plakhov A. 2015. Minimal resistance of curves under the single impact assumption. Society for Industrial and Applied Mathematics. 47(4), 2754–2769. mla: Akopyan, Arseniy, and Alexander Plakhov. “Minimal Resistance of Curves under the Single Impact Assumption.” Society for Industrial and Applied Mathematics, vol. 47, no. 4, SIAM, 2015, pp. 2754–69, doi:10.1137/140993843. short: A. Akopyan, A. Plakhov, Society for Industrial and Applied Mathematics 47 (2015) 2754–2769. date_created: 2018-12-11T11:53:36Z date_published: 2015-07-14T00:00:00Z date_updated: 2021-01-12T06:52:41Z day: '14' department: - _id: HeEd doi: 10.1137/140993843 ec_funded: 1 intvolume: ' 47' issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1410.3736 month: '07' oa: 1 oa_version: Preprint page: 2754 - 2769 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Society for Industrial and Applied Mathematics publication_status: published publisher: SIAM publist_id: '5423' quality_controlled: '1' scopus_import: 1 status: public title: Minimal resistance of curves under the single impact assumption type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 47 year: '2015' ... --- _id: '1828' abstract: - lang: eng text: We construct a non-linear Markov process connected with a biological model of a bacterial genome recombination. The description of invariant measures of this process gives us the solution of one problem in elementary probability theory. article_processing_charge: No author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Sergey full_name: Pirogov, Sergey last_name: Pirogov - first_name: Aleksandr full_name: Rybko, Aleksandr last_name: Rybko citation: ama: Akopyan A, Pirogov S, Rybko A. Invariant measures of genetic recombination process. Journal of Statistical Physics. 2015;160(1):163-167. doi:10.1007/s10955-015-1238-5 apa: Akopyan, A., Pirogov, S., & Rybko, A. (2015). Invariant measures of genetic recombination process. Journal of Statistical Physics. Springer. https://doi.org/10.1007/s10955-015-1238-5 chicago: Akopyan, Arseniy, Sergey Pirogov, and Aleksandr Rybko. “Invariant Measures of Genetic Recombination Process.” Journal of Statistical Physics. Springer, 2015. https://doi.org/10.1007/s10955-015-1238-5. ieee: A. Akopyan, S. Pirogov, and A. Rybko, “Invariant measures of genetic recombination process,” Journal of Statistical Physics, vol. 160, no. 1. Springer, pp. 163–167, 2015. ista: Akopyan A, Pirogov S, Rybko A. 2015. Invariant measures of genetic recombination process. Journal of Statistical Physics. 160(1), 163–167. mla: Akopyan, Arseniy, et al. “Invariant Measures of Genetic Recombination Process.” Journal of Statistical Physics, vol. 160, no. 1, Springer, 2015, pp. 163–67, doi:10.1007/s10955-015-1238-5. short: A. Akopyan, S. Pirogov, A. Rybko, Journal of Statistical Physics 160 (2015) 163–167. date_created: 2018-12-11T11:54:14Z date_published: 2015-07-01T00:00:00Z date_updated: 2021-01-12T06:53:28Z day: '01' department: - _id: HeEd doi: 10.1007/s10955-015-1238-5 ec_funded: 1 intvolume: ' 160' issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: arxiv.org/abs/1406.5313 month: '07' oa: 1 oa_version: Preprint page: 163 - 167 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Journal of Statistical Physics publication_status: published publisher: Springer publist_id: '5276' quality_controlled: '1' scopus_import: 1 status: public title: Invariant measures of genetic recombination process type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 160 year: '2015' ... --- _id: '1938' abstract: - lang: eng text: 'We numerically investigate the distribution of extrema of ''chaotic'' Laplacian eigenfunctions on two-dimensional manifolds. Our contribution is two-fold: (a) we count extrema on grid graphs with a small number of randomly added edges and show the behavior to coincide with the 1957 prediction of Longuet-Higgins for the continuous case and (b) we compute the regularity of their spatial distribution using discrepancy, which is a classical measure from the theory of Monte Carlo integration. The first part suggests that grid graphs with randomly added edges should behave like two-dimensional surfaces with ergodic geodesic flow; in the second part we show that the extrema are more regularly distributed in space than the grid Z2.' acknowledgement: "F.P. was supported by the Graduate School of IST Austria. S.S. was partially supported by CRC1060 of the DFG\r\nThe authors thank Olga Symonova and Michael Kerber for sharing their implementation of the persistence algorithm. " author: - first_name: Florian full_name: Pausinger, Florian id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87 last_name: Pausinger orcid: 0000-0002-8379-3768 - first_name: Stefan full_name: Steinerberger, Stefan last_name: Steinerberger citation: ama: Pausinger F, Steinerberger S. On the distribution of local extrema in quantum chaos. Physics Letters, Section A. 2015;379(6):535-541. doi:10.1016/j.physleta.2014.12.010 apa: Pausinger, F., & Steinerberger, S. (2015). On the distribution of local extrema in quantum chaos. Physics Letters, Section A. Elsevier. https://doi.org/10.1016/j.physleta.2014.12.010 chicago: Pausinger, Florian, and Stefan Steinerberger. “On the Distribution of Local Extrema in Quantum Chaos.” Physics Letters, Section A. Elsevier, 2015. https://doi.org/10.1016/j.physleta.2014.12.010. ieee: F. Pausinger and S. Steinerberger, “On the distribution of local extrema in quantum chaos,” Physics Letters, Section A, vol. 379, no. 6. Elsevier, pp. 535–541, 2015. ista: Pausinger F, Steinerberger S. 2015. On the distribution of local extrema in quantum chaos. Physics Letters, Section A. 379(6), 535–541. mla: Pausinger, Florian, and Stefan Steinerberger. “On the Distribution of Local Extrema in Quantum Chaos.” Physics Letters, Section A, vol. 379, no. 6, Elsevier, 2015, pp. 535–41, doi:10.1016/j.physleta.2014.12.010. short: F. Pausinger, S. Steinerberger, Physics Letters, Section A 379 (2015) 535–541. date_created: 2018-12-11T11:54:49Z date_published: 2015-03-06T00:00:00Z date_updated: 2021-01-12T06:54:12Z day: '06' department: - _id: HeEd doi: 10.1016/j.physleta.2014.12.010 intvolume: ' 379' issue: '6' language: - iso: eng month: '03' oa_version: None page: 535 - 541 publication: Physics Letters, Section A publication_status: published publisher: Elsevier publist_id: '5152' quality_controlled: '1' scopus_import: 1 status: public title: On the distribution of local extrema in quantum chaos type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 379 year: '2015' ... --- _id: '2035' abstract: - lang: eng text: "Considering a continuous self-map and the induced endomorphism on homology, we study the eigenvalues and eigenspaces of the latter. Taking a filtration of representations, we define the persistence of the eigenspaces, effectively introducing a hierarchical organization of the map. The algorithm that computes this information for a finite sample is proved to be stable, and to give the correct answer for a sufficiently dense sample. Results computed with an implementation of the algorithm provide evidence of its practical utility.\r\n" acknowledgement: This research is partially supported by the Toposys project 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 Polish National Science Center under Grant No. N201 419639. author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - 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: Edelsbrunner H, Jablonski G, Mrozek M. The persistent homology of a self-map. Foundations of Computational Mathematics. 2015;15(5):1213-1244. doi:10.1007/s10208-014-9223-y apa: Edelsbrunner, H., Jablonski, G., & Mrozek, M. (2015). The persistent homology of a self-map. Foundations of Computational Mathematics. Springer. https://doi.org/10.1007/s10208-014-9223-y chicago: Edelsbrunner, Herbert, Grzegorz Jablonski, and Marian Mrozek. “The Persistent Homology of a Self-Map.” Foundations of Computational Mathematics. Springer, 2015. https://doi.org/10.1007/s10208-014-9223-y. ieee: H. Edelsbrunner, G. Jablonski, and M. Mrozek, “The persistent homology of a self-map,” Foundations of Computational Mathematics, vol. 15, no. 5. Springer, pp. 1213–1244, 2015. ista: Edelsbrunner H, Jablonski G, Mrozek M. 2015. The persistent homology of a self-map. Foundations of Computational Mathematics. 15(5), 1213–1244. mla: Edelsbrunner, Herbert, et al. “The Persistent Homology of a Self-Map.” Foundations of Computational Mathematics, vol. 15, no. 5, Springer, 2015, pp. 1213–44, doi:10.1007/s10208-014-9223-y. short: H. Edelsbrunner, G. Jablonski, M. Mrozek, Foundations of Computational Mathematics 15 (2015) 1213–1244. date_created: 2018-12-11T11:55:20Z date_published: 2015-10-01T00:00:00Z date_updated: 2021-01-12T06:54:53Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1007/s10208-014-9223-y ec_funded: 1 file: - access_level: open_access checksum: 3566f3a8b0c1bc550e62914a88c584ff content_type: application/pdf creator: system date_created: 2018-12-12T10:08:10Z date_updated: 2020-07-14T12:45:26Z file_id: '4670' file_name: IST-2016-486-v1+1_s10208-014-9223-y.pdf file_size: 1317546 relation: main_file file_date_updated: 2020-07-14T12:45:26Z has_accepted_license: '1' intvolume: ' 15' issue: '5' language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: 1213 - 1244 project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems publication: Foundations of Computational Mathematics publication_status: published publisher: Springer publist_id: '5022' pubrep_id: '486' quality_controlled: '1' scopus_import: 1 status: public title: The persistent homology of a self-map tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 15 year: '2015' ... --- _id: '1805' abstract: - lang: eng text: 'We consider the problem of deciding whether the persistent homology group of a simplicial pair (K,L) can be realized as the homology H∗(X) of some complex X with L ⊂ X ⊂ K. We show that this problem is NP-complete even if K is embedded in double-struck R3. As a consequence, we show that it is NP-hard to simplify level and sublevel sets of scalar functions on double-struck S3 within a given tolerance constraint. This problem has relevance to the visualization of medical images by isosurfaces. We also show an implication to the theory of well groups of scalar functions: not every well group can be realized by some level set, and deciding whether a well group can be realized is NP-hard.' author: - first_name: Dominique full_name: Attali, Dominique last_name: Attali - first_name: Ulrich full_name: Bauer, Ulrich id: 2ADD483A-F248-11E8-B48F-1D18A9856A87 last_name: Bauer orcid: 0000-0002-9683-0724 - first_name: Olivier full_name: Devillers, Olivier last_name: Devillers - first_name: Marc full_name: Glisse, Marc last_name: Glisse - first_name: André full_name: Lieutier, André last_name: Lieutier citation: ama: 'Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. Homological reconstruction and simplification in R3. Computational Geometry: Theory and Applications. 2015;48(8):606-621. doi:10.1016/j.comgeo.2014.08.010' apa: 'Attali, D., Bauer, U., Devillers, O., Glisse, M., & Lieutier, A. (2015). Homological reconstruction and simplification in R3. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2014.08.010' chicago: 'Attali, Dominique, Ulrich Bauer, Olivier Devillers, Marc Glisse, and André Lieutier. “Homological Reconstruction and Simplification in R3.” Computational Geometry: Theory and Applications. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2014.08.010.' ieee: 'D. Attali, U. Bauer, O. Devillers, M. Glisse, and A. Lieutier, “Homological reconstruction and simplification in R3,” Computational Geometry: Theory and Applications, vol. 48, no. 8. Elsevier, pp. 606–621, 2015.' ista: 'Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. 2015. Homological reconstruction and simplification in R3. Computational Geometry: Theory and Applications. 48(8), 606–621.' mla: 'Attali, Dominique, et al. “Homological Reconstruction and Simplification in R3.” Computational Geometry: Theory and Applications, vol. 48, no. 8, Elsevier, 2015, pp. 606–21, doi:10.1016/j.comgeo.2014.08.010.' short: 'D. Attali, U. Bauer, O. Devillers, M. Glisse, A. Lieutier, Computational Geometry: Theory and Applications 48 (2015) 606–621.' date_created: 2018-12-11T11:54:06Z date_published: 2015-06-03T00:00:00Z date_updated: 2023-02-23T10:59:19Z day: '03' department: - _id: HeEd doi: 10.1016/j.comgeo.2014.08.010 ec_funded: 1 intvolume: ' 48' issue: '8' language: - iso: eng month: '06' oa_version: None page: 606 - 621 project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems publication: 'Computational Geometry: Theory and Applications' publication_status: published publisher: Elsevier publist_id: '5305' quality_controlled: '1' related_material: record: - id: '2812' relation: earlier_version status: public scopus_import: 1 status: public title: Homological reconstruction and simplification in R3 type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 48 year: '2015' ... --- _id: '1793' abstract: - lang: eng text: We present a software platform for reconstructing and analyzing the growth of a plant root system from a time-series of 3D voxelized shapes. It aligns the shapes with each other, constructs a geometric graph representation together with the function that records the time of growth, and organizes the branches into a hierarchy that reflects the order of creation. The software includes the automatic computation of structural and dynamic traits for each root in the system enabling the quantification of growth on fine-scale. These are important advances in plant phenotyping with applications to the study of genetic and environmental influences on growth. article_number: e0127657 author: - first_name: Olga full_name: Symonova, Olga id: 3C0C7BC6-F248-11E8-B48F-1D18A9856A87 last_name: Symonova - first_name: Christopher full_name: Topp, Christopher last_name: Topp - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 citation: ama: 'Symonova O, Topp C, Edelsbrunner H. DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots. PLoS One. 2015;10(6). doi:10.1371/journal.pone.0127657' apa: 'Symonova, O., Topp, C., & Edelsbrunner, H. (2015). DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots. PLoS One. Public Library of Science. https://doi.org/10.1371/journal.pone.0127657' chicago: 'Symonova, Olga, Christopher Topp, and Herbert Edelsbrunner. “DynamicRoots: A Software Platform for the Reconstruction and Analysis of Growing Plant Roots.” PLoS One. Public Library of Science, 2015. https://doi.org/10.1371/journal.pone.0127657.' ieee: 'O. Symonova, C. Topp, and H. Edelsbrunner, “DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots,” PLoS One, vol. 10, no. 6. Public Library of Science, 2015.' ista: 'Symonova O, Topp C, Edelsbrunner H. 2015. DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots. PLoS One. 10(6), e0127657.' mla: 'Symonova, Olga, et al. “DynamicRoots: A Software Platform for the Reconstruction and Analysis of Growing Plant Roots.” PLoS One, vol. 10, no. 6, e0127657, Public Library of Science, 2015, doi:10.1371/journal.pone.0127657.' short: O. Symonova, C. Topp, H. Edelsbrunner, PLoS One 10 (2015). date_created: 2018-12-11T11:54:02Z date_published: 2015-06-01T00:00:00Z date_updated: 2023-02-23T14:06:33Z day: '01' ddc: - '000' department: - _id: MaJö - _id: HeEd doi: 10.1371/journal.pone.0127657 file: - access_level: open_access checksum: d20f26461ca575276ad3ed9ce4bfc787 content_type: application/pdf creator: system date_created: 2018-12-12T10:15:30Z date_updated: 2020-07-14T12:45:16Z file_id: '5150' file_name: IST-2016-454-v1+1_journal.pone.0127657.pdf file_size: 1850825 relation: main_file file_date_updated: 2020-07-14T12:45:16Z has_accepted_license: '1' intvolume: ' 10' issue: '6' language: - iso: eng month: '06' oa: 1 oa_version: Published Version publication: PLoS One publication_status: published publisher: Public Library of Science publist_id: '5318' pubrep_id: '454' quality_controlled: '1' related_material: record: - id: '9737' relation: research_data status: public scopus_import: 1 status: public title: 'DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots' tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 10 year: '2015' ... --- _id: '9737' article_processing_charge: No author: - first_name: Olga full_name: Symonova, Olga id: 3C0C7BC6-F248-11E8-B48F-1D18A9856A87 last_name: Symonova - first_name: Christopher full_name: Topp, Christopher last_name: Topp - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 citation: ama: Symonova O, Topp C, Edelsbrunner H. Root traits computed by DynamicRoots for the maize root shown in fig 2. 2015. doi:10.1371/journal.pone.0127657.s001 apa: Symonova, O., Topp, C., & Edelsbrunner, H. (2015). Root traits computed by DynamicRoots for the maize root shown in fig 2. Public Library of Science. https://doi.org/10.1371/journal.pone.0127657.s001 chicago: Symonova, Olga, Christopher Topp, and Herbert Edelsbrunner. “Root Traits Computed by DynamicRoots for the Maize Root Shown in Fig 2.” Public Library of Science, 2015. https://doi.org/10.1371/journal.pone.0127657.s001. ieee: O. Symonova, C. Topp, and H. Edelsbrunner, “Root traits computed by DynamicRoots for the maize root shown in fig 2.” Public Library of Science, 2015. ista: Symonova O, Topp C, Edelsbrunner H. 2015. Root traits computed by DynamicRoots for the maize root shown in fig 2, Public Library of Science, 10.1371/journal.pone.0127657.s001. mla: Symonova, Olga, et al. Root Traits Computed by DynamicRoots for the Maize Root Shown in Fig 2. Public Library of Science, 2015, doi:10.1371/journal.pone.0127657.s001. short: O. Symonova, C. Topp, H. Edelsbrunner, (2015). date_created: 2021-07-28T06:20:13Z date_published: 2015-06-01T00:00:00Z date_updated: 2023-02-23T10:14:42Z day: '01' department: - _id: MaJö - _id: HeEd doi: 10.1371/journal.pone.0127657.s001 month: '06' oa_version: Published Version publisher: Public Library of Science related_material: record: - id: '1793' relation: used_in_publication status: public status: public title: Root traits computed by DynamicRoots for the maize root shown in fig 2 type: research_data_reference user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf year: '2015' ... --- _id: '1792' abstract: - lang: eng text: Motivated by recent ideas of Harman (Unif. Distrib. Theory, 2010) we develop a new concept of variation of multivariate functions on a compact Hausdorff space with respect to a collection D of subsets. We prove a general version of the Koksma-Hlawka theorem that holds for this notion of variation and discrepancy with respect to D. As special cases, we obtain Koksma-Hlawka inequalities for classical notions, such as extreme or isotropic discrepancy. For extreme discrepancy, our result coincides with the usual Koksma-Hlawka theorem. We show that the space of functions of bounded D-variation contains important discontinuous functions and is closed under natural algebraic operations. Finally, we illustrate the results on concrete integration problems from integral geometry and stereology. acknowledgement: F.P. is supported by the Graduate School of IST Austria, A.M.S is supported by the Centre for Stochastic Geometry and Advanced Bioimaging funded by a grant from the Villum Foundation. author: - first_name: Florian full_name: Pausinger, Florian id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87 last_name: Pausinger orcid: 0000-0002-8379-3768 - first_name: Anne full_name: Svane, Anne last_name: Svane citation: ama: Pausinger F, Svane A. A Koksma-Hlawka inequality for general discrepancy systems. Journal of Complexity. 2015;31(6):773-797. doi:10.1016/j.jco.2015.06.002 apa: Pausinger, F., & Svane, A. (2015). A Koksma-Hlawka inequality for general discrepancy systems. Journal of Complexity. Academic Press. https://doi.org/10.1016/j.jco.2015.06.002 chicago: Pausinger, Florian, and Anne Svane. “A Koksma-Hlawka Inequality for General Discrepancy Systems.” Journal of Complexity. Academic Press, 2015. https://doi.org/10.1016/j.jco.2015.06.002. ieee: F. Pausinger and A. Svane, “A Koksma-Hlawka inequality for general discrepancy systems,” Journal of Complexity, vol. 31, no. 6. Academic Press, pp. 773–797, 2015. ista: Pausinger F, Svane A. 2015. A Koksma-Hlawka inequality for general discrepancy systems. Journal of Complexity. 31(6), 773–797. mla: Pausinger, Florian, and Anne Svane. “A Koksma-Hlawka Inequality for General Discrepancy Systems.” Journal of Complexity, vol. 31, no. 6, Academic Press, 2015, pp. 773–97, doi:10.1016/j.jco.2015.06.002. short: F. Pausinger, A. Svane, Journal of Complexity 31 (2015) 773–797. date_created: 2018-12-11T11:54:02Z date_published: 2015-12-01T00:00:00Z date_updated: 2023-09-07T11:41:25Z day: '01' department: - _id: HeEd doi: 10.1016/j.jco.2015.06.002 intvolume: ' 31' issue: '6' language: - iso: eng month: '12' oa_version: None page: 773 - 797 publication: Journal of Complexity publication_status: published publisher: Academic Press publist_id: '5320' quality_controlled: '1' related_material: record: - id: '1399' relation: dissertation_contains status: public scopus_import: 1 status: public title: A Koksma-Hlawka inequality for general discrepancy systems type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 31 year: '2015' ... --- _id: '1399' abstract: - lang: eng text: This thesis is concerned with the computation and approximation of intrinsic volumes. Given a smooth body M and a certain digital approximation of it, we develop algorithms to approximate various intrinsic volumes of M using only measurements taken from its digital approximations. The crucial idea behind our novel algorithms is to link the recent theory of persistent homology to the theory of intrinsic volumes via the Crofton formula from integral geometry and, in particular, via Euler characteristic computations. Our main contributions are a multigrid convergent digital algorithm to compute the first intrinsic volume of a solid body in R^n as well as an appropriate integration pipeline to approximate integral-geometric integrals defined over the Grassmannian manifold. alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Florian full_name: Pausinger, Florian id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87 last_name: Pausinger orcid: 0000-0002-8379-3768 citation: ama: Pausinger F. On the approximation of intrinsic volumes. 2015. apa: Pausinger, F. (2015). On the approximation of intrinsic volumes. Institute of Science and Technology Austria. chicago: Pausinger, Florian. “On the Approximation of Intrinsic Volumes.” Institute of Science and Technology Austria, 2015. ieee: F. Pausinger, “On the approximation of intrinsic volumes,” Institute of Science and Technology Austria, 2015. ista: Pausinger F. 2015. On the approximation of intrinsic volumes. Institute of Science and Technology Austria. mla: Pausinger, Florian. On the Approximation of Intrinsic Volumes. Institute of Science and Technology Austria, 2015. short: F. Pausinger, On the Approximation of Intrinsic Volumes, Institute of Science and Technology Austria, 2015. date_created: 2018-12-11T11:51:48Z date_published: 2015-06-01T00:00:00Z date_updated: 2023-09-07T11:41:25Z day: '01' degree_awarded: PhD department: - _id: HeEd language: - iso: eng month: '06' oa_version: None page: '144' publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria publist_id: '5808' related_material: record: - id: '1662' relation: part_of_dissertation status: public - id: '1792' relation: part_of_dissertation status: public - id: '2255' relation: part_of_dissertation status: public status: public supervisor: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 title: On the approximation of intrinsic volumes type: dissertation user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2015' ... --- _id: '10893' abstract: - lang: eng text: Saddle periodic orbits are an essential and stable part of the topological skeleton of a 3D vector field. Nevertheless, there is currently no efficient algorithm to robustly extract these features. In this chapter, we present a novel technique to extract saddle periodic orbits. Exploiting the analytic properties of such an orbit, we propose a scalar measure based on the finite-time Lyapunov exponent (FTLE) that indicates its presence. Using persistent homology, we can then extract the robust cycles of this field. These cycles thereby represent the saddle periodic orbits of the given vector field. We discuss the different existing FTLE approximation schemes regarding their applicability to this specific problem and propose an adapted version of FTLE called Normalized Velocity Separation. Finally, we evaluate our method using simple analytic vector field data. acknowledgement: First, we thank the reviewers of this paper for their ideas and critical comments. In addition, we thank Ronny Peikert and Filip Sadlo for a fruitful discussions. This research is supported by the European Commission under the TOPOSYS project FP7-ICT-318493-STREP, the European Social Fund (ESF App. No. 100098251), and the European Science Foundation under the ACAT Research Network Program. article_processing_charge: No author: - first_name: Jens full_name: Kasten, Jens last_name: Kasten - first_name: Jan full_name: Reininghaus, Jan id: 4505473A-F248-11E8-B48F-1D18A9856A87 last_name: Reininghaus - first_name: Wieland full_name: Reich, Wieland last_name: Reich - first_name: Gerik full_name: Scheuermann, Gerik last_name: Scheuermann citation: ama: 'Kasten J, Reininghaus J, Reich W, Scheuermann G. Toward the extraction of saddle periodic orbits. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds. Topological Methods in Data Analysis and Visualization III . Vol 1. Mathematics and Visualization. Cham: Springer; 2014:55-69. doi:10.1007/978-3-319-04099-8_4' apa: 'Kasten, J., Reininghaus, J., Reich, W., & Scheuermann, G. (2014). Toward the extraction of saddle periodic orbits. In P.-T. Bremer, I. Hotz, V. Pascucci, & R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III (Vol. 1, pp. 55–69). Cham: Springer. https://doi.org/10.1007/978-3-319-04099-8_4' chicago: 'Kasten, Jens, Jan Reininghaus, Wieland Reich, and Gerik Scheuermann. “Toward the Extraction of Saddle Periodic Orbits.” In Topological Methods in Data Analysis and Visualization III , edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci, and Ronald Peikert, 1:55–69. Mathematics and Visualization. Cham: Springer, 2014. https://doi.org/10.1007/978-3-319-04099-8_4.' ieee: 'J. Kasten, J. Reininghaus, W. Reich, and G. Scheuermann, “Toward the extraction of saddle periodic orbits,” in Topological Methods in Data Analysis and Visualization III , vol. 1, P.-T. Bremer, I. Hotz, V. Pascucci, and R. Peikert, Eds. Cham: Springer, 2014, pp. 55–69.' ista: 'Kasten J, Reininghaus J, Reich W, Scheuermann G. 2014.Toward the extraction of saddle periodic orbits. In: Topological Methods in Data Analysis and Visualization III . vol. 1, 55–69.' mla: Kasten, Jens, et al. “Toward the Extraction of Saddle Periodic Orbits.” Topological Methods in Data Analysis and Visualization III , edited by Peer-Timo Bremer et al., vol. 1, Springer, 2014, pp. 55–69, doi:10.1007/978-3-319-04099-8_4. short: J. Kasten, J. Reininghaus, W. Reich, G. Scheuermann, in:, P.-T. Bremer, I. Hotz, V. Pascucci, R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III , Springer, Cham, 2014, pp. 55–69. date_created: 2022-03-21T07:11:23Z date_published: 2014-03-19T00:00:00Z date_updated: 2022-06-21T12:01:47Z day: '19' department: - _id: HeEd doi: 10.1007/978-3-319-04099-8_4 ec_funded: 1 editor: - first_name: Peer-Timo full_name: Bremer, Peer-Timo last_name: Bremer - first_name: Ingrid full_name: Hotz, Ingrid last_name: Hotz - first_name: Valerio full_name: Pascucci, Valerio last_name: Pascucci - first_name: Ronald full_name: Peikert, Ronald last_name: Peikert intvolume: ' 1' language: - iso: eng month: '03' oa_version: None page: 55-69 place: Cham project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems publication: 'Topological Methods in Data Analysis and Visualization III ' publication_identifier: eisbn: - '9783319040998' eissn: - 2197-666X isbn: - '9783319040981' issn: - 1612-3786 publication_status: published publisher: Springer quality_controlled: '1' scopus_import: '1' series_title: Mathematics and Visualization status: public title: Toward the extraction of saddle periodic orbits type: book_chapter user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 1 year: '2014' ... --- _id: '1816' abstract: - lang: eng text: Watermarking techniques for vector graphics dislocate vertices in order to embed imperceptible, yet detectable, statistical features into the input data. The embedding process may result in a change of the topology of the input data, e.g., by introducing self-intersections, which is undesirable or even disastrous for many applications. In this paper we present a watermarking framework for two-dimensional vector graphics that employs conventional watermarking techniques but still provides the guarantee that the topology of the input data is preserved. The geometric part of this framework computes so-called maximum perturbation regions (MPR) of vertices. We propose two efficient algorithms to compute MPRs based on Voronoi diagrams and constrained triangulations. Furthermore, we present two algorithms to conditionally correct the watermarked data in order to increase the watermark embedding capacity and still guarantee topological correctness. While we focus on the watermarking of input formed by straight-line segments, one of our approaches can also be extended to circular arcs. We conclude the paper by demonstrating and analyzing the applicability of our framework in conjunction with two well-known watermarking techniques. acknowledgement: 'Work by Martin Held and Stefan Huber was supported by Austrian Science Fund (FWF): L367-N15 and P25816-N15.' author: - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Martin full_name: Held, Martin last_name: Held - first_name: Peter full_name: Meerwald, Peter last_name: Meerwald - first_name: Roland full_name: Kwitt, Roland last_name: Kwitt citation: ama: Huber S, Held M, Meerwald P, Kwitt R. Topology-preserving watermarking of vector graphics. International Journal of Computational Geometry and Applications. 2014;24(1):61-86. doi:10.1142/S0218195914500034 apa: Huber, S., Held, M., Meerwald, P., & Kwitt, R. (2014). Topology-preserving watermarking of vector graphics. International Journal of Computational Geometry and Applications. World Scientific Publishing. https://doi.org/10.1142/S0218195914500034 chicago: Huber, Stefan, Martin Held, Peter Meerwald, and Roland Kwitt. “Topology-Preserving Watermarking of Vector Graphics.” International Journal of Computational Geometry and Applications. World Scientific Publishing, 2014. https://doi.org/10.1142/S0218195914500034. ieee: S. Huber, M. Held, P. Meerwald, and R. Kwitt, “Topology-preserving watermarking of vector graphics,” International Journal of Computational Geometry and Applications, vol. 24, no. 1. World Scientific Publishing, pp. 61–86, 2014. ista: Huber S, Held M, Meerwald P, Kwitt R. 2014. Topology-preserving watermarking of vector graphics. International Journal of Computational Geometry and Applications. 24(1), 61–86. mla: Huber, Stefan, et al. “Topology-Preserving Watermarking of Vector Graphics.” International Journal of Computational Geometry and Applications, vol. 24, no. 1, World Scientific Publishing, 2014, pp. 61–86, doi:10.1142/S0218195914500034. short: S. Huber, M. Held, P. Meerwald, R. Kwitt, International Journal of Computational Geometry and Applications 24 (2014) 61–86. date_created: 2018-12-11T11:54:10Z date_published: 2014-03-16T00:00:00Z date_updated: 2021-01-12T06:53:23Z day: '16' ddc: - '000' department: - _id: HeEd doi: 10.1142/S0218195914500034 file: - access_level: open_access checksum: be45c133ab4d43351260e21beaa8f4b1 content_type: application/pdf creator: system date_created: 2018-12-12T10:08:43Z date_updated: 2020-07-14T12:45:17Z file_id: '4704' file_name: IST-2016-443-v1+1_S0218195914500034.pdf file_size: 991734 relation: main_file file_date_updated: 2020-07-14T12:45:17Z has_accepted_license: '1' intvolume: ' 24' issue: '1' language: - iso: eng month: '03' oa: 1 oa_version: Published Version page: 61 - 86 publication: International Journal of Computational Geometry and Applications publication_status: published publisher: World Scientific Publishing publist_id: '5290' pubrep_id: '443' quality_controlled: '1' scopus_import: 1 status: public title: Topology-preserving watermarking of vector graphics tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 24 year: '2014' ... --- _id: '1842' abstract: - lang: eng text: We prove polynomial upper bounds of geometric Ramsey numbers of pathwidth-2 outerplanar triangulations in both convex and general cases. We also prove that the geometric Ramsey numbers of the ladder graph on 2n vertices are bounded by O(n3) and O(n10), in the convex and general case, respectively. We then apply similar methods to prove an (Formula presented.) upper bound on the Ramsey number of a path with n ordered vertices. acknowledgement: Marek Krčál was supported by the ERC Advanced Grant No. 267165. author: - first_name: Josef full_name: Cibulka, Josef last_name: Cibulka - first_name: Pu full_name: Gao, Pu last_name: Gao - first_name: Marek full_name: Krcál, Marek id: 33E21118-F248-11E8-B48F-1D18A9856A87 last_name: Krcál - first_name: Tomáš full_name: Valla, Tomáš last_name: Valla - first_name: Pavel full_name: Valtr, Pavel last_name: Valtr citation: ama: Cibulka J, Gao P, Krcál M, Valla T, Valtr P. On the geometric ramsey number of outerplanar graphs. Discrete & Computational Geometry. 2014;53(1):64-79. doi:10.1007/s00454-014-9646-x apa: Cibulka, J., Gao, P., Krcál, M., Valla, T., & Valtr, P. (2014). On the geometric ramsey number of outerplanar graphs. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-014-9646-x chicago: Cibulka, Josef, Pu Gao, Marek Krcál, Tomáš Valla, and Pavel Valtr. “On the Geometric Ramsey Number of Outerplanar Graphs.” Discrete & Computational Geometry. Springer, 2014. https://doi.org/10.1007/s00454-014-9646-x. ieee: J. Cibulka, P. Gao, M. Krcál, T. Valla, and P. Valtr, “On the geometric ramsey number of outerplanar graphs,” Discrete & Computational Geometry, vol. 53, no. 1. Springer, pp. 64–79, 2014. ista: Cibulka J, Gao P, Krcál M, Valla T, Valtr P. 2014. On the geometric ramsey number of outerplanar graphs. Discrete & Computational Geometry. 53(1), 64–79. mla: Cibulka, Josef, et al. “On the Geometric Ramsey Number of Outerplanar Graphs.” Discrete & Computational Geometry, vol. 53, no. 1, Springer, 2014, pp. 64–79, doi:10.1007/s00454-014-9646-x. short: J. Cibulka, P. Gao, M. Krcál, T. Valla, P. Valtr, Discrete & Computational Geometry 53 (2014) 64–79. date_created: 2018-12-11T11:54:18Z date_published: 2014-11-14T00:00:00Z date_updated: 2021-01-12T06:53:33Z day: '14' department: - _id: UlWa - _id: HeEd doi: 10.1007/s00454-014-9646-x intvolume: ' 53' issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1310.7004 month: '11' oa: 1 oa_version: Submitted Version page: 64 - 79 publication: Discrete & Computational Geometry publication_status: published publisher: Springer publist_id: '5260' scopus_import: 1 status: public title: On the geometric ramsey number of outerplanar graphs type: journal_article user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 53 year: '2014' ... --- _id: '1876' abstract: - lang: eng text: We study densities of functionals over uniformly bounded triangulations of a Delaunay set of vertices, and prove that the minimum is attained for the Delaunay triangulation if this is the case for finite sets. article_processing_charge: No article_type: original author: - first_name: Nikolai full_name: Dolbilin, Nikolai last_name: Dolbilin - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Alexey full_name: Glazyrin, Alexey last_name: Glazyrin - first_name: Oleg full_name: Musin, Oleg last_name: Musin citation: ama: Dolbilin N, Edelsbrunner H, Glazyrin A, Musin O. Functionals on triangulations of delaunay sets. Moscow Mathematical Journal. 2014;14(3):491-504. doi:10.17323/1609-4514-2014-14-3-491-504 apa: Dolbilin, N., Edelsbrunner, H., Glazyrin, A., & Musin, O. (2014). Functionals on triangulations of delaunay sets. Moscow Mathematical Journal. Independent University of Moscow. https://doi.org/10.17323/1609-4514-2014-14-3-491-504 chicago: Dolbilin, Nikolai, Herbert Edelsbrunner, Alexey Glazyrin, and Oleg Musin. “Functionals on Triangulations of Delaunay Sets.” Moscow Mathematical Journal. Independent University of Moscow, 2014. https://doi.org/10.17323/1609-4514-2014-14-3-491-504. ieee: N. Dolbilin, H. Edelsbrunner, A. Glazyrin, and O. Musin, “Functionals on triangulations of delaunay sets,” Moscow Mathematical Journal, vol. 14, no. 3. Independent University of Moscow, pp. 491–504, 2014. ista: Dolbilin N, Edelsbrunner H, Glazyrin A, Musin O. 2014. Functionals on triangulations of delaunay sets. Moscow Mathematical Journal. 14(3), 491–504. mla: Dolbilin, Nikolai, et al. “Functionals on Triangulations of Delaunay Sets.” Moscow Mathematical Journal, vol. 14, no. 3, Independent University of Moscow, 2014, pp. 491–504, doi:10.17323/1609-4514-2014-14-3-491-504. short: N. Dolbilin, H. Edelsbrunner, A. Glazyrin, O. Musin, Moscow Mathematical Journal 14 (2014) 491–504. date_created: 2018-12-11T11:54:29Z date_published: 2014-07-01T00:00:00Z date_updated: 2022-03-03T11:47:09Z day: '01' department: - _id: HeEd doi: 10.17323/1609-4514-2014-14-3-491-504 external_id: arxiv: - '1211.7053' intvolume: ' 14' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1211.7053 month: '07' oa: 1 oa_version: Submitted Version page: 491 - 504 publication: Moscow Mathematical Journal publication_identifier: issn: - '16093321' publication_status: published publisher: Independent University of Moscow publist_id: '5220' quality_controlled: '1' scopus_import: '1' status: public title: Functionals on triangulations of delaunay sets type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 14 year: '2014' ... --- _id: '1929' abstract: - lang: eng text: We propose an algorithm for the generalization of cartographic objects that can be used to represent maps on different scales. acknowledgement: We would like to offer our special thanks to students of the Department of Mathematics of Demidov Yaroslavl State University A. A. Gorokhov and V. N. Knyazev for participation in developing the program and assistance in preparation of test data. This work was supported by grant 11.G34.31.0053 from the government of the Russian Federation. article_processing_charge: No article_type: original author: - first_name: V V full_name: Alexeev, V V last_name: Alexeev - first_name: V G full_name: Bogaevskaya, V G last_name: Bogaevskaya - first_name: M M full_name: Preobrazhenskaya, M M last_name: Preobrazhenskaya - first_name: A Y full_name: Ukhalov, A Y last_name: Ukhalov - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Olga full_name: Yakimova, Olga last_name: Yakimova citation: ama: Alexeev VV, Bogaevskaya VG, Preobrazhenskaya MM, Ukhalov AY, Edelsbrunner H, Yakimova O. An algorithm for cartographic generalization that preserves global topology. Journal of Mathematical Sciences. 2014;203(6):754-760. doi:10.1007/s10958-014-2165-8 apa: Alexeev, V. V., Bogaevskaya, V. G., Preobrazhenskaya, M. M., Ukhalov, A. Y., Edelsbrunner, H., & Yakimova, O. (2014). An algorithm for cartographic generalization that preserves global topology. Journal of Mathematical Sciences. Springer. https://doi.org/10.1007/s10958-014-2165-8 chicago: Alexeev, V V, V G Bogaevskaya, M M Preobrazhenskaya, A Y Ukhalov, Herbert Edelsbrunner, and Olga Yakimova. “An Algorithm for Cartographic Generalization That Preserves Global Topology.” Journal of Mathematical Sciences. Springer, 2014. https://doi.org/10.1007/s10958-014-2165-8. ieee: V. V. Alexeev, V. G. Bogaevskaya, M. M. Preobrazhenskaya, A. Y. Ukhalov, H. Edelsbrunner, and O. Yakimova, “An algorithm for cartographic generalization that preserves global topology,” Journal of Mathematical Sciences, vol. 203, no. 6. Springer, pp. 754–760, 2014. ista: Alexeev VV, Bogaevskaya VG, Preobrazhenskaya MM, Ukhalov AY, Edelsbrunner H, Yakimova O. 2014. An algorithm for cartographic generalization that preserves global topology. Journal of Mathematical Sciences. 203(6), 754–760. mla: Alexeev, V. V., et al. “An Algorithm for Cartographic Generalization That Preserves Global Topology.” Journal of Mathematical Sciences, vol. 203, no. 6, Springer, 2014, pp. 754–60, doi:10.1007/s10958-014-2165-8. short: V.V. Alexeev, V.G. Bogaevskaya, M.M. Preobrazhenskaya, A.Y. Ukhalov, H. Edelsbrunner, O. Yakimova, Journal of Mathematical Sciences 203 (2014) 754–760. date_created: 2018-12-11T11:54:46Z date_published: 2014-11-16T00:00:00Z date_updated: 2022-05-24T10:39:06Z day: '16' department: - _id: HeEd doi: 10.1007/s10958-014-2165-8 intvolume: ' 203' issue: '6' language: - iso: eng month: '11' oa_version: None page: 754 - 760 publication: Journal of Mathematical Sciences publication_identifier: eissn: - 1573-8795 issn: - 1072-3374 publication_status: published publisher: Springer publist_id: '5165' quality_controlled: '1' scopus_import: '1' status: public title: An algorithm for cartographic generalization that preserves global topology type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 203 year: '2014' ... --- _id: '1930' abstract: - lang: eng text: (Figure Presented) Data acquisition, numerical inaccuracies, and sampling often introduce noise in measurements and simulations. Removing this noise is often necessary for efficient analysis and visualization of this data, yet many denoising techniques change the minima and maxima of a scalar field. For example, the extrema can appear or disappear, spatially move, and change their value. This can lead to wrong interpretations of the data, e.g., when the maximum temperature over an area is falsely reported being a few degrees cooler because the denoising method is unaware of these features. Recently, a topological denoising technique based on a global energy optimization was proposed, which allows the topology-controlled denoising of 2D scalar fields. While this method preserves the minima and maxima, it is constrained by the size of the data. We extend this work to large 2D data and medium-sized 3D data by introducing a novel domain decomposition approach. It allows processing small patches of the domain independently while still avoiding the introduction of new critical points. Furthermore, we propose an iterative refinement of the solution, which decreases the optimization energy compared to the previous approach and therefore gives smoother results that are closer to the input. We illustrate our technique on synthetic and real-world 2D and 3D data sets that highlight potential applications. acknowledgement: RTRA Digiteoproject; ERC grant; SNF award; Intel Doctoral Fellowship; MPC-VCC author: - first_name: David full_name: Günther, David last_name: Günther - first_name: Alec full_name: Jacobson, Alec last_name: Jacobson - first_name: Jan full_name: Reininghaus, Jan id: 4505473A-F248-11E8-B48F-1D18A9856A87 last_name: Reininghaus - first_name: Hans full_name: Seidel, Hans last_name: Seidel - first_name: Olga full_name: Sorkine Hornung, Olga last_name: Sorkine Hornung - first_name: Tino full_name: Weinkauf, Tino last_name: Weinkauf citation: ama: Günther D, Jacobson A, Reininghaus J, Seidel H, Sorkine Hornung O, Weinkauf T. Fast and memory-efficient topological denoising of 2D and 3D scalar fields. IEEE Transactions on Visualization and Computer Graphics. 2014;20(12):2585-2594. doi:10.1109/TVCG.2014.2346432 apa: Günther, D., Jacobson, A., Reininghaus, J., Seidel, H., Sorkine Hornung, O., & Weinkauf, T. (2014). Fast and memory-efficient topological denoising of 2D and 3D scalar fields. IEEE Transactions on Visualization and Computer Graphics. IEEE. https://doi.org/10.1109/TVCG.2014.2346432 chicago: Günther, David, Alec Jacobson, Jan Reininghaus, Hans Seidel, Olga Sorkine Hornung, and Tino Weinkauf. “Fast and Memory-Efficient Topological Denoising of 2D and 3D Scalar Fields.” IEEE Transactions on Visualization and Computer Graphics. IEEE, 2014. https://doi.org/10.1109/TVCG.2014.2346432. ieee: D. Günther, A. Jacobson, J. Reininghaus, H. Seidel, O. Sorkine Hornung, and T. Weinkauf, “Fast and memory-efficient topological denoising of 2D and 3D scalar fields,” IEEE Transactions on Visualization and Computer Graphics, vol. 20, no. 12. IEEE, pp. 2585–2594, 2014. ista: Günther D, Jacobson A, Reininghaus J, Seidel H, Sorkine Hornung O, Weinkauf T. 2014. Fast and memory-efficient topological denoising of 2D and 3D scalar fields. IEEE Transactions on Visualization and Computer Graphics. 20(12), 2585–2594. mla: Günther, David, et al. “Fast and Memory-Efficient Topological Denoising of 2D and 3D Scalar Fields.” IEEE Transactions on Visualization and Computer Graphics, vol. 20, no. 12, IEEE, 2014, pp. 2585–94, doi:10.1109/TVCG.2014.2346432. short: D. Günther, A. Jacobson, J. Reininghaus, H. Seidel, O. Sorkine Hornung, T. Weinkauf, IEEE Transactions on Visualization and Computer Graphics 20 (2014) 2585–2594. date_created: 2018-12-11T11:54:46Z date_published: 2014-12-31T00:00:00Z date_updated: 2021-01-12T06:54:09Z day: '31' department: - _id: HeEd doi: 10.1109/TVCG.2014.2346432 intvolume: ' 20' issue: '12' language: - iso: eng month: '12' oa_version: None page: 2585 - 2594 publication: IEEE Transactions on Visualization and Computer Graphics publication_status: published publisher: IEEE publist_id: '5164' quality_controlled: '1' scopus_import: 1 status: public title: Fast and memory-efficient topological denoising of 2D and 3D scalar fields type: journal_article user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 20 year: '2014' ... --- _id: '2043' abstract: - lang: eng text: Persistent homology is a popular and powerful tool for capturing topological features of data. Advances in algorithms for computing persistent homology have reduced the computation time drastically – as long as the algorithm does not exhaust the available memory. Following up on a recently presented parallel method for persistence computation on shared memory systems [1], we demonstrate that a simple adaption of the standard reduction algorithm leads to a variant for distributed systems. Our algorithmic design ensures that the data is distributed over the nodes without redundancy; this permits the computation of much larger instances than on a single machine. Moreover, we observe that the parallelism at least compensates for the overhead caused by communication between nodes, and often even speeds up the computation compared to sequential and even parallel shared memory algorithms. In our experiments, we were able to compute the persistent homology of filtrations with more than a billion (109) elements within seconds on a cluster with 32 nodes using less than 6GB of memory per node. author: - first_name: Ulrich full_name: Bauer, Ulrich id: 2ADD483A-F248-11E8-B48F-1D18A9856A87 last_name: Bauer orcid: 0000-0002-9683-0724 - first_name: Michael full_name: Kerber, Michael last_name: Kerber orcid: 0000-0002-8030-9299 - first_name: Jan full_name: Reininghaus, Jan id: 4505473A-F248-11E8-B48F-1D18A9856A87 last_name: Reininghaus citation: ama: 'Bauer U, Kerber M, Reininghaus J. Distributed computation of persistent homology. In: McGeoch C, Meyer U, eds. Proceedings of the Workshop on Algorithm Engineering and Experiments. Society of Industrial and Applied Mathematics; 2014:31-38. doi:10.1137/1.9781611973198.4' apa: 'Bauer, U., Kerber, M., & Reininghaus, J. (2014). Distributed computation of persistent homology. In C. McGeoch & U. Meyer (Eds.), Proceedings of the Workshop on Algorithm Engineering and Experiments (pp. 31–38). Portland, USA: Society of Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611973198.4' chicago: Bauer, Ulrich, Michael Kerber, and Jan Reininghaus. “Distributed Computation of Persistent Homology.” In Proceedings of the Workshop on Algorithm Engineering and Experiments, edited by Catherine McGeoch and Ulrich Meyer, 31–38. Society of Industrial and Applied Mathematics, 2014. https://doi.org/10.1137/1.9781611973198.4. ieee: U. Bauer, M. Kerber, and J. Reininghaus, “Distributed computation of persistent homology,” in Proceedings of the Workshop on Algorithm Engineering and Experiments, Portland, USA, 2014, pp. 31–38. ista: 'Bauer U, Kerber M, Reininghaus J. 2014. Distributed computation of persistent homology. Proceedings of the Workshop on Algorithm Engineering and Experiments. ALENEX: Algorithm Engineering and Experiments, 31–38.' mla: Bauer, Ulrich, et al. “Distributed Computation of Persistent Homology.” Proceedings of the Workshop on Algorithm Engineering and Experiments, edited by Catherine McGeoch and Ulrich Meyer, Society of Industrial and Applied Mathematics, 2014, pp. 31–38, doi:10.1137/1.9781611973198.4. short: U. Bauer, M. Kerber, J. Reininghaus, in:, C. McGeoch, U. Meyer (Eds.), Proceedings of the Workshop on Algorithm Engineering and Experiments, Society of Industrial and Applied Mathematics, 2014, pp. 31–38. conference: end_date: 2014-01-05 location: Portland, USA name: 'ALENEX: Algorithm Engineering and Experiments' start_date: 2014-01-05 date_created: 2018-12-11T11:55:23Z date_published: 2014-01-01T00:00:00Z date_updated: 2021-01-12T06:54:56Z day: '01' department: - _id: HeEd doi: 10.1137/1.9781611973198.4 ec_funded: 1 editor: - first_name: Catherine full_name: ' McGeoch, Catherine' last_name: ' McGeoch' - first_name: Ulrich full_name: Meyer, Ulrich last_name: Meyer language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1310.0710 month: '01' oa: 1 oa_version: Submitted Version page: 31 - 38 project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems publication: Proceedings of the Workshop on Algorithm Engineering and Experiments publication_status: published publisher: Society of Industrial and Applied Mathematics publist_id: '5008' quality_controlled: '1' scopus_import: 1 status: public title: Distributed computation of persistent homology type: conference user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 year: '2014' ... --- _id: '2044' abstract: - lang: eng text: We present a parallel algorithm for computing the persistent homology of a filtered chain complex. Our approach differs from the commonly used reduction algorithm by first computing persistence pairs within local chunks, then simplifying the unpaired columns, and finally applying standard reduction on the simplified matrix. The approach generalizes a technique by Günther et al., which uses discrete Morse Theory to compute persistence; we derive the same worst-case complexity bound in a more general context. The algorithm employs several practical optimization techniques, which are of independent interest. Our sequential implementation of the algorithm is competitive with state-of-the-art methods, and we further improve the performance through parallel computation. author: - first_name: Ulrich full_name: Bauer, Ulrich id: 2ADD483A-F248-11E8-B48F-1D18A9856A87 last_name: Bauer orcid: 0000-0002-9683-0724 - first_name: Michael full_name: Kerber, Michael last_name: Kerber orcid: 0000-0002-8030-9299 - first_name: Jan full_name: Reininghaus, Jan id: 4505473A-F248-11E8-B48F-1D18A9856A87 last_name: Reininghaus citation: ama: 'Bauer U, Kerber M, Reininghaus J. Clear and Compress: Computing Persistent Homology in Chunks. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds. Topological Methods in Data Analysis and Visualization III. Mathematics and Visualization. Springer; 2014:103-117. doi:10.1007/978-3-319-04099-8_7' apa: 'Bauer, U., Kerber, M., & Reininghaus, J. (2014). Clear and Compress: Computing Persistent Homology in Chunks. In P.-T. Bremer, I. Hotz, V. Pascucci, & R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III (pp. 103–117). Springer. https://doi.org/10.1007/978-3-319-04099-8_7' chicago: 'Bauer, Ulrich, Michael Kerber, and Jan Reininghaus. “Clear and Compress: Computing Persistent Homology in Chunks.” In Topological Methods in Data Analysis and Visualization III, edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci, and Ronald Peikert, 103–17. Mathematics and Visualization. Springer, 2014. https://doi.org/10.1007/978-3-319-04099-8_7.' ieee: 'U. Bauer, M. Kerber, and J. Reininghaus, “Clear and Compress: Computing Persistent Homology in Chunks,” in Topological Methods in Data Analysis and Visualization III, P.-T. Bremer, I. Hotz, V. Pascucci, and R. Peikert, Eds. Springer, 2014, pp. 103–117.' ista: 'Bauer U, Kerber M, Reininghaus J. 2014.Clear and Compress: Computing Persistent Homology in Chunks. In: Topological Methods in Data Analysis and Visualization III. , 103–117.' mla: 'Bauer, Ulrich, et al. “Clear and Compress: Computing Persistent Homology in Chunks.” Topological Methods in Data Analysis and Visualization III, edited by Peer-Timo Bremer et al., Springer, 2014, pp. 103–17, doi:10.1007/978-3-319-04099-8_7.' short: U. Bauer, M. Kerber, J. Reininghaus, in:, P.-T. Bremer, I. Hotz, V. Pascucci, R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III, Springer, 2014, pp. 103–117. date_created: 2018-12-11T11:55:23Z date_published: 2014-03-19T00:00:00Z date_updated: 2021-01-12T06:54:56Z day: '19' department: - _id: HeEd doi: 10.1007/978-3-319-04099-8_7 ec_funded: 1 editor: - first_name: Peer-Timo full_name: Bremer, Peer-Timo last_name: Bremer - first_name: Ingrid full_name: Hotz, Ingrid last_name: Hotz - first_name: Valerio full_name: Pascucci, Valerio last_name: Pascucci - first_name: Ronald full_name: Peikert, Ronald last_name: Peikert language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1303.0477 month: '03' oa: 1 oa_version: Submitted Version page: 103 - 117 project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems publication: Topological Methods in Data Analysis and Visualization III publication_status: published publisher: Springer publist_id: '5007' quality_controlled: '1' scopus_import: 1 series_title: Mathematics and Visualization status: public title: 'Clear and Compress: Computing Persistent Homology in Chunks' type: book_chapter user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 year: '2014' ... --- _id: '2153' abstract: - lang: eng text: 'We define a simple, explicit map sending a morphism f : M → N of pointwise finite dimensional persistence modules to a matching between the barcodes of M and N. Our main result is that, in a precise sense, the quality of this matching is tightly controlled by the lengths of the longest intervals in the barcodes of ker f and coker f . As an immediate corollary, we obtain a new proof of the algebraic stability theorem for persistence barcodes [5, 9], a fundamental result in the theory of persistent homology. In contrast to previous proofs, ours shows explicitly how a δ-interleaving morphism between two persistence modules induces a δ-matching between the barcodes of the two modules. Our main result also specializes to a structure theorem for submodules and quotients of persistence modules. Copyright is held by the owner/author(s).' author: - first_name: Ulrich full_name: Bauer, Ulrich id: 2ADD483A-F248-11E8-B48F-1D18A9856A87 last_name: Bauer orcid: 0000-0002-9683-0724 - first_name: Michael full_name: Lesnick, Michael last_name: Lesnick citation: ama: 'Bauer U, Lesnick M. Induced matchings of barcodes and the algebraic stability of persistence. In: Proceedings of the Annual Symposium on Computational Geometry. ACM; 2014:355-364. doi:10.1145/2582112.2582168' apa: 'Bauer, U., & Lesnick, M. (2014). Induced matchings of barcodes and the algebraic stability of persistence. In Proceedings of the Annual Symposium on Computational Geometry (pp. 355–364). Kyoto, Japan: ACM. https://doi.org/10.1145/2582112.2582168' chicago: Bauer, Ulrich, and Michael Lesnick. “Induced Matchings of Barcodes and the Algebraic Stability of Persistence.” In Proceedings of the Annual Symposium on Computational Geometry, 355–64. ACM, 2014. https://doi.org/10.1145/2582112.2582168. ieee: U. Bauer and M. Lesnick, “Induced matchings of barcodes and the algebraic stability of persistence,” in Proceedings of the Annual Symposium on Computational Geometry, Kyoto, Japan, 2014, pp. 355–364. ista: 'Bauer U, Lesnick M. 2014. Induced matchings of barcodes and the algebraic stability of persistence. Proceedings of the Annual Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, 355–364.' mla: Bauer, Ulrich, and Michael Lesnick. “Induced Matchings of Barcodes and the Algebraic Stability of Persistence.” Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 355–64, doi:10.1145/2582112.2582168. short: U. Bauer, M. Lesnick, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 355–364. conference: end_date: 2014-06-11 location: Kyoto, Japan name: 'SoCG: Symposium on Computational Geometry' start_date: 2014-06-08 date_created: 2018-12-11T11:56:01Z date_published: 2014-06-01T00:00:00Z date_updated: 2021-01-12T06:55:38Z day: '01' department: - _id: HeEd doi: 10.1145/2582112.2582168 ec_funded: 1 language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1311.3681 month: '06' oa: 1 oa_version: Submitted Version page: 355 - 364 project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems publication: Proceedings of the Annual Symposium on Computational Geometry publication_status: published publisher: ACM publist_id: '4853' quality_controlled: '1' scopus_import: 1 status: public title: Induced matchings of barcodes and the algebraic stability of persistence type: conference user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 year: '2014' ... --- _id: '2156' abstract: - lang: eng text: We propose a metric for Reeb graphs, called the functional distortion distance. Under this distance, the Reeb graph is stable against small changes of input functions. At the same time, it remains discriminative at differentiating input functions. In particular, the main result is that the functional distortion distance between two Reeb graphs is bounded from below by the bottleneck distance between both the ordinary and extended persistence diagrams for appropriate dimensions. As an application of our results, we analyze a natural simplification scheme for Reeb graphs, and show that persistent features in Reeb graph remains persistent under simplification. Understanding the stability of important features of the Reeb graph under simplification is an interesting problem on its own right, and critical to the practical usage of Reeb graphs. Copyright is held by the owner/author(s). acknowledgement: National Science Foundation under grants CCF-1319406, CCF-1116258. author: - first_name: Ulrich full_name: Bauer, Ulrich id: 2ADD483A-F248-11E8-B48F-1D18A9856A87 last_name: Bauer orcid: 0000-0002-9683-0724 - first_name: Xiaoyin full_name: Ge, Xiaoyin last_name: Ge - first_name: Yusu full_name: Wang, Yusu last_name: Wang citation: ama: 'Bauer U, Ge X, Wang Y. Measuring distance between Reeb graphs. In: Proceedings of the Annual Symposium on Computational Geometry. ACM; 2014:464-473. doi:10.1145/2582112.2582169' apa: 'Bauer, U., Ge, X., & Wang, Y. (2014). Measuring distance between Reeb graphs. In Proceedings of the Annual Symposium on Computational Geometry (pp. 464–473). Kyoto, Japan: ACM. https://doi.org/10.1145/2582112.2582169' chicago: Bauer, Ulrich, Xiaoyin Ge, and Yusu Wang. “Measuring Distance between Reeb Graphs.” In Proceedings of the Annual Symposium on Computational Geometry, 464–73. ACM, 2014. https://doi.org/10.1145/2582112.2582169. ieee: U. Bauer, X. Ge, and Y. Wang, “Measuring distance between Reeb graphs,” in Proceedings of the Annual Symposium on Computational Geometry, Kyoto, Japan, 2014, pp. 464–473. ista: 'Bauer U, Ge X, Wang Y. 2014. Measuring distance between Reeb graphs. Proceedings of the Annual Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, 464–473.' mla: Bauer, Ulrich, et al. “Measuring Distance between Reeb Graphs.” Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 464–73, doi:10.1145/2582112.2582169. short: U. Bauer, X. Ge, Y. Wang, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 464–473. conference: end_date: 2014-06-11 location: Kyoto, Japan name: 'SoCG: Symposium on Computational Geometry' start_date: 2014-06-08 date_created: 2018-12-11T11:56:02Z date_published: 2014-06-01T00:00:00Z date_updated: 2021-01-12T06:55:39Z day: '01' department: - _id: HeEd doi: 10.1145/2582112.2582169 ec_funded: 1 language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1307.2839 month: '06' oa: 1 oa_version: Submitted Version page: 464 - 473 project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems publication: Proceedings of the Annual Symposium on Computational Geometry publication_status: published publisher: ACM publist_id: '4850' quality_controlled: '1' scopus_import: 1 status: public title: Measuring distance between Reeb graphs type: conference user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 year: '2014' ... --- _id: '2155' abstract: - lang: eng text: Given a finite set of points in Rn and a positive radius, we study the Čech, Delaunay-Čech, alpha, and wrap complexes as instances of a generalized discrete Morse theory. We prove that the latter three complexes are simple-homotopy equivalent. Our results have applications in topological data analysis and in the reconstruction of shapes from sampled data. Copyright is held by the owner/author(s). acknowledgement: This research is partially supported by ESF under the ACAT Research Network Programme, and by the Russian Government under mega project 11.G34.31.0053 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 filtrations. In: Proceedings of the Annual Symposium on Computational Geometry. ACM; 2014:484-490. doi:10.1145/2582112.2582167' apa: 'Bauer, U., & Edelsbrunner, H. (2014). The morse theory of Čech and Delaunay filtrations. In Proceedings of the Annual Symposium on Computational Geometry (pp. 484–490). Kyoto, Japan: ACM. https://doi.org/10.1145/2582112.2582167' chicago: Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay Filtrations.” In Proceedings of the Annual Symposium on Computational Geometry, 484–90. ACM, 2014. https://doi.org/10.1145/2582112.2582167. ieee: U. Bauer and H. Edelsbrunner, “The morse theory of Čech and Delaunay filtrations,” in Proceedings of the Annual Symposium on Computational Geometry, Kyoto, Japan, 2014, pp. 484–490. ista: 'Bauer U, Edelsbrunner H. 2014. The morse theory of Čech and Delaunay filtrations. Proceedings of the Annual Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, 484–490.' mla: Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay Filtrations.” Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 484–90, doi:10.1145/2582112.2582167. short: U. Bauer, H. Edelsbrunner, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 484–490. conference: end_date: 2014-06-11 location: Kyoto, Japan name: 'SoCG: Symposium on Computational Geometry' start_date: 2014-06-08 date_created: 2018-12-11T11:56:01Z date_published: 2014-06-01T00:00:00Z date_updated: 2021-01-12T06:55:38Z day: '01' department: - _id: HeEd doi: 10.1145/2582112.2582167 ec_funded: 1 language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1312.1231 month: '06' oa: 1 oa_version: Submitted Version page: 484 - 490 project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems publication: Proceedings of the Annual Symposium on Computational Geometry publication_status: published publisher: ACM publist_id: '4851' quality_controlled: '1' scopus_import: 1 status: public title: The morse theory of Čech and Delaunay filtrations type: conference user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 year: '2014' ... --- _id: '2177' abstract: - lang: eng text: We give evidence for the difficulty of computing Betti numbers of simplicial complexes over a finite field. We do this by reducing the rank computation for sparse matrices with to non-zero entries to computing Betti numbers of simplicial complexes consisting of at most a constant times to simplices. Together with the known reduction in the other direction, this implies that the two problems have the same computational complexity. author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Salman full_name: Parsa, Salman id: 4BDBD4F2-F248-11E8-B48F-1D18A9856A87 last_name: Parsa citation: ama: 'Edelsbrunner H, Parsa S. On the computational complexity of betti numbers reductions from matrix rank. In: Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. SIAM; 2014:152-160. doi:10.1137/1.9781611973402.11' apa: 'Edelsbrunner, H., & Parsa, S. (2014). On the computational complexity of betti numbers reductions from matrix rank. In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (pp. 152–160). Portland, USA: SIAM. https://doi.org/10.1137/1.9781611973402.11' chicago: Edelsbrunner, Herbert, and Salman Parsa. “On the Computational Complexity of Betti Numbers Reductions from Matrix Rank.” In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, 152–60. SIAM, 2014. https://doi.org/10.1137/1.9781611973402.11. ieee: H. Edelsbrunner and S. Parsa, “On the computational complexity of betti numbers reductions from matrix rank,” in Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, Portland, USA, 2014, pp. 152–160. ista: 'Edelsbrunner H, Parsa S. 2014. On the computational complexity of betti numbers reductions from matrix rank. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms, 152–160.' mla: Edelsbrunner, Herbert, and Salman Parsa. “On the Computational Complexity of Betti Numbers Reductions from Matrix Rank.” Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 2014, pp. 152–60, doi:10.1137/1.9781611973402.11. short: H. Edelsbrunner, S. Parsa, in:, Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 2014, pp. 152–160. conference: end_date: 2014-01-07 location: Portland, USA name: 'SODA: Symposium on Discrete Algorithms' start_date: 2014-01-05 date_created: 2018-12-11T11:56:09Z date_published: 2014-01-01T00:00:00Z date_updated: 2021-01-12T06:55:48Z day: '01' department: - _id: HeEd doi: 10.1137/1.9781611973402.11 language: - iso: eng month: '01' oa_version: None page: 152 - 160 publication: Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms publication_status: published publisher: SIAM publist_id: '4805' quality_controlled: '1' scopus_import: 1 status: public title: On the computational complexity of betti numbers reductions from matrix rank type: conference user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 year: '2014' ... --- _id: '2184' abstract: - lang: eng text: 'Given topological spaces X,Y, a fundamental problem of algebraic topology is understanding the structure of all continuous maps X→ Y. We consider a computational version, where X,Y are given as finite simplicial complexes, and the goal is to compute [X,Y], that is, all homotopy classes of suchmaps.We solve this problem in the stable range, where for some d ≥ 2, we have dim X ≤ 2d-2 and Y is (d-1)-connected; in particular, Y can be the d-dimensional sphere Sd. The algorithm combines classical tools and ideas from homotopy theory (obstruction theory, Postnikov systems, and simplicial sets) with algorithmic tools from effective algebraic topology (locally effective simplicial sets and objects with effective homology). In contrast, [X,Y] is known to be uncomputable for general X,Y, since for X = S1 it includes a well known undecidable problem: testing triviality of the fundamental group of Y. In follow-up papers, the algorithm is shown to run in polynomial time for d fixed, and extended to other problems, such as the extension problem, where we are given a subspace A ⊂ X and a map A→ Y and ask whether it extends to a map X → Y, or computing the Z2-index-everything in the stable range. Outside the stable range, the extension problem is undecidable.' acknowledgement: The research by M. K. was supported by project GAUK 49209. The research by M. K. was also supported by project 1M0545 by the Ministry of Education of the Czech Republic and by Center of Excellence { Inst. for Theor. Comput. Sci., Prague (project P202/12/G061 of GACR). The research by U. W. was supported by the Swiss National Science Foundation (SNF Projects 200021-125309, 200020-138230, and PP00P2-138948). article_number: '17 ' author: - first_name: Martin full_name: Čadek, Martin last_name: Čadek - first_name: Marek full_name: Krcál, Marek id: 33E21118-F248-11E8-B48F-1D18A9856A87 last_name: Krcál - first_name: Jiří full_name: Matoušek, Jiří last_name: Matoušek - first_name: Francis full_name: Sergeraert, Francis last_name: Sergeraert - first_name: Lukáš full_name: Vokřínek, Lukáš last_name: Vokřínek - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 citation: ama: Čadek M, Krcál M, Matoušek J, Sergeraert F, Vokřínek L, Wagner U. Computing all maps into a sphere. Journal of the ACM. 2014;61(3). doi:10.1145/2597629 apa: Čadek, M., Krcál, M., Matoušek, J., Sergeraert, F., Vokřínek, L., & Wagner, U. (2014). Computing all maps into a sphere. Journal of the ACM. ACM. https://doi.org/10.1145/2597629 chicago: Čadek, Martin, Marek Krcál, Jiří Matoušek, Francis Sergeraert, Lukáš Vokřínek, and Uli Wagner. “Computing All Maps into a Sphere.” Journal of the ACM. ACM, 2014. https://doi.org/10.1145/2597629. ieee: M. Čadek, M. Krcál, J. Matoušek, F. Sergeraert, L. Vokřínek, and U. Wagner, “Computing all maps into a sphere,” Journal of the ACM, vol. 61, no. 3. ACM, 2014. ista: Čadek M, Krcál M, Matoušek J, Sergeraert F, Vokřínek L, Wagner U. 2014. Computing all maps into a sphere. Journal of the ACM. 61(3), 17. mla: Čadek, Martin, et al. “Computing All Maps into a Sphere.” Journal of the ACM, vol. 61, no. 3, 17, ACM, 2014, doi:10.1145/2597629. short: M. Čadek, M. Krcál, J. Matoušek, F. Sergeraert, L. Vokřínek, U. Wagner, Journal of the ACM 61 (2014). date_created: 2018-12-11T11:56:12Z date_published: 2014-05-01T00:00:00Z date_updated: 2021-01-12T06:55:50Z day: '01' department: - _id: UlWa - _id: HeEd doi: 10.1145/2597629 intvolume: ' 61' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1105.6257 month: '05' oa: 1 oa_version: Preprint publication: Journal of the ACM publication_status: published publisher: ACM publist_id: '4797' quality_controlled: '1' scopus_import: 1 status: public title: Computing all maps into a sphere type: journal_article user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 61 year: '2014' ... --- _id: '2905' abstract: - lang: eng text: "Persistent homology is a recent grandchild of homology that has found use in\r\nscience and engineering as well as in mathematics. This paper surveys the method as well\r\nas the applications, neglecting completeness in favor of highlighting ideas and directions." acknowledgement: This research is partially supported by NSF under grant DBI-0820624, by ESF under the Research Networking Programme, and by the Russian Government Project 11.G34.31.0053. article_processing_charge: No author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Dmitriy full_name: Morozovy, Dmitriy last_name: Morozovy citation: ama: 'Edelsbrunner H, Morozovy D. Persistent homology: Theory and practice. In: European Mathematical Society Publishing House; 2014:31-50. doi:10.4171/120-1/3' apa: 'Edelsbrunner, H., & Morozovy, D. (2014). Persistent homology: Theory and practice (pp. 31–50). Presented at the ECM: European Congress of Mathematics, Kraków, Poland: European Mathematical Society Publishing House. https://doi.org/10.4171/120-1/3' chicago: 'Edelsbrunner, Herbert, and Dmitriy Morozovy. “Persistent Homology: Theory and Practice,” 31–50. European Mathematical Society Publishing House, 2014. https://doi.org/10.4171/120-1/3.' ieee: 'H. Edelsbrunner and D. Morozovy, “Persistent homology: Theory and practice,” presented at the ECM: European Congress of Mathematics, Kraków, Poland, 2014, pp. 31–50.' ista: 'Edelsbrunner H, Morozovy D. 2014. Persistent homology: Theory and practice. ECM: European Congress of Mathematics, 31–50.' mla: 'Edelsbrunner, Herbert, and Dmitriy Morozovy. Persistent Homology: Theory and Practice. European Mathematical Society Publishing House, 2014, pp. 31–50, doi:10.4171/120-1/3.' short: H. Edelsbrunner, D. Morozovy, in:, European Mathematical Society Publishing House, 2014, pp. 31–50. conference: end_date: 2012-07-07 location: Kraków, Poland name: 'ECM: European Congress of Mathematics' start_date: 2012-07-02 date_created: 2018-12-11T12:00:16Z date_published: 2014-01-01T00:00:00Z date_updated: 2021-01-12T07:00:36Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.4171/120-1/3 file: - access_level: open_access checksum: 1d4a046f1af945c407c5c4d411d4c5e4 content_type: application/pdf creator: system date_created: 2018-12-12T10:16:43Z date_updated: 2020-07-14T12:45:52Z file_id: '5232' file_name: IST-2016-544-v1+1_2012-P-11-PHTheoryPractice.pdf file_size: 435320 relation: main_file file_date_updated: 2020-07-14T12:45:52Z has_accepted_license: '1' language: - iso: eng month: '01' oa: 1 oa_version: Submitted Version page: 31 - 50 publication_status: published publisher: European Mathematical Society Publishing House publist_id: '3842' pubrep_id: '544' quality_controlled: '1' status: public title: 'Persistent homology: Theory and practice' type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2014' ... --- _id: '10892' abstract: - lang: eng text: "In this paper, we introduce planar matchings on directed pseudo-line arrangements, which yield a planar set of pseudo-line segments such that only matching-partners are adjacent. By translating the planar matching problem into a corresponding stable roommates problem we show that such matchings always exist.\r\nUsing our new framework, we establish, for the first time, a complete, rigorous definition of weighted straight skeletons, which are based on a so-called wavefront propagation process. We present a generalized and unified approach to treat structural changes in the wavefront that focuses on the restoration of weak planarity by finding planar matchings." acknowledgement: 'T. Biedl was supported by NSERC and the Ross and Muriel Cheriton Fellowship. P. Palfrader was supported by Austrian Science Fund (FWF): P25816-N15.' alternative_title: - LNCS article_processing_charge: No author: - first_name: Therese full_name: Biedl, Therese last_name: Biedl - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Peter full_name: Palfrader, Peter last_name: Palfrader citation: ama: 'Biedl T, Huber S, Palfrader P. Planar matchings for weighted straight skeletons. In: 25th International Symposium, ISAAC 2014. Vol 8889. Springer Nature; 2014:117-127. doi:10.1007/978-3-319-13075-0_10' apa: 'Biedl, T., Huber, S., & Palfrader, P. (2014). Planar matchings for weighted straight skeletons. In 25th International Symposium, ISAAC 2014 (Vol. 8889, pp. 117–127). Jeonju, Korea: Springer Nature. https://doi.org/10.1007/978-3-319-13075-0_10' chicago: Biedl, Therese, Stefan Huber, and Peter Palfrader. “Planar Matchings for Weighted Straight Skeletons.” In 25th International Symposium, ISAAC 2014, 8889:117–27. Springer Nature, 2014. https://doi.org/10.1007/978-3-319-13075-0_10. ieee: T. Biedl, S. Huber, and P. Palfrader, “Planar matchings for weighted straight skeletons,” in 25th International Symposium, ISAAC 2014, Jeonju, Korea, 2014, vol. 8889, pp. 117–127. ista: 'Biedl T, Huber S, Palfrader P. 2014. Planar matchings for weighted straight skeletons. 25th International Symposium, ISAAC 2014. ISAAC: International Symposium on Algorithms and Computation, LNCS, vol. 8889, 117–127.' mla: Biedl, Therese, et al. “Planar Matchings for Weighted Straight Skeletons.” 25th International Symposium, ISAAC 2014, vol. 8889, Springer Nature, 2014, pp. 117–27, doi:10.1007/978-3-319-13075-0_10. short: T. Biedl, S. Huber, P. Palfrader, in:, 25th International Symposium, ISAAC 2014, Springer Nature, 2014, pp. 117–127. conference: end_date: 2014-12-17 location: Jeonju, Korea name: 'ISAAC: International Symposium on Algorithms and Computation' start_date: 2014-12-15 date_created: 2022-03-21T07:09:03Z date_published: 2014-11-08T00:00:00Z date_updated: 2023-02-23T12:20:55Z day: '08' department: - _id: HeEd doi: 10.1007/978-3-319-13075-0_10 intvolume: ' 8889' language: - iso: eng month: '11' oa_version: None page: 117-127 publication: 25th International Symposium, ISAAC 2014 publication_identifier: eisbn: - '9783319130750' eissn: - 1611-3349 isbn: - '9783319130743' issn: - 0302-9743 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '481' relation: later_version status: public scopus_import: '1' status: public title: Planar matchings for weighted straight skeletons type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 8889 year: '2014' ... --- _id: '6853' abstract: - lang: eng text: This monograph presents a short course in computational geometry and topology. In the first part the book covers Voronoi diagrams and Delaunay triangulations, then it presents the theory of alpha complexes which play a crucial role in biology. The central part of the book is the homology theory and their computation, including the theory of persistence which is indispensable for applications, e.g. shape reconstruction. The target audience comprises researchers and practitioners in mathematics, biology, neuroscience and computer science, but the book may also be beneficial to graduate students of these fields. alternative_title: - SpringerBriefs in Applied Sciences and Technology article_processing_charge: No author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 citation: ama: 'Edelsbrunner H. A Short Course in Computational Geometry and Topology. 1st ed. Cham: Springer Nature; 2014. doi:10.1007/978-3-319-05957-0' apa: 'Edelsbrunner, H. (2014). A Short Course in Computational Geometry and Topology (1st ed.). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-05957-0' chicago: 'Edelsbrunner, Herbert. A Short Course in Computational Geometry and Topology. 1st ed. SpringerBriefs in Applied Sciences and Technology. Cham: Springer Nature, 2014. https://doi.org/10.1007/978-3-319-05957-0.' ieee: 'H. Edelsbrunner, A Short Course in Computational Geometry and Topology, 1st ed. Cham: Springer Nature, 2014.' ista: 'Edelsbrunner H. 2014. A Short Course in Computational Geometry and Topology 1st ed., Cham: Springer Nature, IX, 110p.' mla: Edelsbrunner, Herbert. A Short Course in Computational Geometry and Topology. 1st ed., Springer Nature, 2014, doi:10.1007/978-3-319-05957-0. short: H. Edelsbrunner, A Short Course in Computational Geometry and Topology, 1st ed., Springer Nature, Cham, 2014. date_created: 2019-09-06T09:22:33Z date_published: 2014-01-01T00:00:00Z date_updated: 2022-03-04T07:47:54Z day: '01' department: - _id: HeEd doi: 10.1007/978-3-319-05957-0 edition: '1' language: - iso: eng month: '01' oa_version: None page: IX, 110 place: Cham publication_identifier: eisbn: - 9-783-3190-5957-0 eissn: - 2191-5318 isbn: - 9-783-3190-5956-3 issn: - 2191-530X publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: link: - description: available as eBook via catalog IST BookList relation: other url: https://koha.app.ist.ac.at/cgi-bin/koha/opac-detail.pl?biblionumber=356106 - description: available via catalog IST BookList relation: other url: https://koha.app.ist.ac.at/cgi-bin/koha/opac-detail.pl?biblionumber=373842 scopus_import: '1' series_title: SpringerBriefs in Applied Sciences and Technology status: public title: A Short Course in Computational Geometry and Topology type: book user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2014' ... --- _id: '10886' abstract: - lang: eng text: We propose a method for visualizing two-dimensional symmetric positive definite tensor fields using the Heat Kernel Signature (HKS). The HKS is derived from the heat kernel and was originally introduced as an isometry invariant shape signature. Each positive definite tensor field defines a Riemannian manifold by considering the tensor field as a Riemannian metric. On this Riemmanian manifold we can apply the definition of the HKS. The resulting scalar quantity is used for the visualization of tensor fields. The HKS is closely related to the Gaussian curvature of the Riemannian manifold and the time parameter of the heat kernel allows a multiscale analysis in a natural way. In this way, the HKS represents field related scale space properties, enabling a level of detail analysis of tensor fields. This makes the HKS an interesting new scalar quantity for tensor fields, which differs significantly from usual tensor invariants like the trace or the determinant. A method for visualization and a numerical realization of the HKS for tensor fields is proposed in this chapter. To validate the approach we apply it to some illustrating simple examples as isolated critical points and to a medical diffusion tensor data set. acknowledgement: This research is partially supported by the TOPOSYS project FP7-ICT-318493-STREP. alternative_title: - Mathematics and Visualization article_processing_charge: No author: - first_name: Valentin full_name: Zobel, Valentin last_name: Zobel - first_name: Jan full_name: Reininghaus, Jan id: 4505473A-F248-11E8-B48F-1D18A9856A87 last_name: Reininghaus - first_name: Ingrid full_name: Hotz, Ingrid last_name: Hotz citation: ama: 'Zobel V, Reininghaus J, Hotz I. Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature. In: Topological Methods in Data Analysis and Visualization III . Springer; 2014:249-262. doi:10.1007/978-3-319-04099-8_16' apa: Zobel, V., Reininghaus, J., & Hotz, I. (2014). Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature. In Topological Methods in Data Analysis and Visualization III (pp. 249–262). Springer. https://doi.org/10.1007/978-3-319-04099-8_16 chicago: Zobel, Valentin, Jan Reininghaus, and Ingrid Hotz. “Visualization of Two-Dimensional Symmetric Positive Definite Tensor Fields Using the Heat Kernel Signature.” In Topological Methods in Data Analysis and Visualization III , 249–62. Springer, 2014. https://doi.org/10.1007/978-3-319-04099-8_16. ieee: V. Zobel, J. Reininghaus, and I. Hotz, “Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature,” in Topological Methods in Data Analysis and Visualization III , 2014, pp. 249–262. ista: Zobel V, Reininghaus J, Hotz I. 2014. Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature. Topological Methods in Data Analysis and Visualization III . , Mathematics and Visualization, , 249–262. mla: Zobel, Valentin, et al. “Visualization of Two-Dimensional Symmetric Positive Definite Tensor Fields Using the Heat Kernel Signature.” Topological Methods in Data Analysis and Visualization III , Springer, 2014, pp. 249–62, doi:10.1007/978-3-319-04099-8_16. short: V. Zobel, J. Reininghaus, I. Hotz, in:, Topological Methods in Data Analysis and Visualization III , Springer, 2014, pp. 249–262. date_created: 2022-03-18T13:05:39Z date_published: 2014-03-19T00:00:00Z date_updated: 2023-09-05T14:13:16Z day: '19' department: - _id: HeEd doi: 10.1007/978-3-319-04099-8_16 language: - iso: eng month: '03' oa_version: None page: 249-262 publication: 'Topological Methods in Data Analysis and Visualization III ' publication_identifier: eisbn: - '9783319040998' eissn: - 2197-666X isbn: - '9783319040981' issn: - 1612-3786 publication_status: published publisher: Springer quality_controlled: '1' scopus_import: '1' status: public title: Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature type: conference user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2014' ... --- _id: '10817' abstract: - lang: eng text: The Morse-Smale complex can be either explicitly or implicitly represented. Depending on the type of representation, the simplification of the Morse-Smale complex works differently. In the explicit representation, the Morse-Smale complex is directly simplified by explicitly reconnecting the critical points during the simplification. In the implicit representation, on the other hand, the Morse-Smale complex is given by a combinatorial gradient field. In this setting, the simplification changes the combinatorial flow, which yields an indirect simplification of the Morse-Smale complex. The topological complexity of the Morse-Smale complex is reduced in both representations. However, the simplifications generally yield different results. In this chapter, we emphasize properties of the two representations that cause these differences. We also provide a complexity analysis of the two schemes with respect to running time and memory consumption. acknowledgement: This research is supported and funded by the Digiteo unTopoVis project, the TOPOSYS project FP7-ICT-318493-STREP, and MPC-VCC. article_processing_charge: No author: - first_name: David full_name: Günther, David last_name: Günther - first_name: Jan full_name: Reininghaus, Jan id: 4505473A-F248-11E8-B48F-1D18A9856A87 last_name: Reininghaus - first_name: Hans-Peter full_name: Seidel, Hans-Peter last_name: Seidel - first_name: Tino full_name: Weinkauf, Tino last_name: Weinkauf citation: ama: 'Günther D, Reininghaus J, Seidel H-P, Weinkauf T. Notes on the simplification of the Morse-Smale complex. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds. Topological Methods in Data Analysis and Visualization III. Mathematics and Visualization. Cham: Springer Nature; 2014:135-150. doi:10.1007/978-3-319-04099-8_9' apa: 'Günther, D., Reininghaus, J., Seidel, H.-P., & Weinkauf, T. (2014). Notes on the simplification of the Morse-Smale complex. In P.-T. Bremer, I. Hotz, V. Pascucci, & R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III. (pp. 135–150). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-04099-8_9' chicago: 'Günther, David, Jan Reininghaus, Hans-Peter Seidel, and Tino Weinkauf. “Notes on the Simplification of the Morse-Smale Complex.” In Topological Methods in Data Analysis and Visualization III., edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci, and Ronald Peikert, 135–50. Mathematics and Visualization. Cham: Springer Nature, 2014. https://doi.org/10.1007/978-3-319-04099-8_9.' ieee: 'D. Günther, J. Reininghaus, H.-P. Seidel, and T. Weinkauf, “Notes on the simplification of the Morse-Smale complex,” in Topological Methods in Data Analysis and Visualization III., P.-T. Bremer, I. Hotz, V. Pascucci, and R. Peikert, Eds. Cham: Springer Nature, 2014, pp. 135–150.' ista: 'Günther D, Reininghaus J, Seidel H-P, Weinkauf T. 2014.Notes on the simplification of the Morse-Smale complex. In: Topological Methods in Data Analysis and Visualization III. , 135–150.' mla: Günther, David, et al. “Notes on the Simplification of the Morse-Smale Complex.” Topological Methods in Data Analysis and Visualization III., edited by Peer-Timo Bremer et al., Springer Nature, 2014, pp. 135–50, doi:10.1007/978-3-319-04099-8_9. short: D. Günther, J. Reininghaus, H.-P. Seidel, T. Weinkauf, in:, P.-T. Bremer, I. Hotz, V. Pascucci, R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III., Springer Nature, Cham, 2014, pp. 135–150. date_created: 2022-03-04T08:33:57Z date_published: 2014-03-19T00:00:00Z date_updated: 2023-09-05T15:33:45Z day: '19' department: - _id: HeEd doi: 10.1007/978-3-319-04099-8_9 ec_funded: 1 editor: - first_name: Peer-Timo full_name: Bremer, Peer-Timo last_name: Bremer - first_name: Ingrid full_name: Hotz, Ingrid last_name: Hotz - first_name: Valerio full_name: Pascucci, Valerio last_name: Pascucci - first_name: Ronald full_name: Peikert, Ronald last_name: Peikert language: - iso: eng month: '03' oa_version: None page: 135-150 place: Cham project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems publication: Topological Methods in Data Analysis and Visualization III. publication_identifier: eisbn: - '9783319040998' eissn: - 2197-666X isbn: - '9783319040981' issn: - 1612-3786 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' series_title: Mathematics and Visualization status: public title: Notes on the simplification of the Morse-Smale complex type: book_chapter user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2014' ... --- _id: '2255' abstract: - lang: eng text: Motivated by applications in biology, we present an algorithm for estimating the length of tube-like shapes in 3-dimensional Euclidean space. In a first step, we combine the tube formula of Weyl with integral geometric methods to obtain an integral representation of the length, which we approximate using a variant of the Koksma-Hlawka Theorem. In a second step, we use tools from computational topology to decrease the dependence on small perturbations of the shape. We present computational experiments that shed light on the stability and the convergence rate of our algorithm. author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Florian full_name: Pausinger, Florian id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87 last_name: Pausinger orcid: 0000-0002-8379-3768 citation: ama: Edelsbrunner H, Pausinger F. Stable length estimates of tube-like shapes. Journal of Mathematical Imaging and Vision. 2014;50(1):164-177. doi:10.1007/s10851-013-0468-x apa: Edelsbrunner, H., & Pausinger, F. (2014). Stable length estimates of tube-like shapes. Journal of Mathematical Imaging and Vision. Springer. https://doi.org/10.1007/s10851-013-0468-x chicago: Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like Shapes.” Journal of Mathematical Imaging and Vision. Springer, 2014. https://doi.org/10.1007/s10851-013-0468-x. ieee: H. Edelsbrunner and F. Pausinger, “Stable length estimates of tube-like shapes,” Journal of Mathematical Imaging and Vision, vol. 50, no. 1. Springer, pp. 164–177, 2014. ista: Edelsbrunner H, Pausinger F. 2014. Stable length estimates of tube-like shapes. Journal of Mathematical Imaging and Vision. 50(1), 164–177. mla: Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like Shapes.” Journal of Mathematical Imaging and Vision, vol. 50, no. 1, Springer, 2014, pp. 164–77, doi:10.1007/s10851-013-0468-x. short: H. Edelsbrunner, F. Pausinger, Journal of Mathematical Imaging and Vision 50 (2014) 164–177. date_created: 2018-12-11T11:56:36Z date_published: 2014-09-01T00:00:00Z date_updated: 2023-09-07T11:41:25Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1007/s10851-013-0468-x ec_funded: 1 file: - access_level: open_access checksum: 2f93f3e63a38a85cd4404d7953913b14 content_type: application/pdf creator: system date_created: 2018-12-12T10:16:18Z date_updated: 2020-07-14T12:45:35Z file_id: '5204' file_name: IST-2016-549-v1+1_2014-J-06-LengthEstimate.pdf file_size: 3941391 relation: main_file file_date_updated: 2020-07-14T12:45:35Z has_accepted_license: '1' intvolume: ' 50' issue: '1' language: - iso: eng month: '09' oa: 1 oa_version: Submitted Version page: 164 - 177 project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems publication: Journal of Mathematical Imaging and Vision publication_identifier: issn: - '09249907' publication_status: published publisher: Springer publist_id: '4691' pubrep_id: '549' quality_controlled: '1' related_material: record: - id: '2843' relation: earlier_version status: public - id: '1399' relation: dissertation_contains status: public scopus_import: 1 status: public title: Stable length estimates of tube-like shapes type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 50 year: '2014' ... --- _id: '10894' abstract: - lang: eng text: PHAT is a C++ library for the computation of persistent homology by matrix reduction. We aim for a simple generic design that decouples algorithms from data structures without sacrificing efficiency or user-friendliness. This makes PHAT a versatile platform for experimenting with algorithmic ideas and comparing them to state of the art implementations. article_processing_charge: No author: - first_name: Ulrich full_name: Bauer, Ulrich id: 2ADD483A-F248-11E8-B48F-1D18A9856A87 last_name: Bauer orcid: 0000-0002-9683-0724 - first_name: Michael full_name: Kerber, Michael last_name: Kerber - first_name: Jan full_name: Reininghaus, Jan id: 4505473A-F248-11E8-B48F-1D18A9856A87 last_name: Reininghaus - first_name: Hubert full_name: Wagner, Hubert last_name: Wagner citation: ama: 'Bauer U, Kerber M, Reininghaus J, Wagner H. PHAT – Persistent Homology Algorithms Toolbox. In: ICMS 2014: International Congress on Mathematical Software. Vol 8592. LNCS. Berlin, Heidelberg: Springer Berlin Heidelberg; 2014:137-143. doi:10.1007/978-3-662-44199-2_24' apa: 'Bauer, U., Kerber, M., Reininghaus, J., & Wagner, H. (2014). PHAT – Persistent Homology Algorithms Toolbox. In ICMS 2014: International Congress on Mathematical Software (Vol. 8592, pp. 137–143). Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-662-44199-2_24' chicago: 'Bauer, Ulrich, Michael Kerber, Jan Reininghaus, and Hubert Wagner. “PHAT – Persistent Homology Algorithms Toolbox.” In ICMS 2014: International Congress on Mathematical Software, 8592:137–43. LNCS. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. https://doi.org/10.1007/978-3-662-44199-2_24.' ieee: 'U. Bauer, M. Kerber, J. Reininghaus, and H. Wagner, “PHAT – Persistent Homology Algorithms Toolbox,” in ICMS 2014: International Congress on Mathematical Software, Seoul, South Korea, 2014, vol. 8592, pp. 137–143.' ista: 'Bauer U, Kerber M, Reininghaus J, Wagner H. 2014. PHAT – Persistent Homology Algorithms Toolbox. ICMS 2014: International Congress on Mathematical Software. ICMS: International Congress on Mathematical SoftwareLNCS vol. 8592, 137–143.' mla: 'Bauer, Ulrich, et al. “PHAT – Persistent Homology Algorithms Toolbox.” ICMS 2014: International Congress on Mathematical Software, vol. 8592, Springer Berlin Heidelberg, 2014, pp. 137–43, doi:10.1007/978-3-662-44199-2_24.' short: 'U. Bauer, M. Kerber, J. Reininghaus, H. Wagner, in:, ICMS 2014: International Congress on Mathematical Software, Springer Berlin Heidelberg, Berlin, Heidelberg, 2014, pp. 137–143.' conference: end_date: 2014-08-09 location: Seoul, South Korea name: 'ICMS: International Congress on Mathematical Software' start_date: 2014-08-05 date_created: 2022-03-21T07:12:16Z date_published: 2014-09-01T00:00:00Z date_updated: 2023-09-20T09:42:40Z day: '01' department: - _id: HeEd doi: 10.1007/978-3-662-44199-2_24 intvolume: ' 8592' language: - iso: eng month: '09' oa_version: None page: 137-143 place: Berlin, Heidelberg publication: 'ICMS 2014: International Congress on Mathematical Software' publication_identifier: eisbn: - '9783662441992' eissn: - 1611-3349 isbn: - '9783662441985' issn: - 0302-9743 publication_status: published publisher: Springer Berlin Heidelberg quality_controlled: '1' related_material: record: - id: '1433' relation: later_version status: public scopus_import: '1' series_title: LNCS status: public title: PHAT – Persistent Homology Algorithms Toolbox type: conference user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 8592 year: '2014' ... --- _id: '2012' abstract: - lang: eng text: The classical sphere packing problem asks for the best (infinite) arrangement of non-overlapping unit balls which cover as much space as possible. We define a generalized version of the problem, where we allow each ball a limited amount of overlap with other balls. We study two natural choices of overlap measures and obtain the optimal lattice packings in a parameterized family of lattices which contains the FCC, BCC, and integer lattice. acknowledgement: We thank Herbert Edelsbrunner for his valuable discussions and ideas on the topic of this paper. The second author has been supported by the Max Planck Center for Visual Computing and Communication article_number: '1401.0468' article_processing_charge: No author: - first_name: Mabel full_name: Iglesias Ham, Mabel id: 41B58C0C-F248-11E8-B48F-1D18A9856A87 last_name: Iglesias Ham - first_name: Michael full_name: Kerber, Michael last_name: Kerber orcid: 0000-0002-8030-9299 - first_name: Caroline full_name: Uhler, Caroline id: 49ADD78E-F248-11E8-B48F-1D18A9856A87 last_name: Uhler orcid: 0000-0002-7008-0216 citation: ama: Iglesias Ham M, Kerber M, Uhler C. Sphere packing with limited overlap. arXiv. doi:10.48550/arXiv.1401.0468 apa: Iglesias Ham, M., Kerber, M., & Uhler, C. (n.d.). Sphere packing with limited overlap. arXiv. https://doi.org/10.48550/arXiv.1401.0468 chicago: Iglesias Ham, Mabel, Michael Kerber, and Caroline Uhler. “Sphere Packing with Limited Overlap.” ArXiv, n.d. https://doi.org/10.48550/arXiv.1401.0468. ieee: M. Iglesias Ham, M. Kerber, and C. Uhler, “Sphere packing with limited overlap,” arXiv. . ista: Iglesias Ham M, Kerber M, Uhler C. Sphere packing with limited overlap. arXiv, 1401.0468. mla: Iglesias Ham, Mabel, et al. “Sphere Packing with Limited Overlap.” ArXiv, 1401.0468, doi:10.48550/arXiv.1401.0468. short: M. Iglesias Ham, M. Kerber, C. Uhler, ArXiv (n.d.). date_created: 2018-12-11T11:55:12Z date_published: 2014-01-01T00:00:00Z date_updated: 2023-10-18T08:06:45Z day: '01' department: - _id: HeEd - _id: CaUh doi: 10.48550/arXiv.1401.0468 external_id: arxiv: - '1401.0468' language: - iso: eng main_file_link: - open_access: '1' url: http://cccg.ca/proceedings/2014/papers/paper23.pdf month: '01' oa: 1 oa_version: Submitted Version publication: arXiv publication_status: submitted publist_id: '5064' status: public title: Sphere packing with limited overlap type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2014' ... --- _id: '2209' abstract: - lang: eng text: "A straight skeleton is a well-known geometric structure, and several algorithms exist to construct the straight skeleton for a given polygon or planar straight-line graph. In this paper, we ask the reverse question: Given the straight skeleton (in form of a planar straight-line graph, with some rays to infinity), can we reconstruct a planar straight-line graph for which this was the straight skeleton? We show how to reduce this problem to the problem of finding a line that intersects a set of convex polygons. We can find these convex polygons and all such lines in $O(nlog n)$ time in the Real RAM computer model, where $n$ denotes the number of edges of the input graph. We also explain how our approach can be used for recognizing Voronoi diagrams of points, thereby completing a partial solution provided by Ash and Bolker in 1985.\r\n" alternative_title: - '2013 10th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2013) ' author: - first_name: Therese full_name: Biedl, Therese last_name: Biedl - first_name: Martin full_name: Held, Martin last_name: Held - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 citation: ama: 'Biedl T, Held M, Huber S. Recognizing straight skeletons and Voronoi diagrams and reconstructing their input. In: IEEE; 2013:37-46. doi:10.1109/ISVD.2013.11' apa: 'Biedl, T., Held, M., & Huber, S. (2013). Recognizing straight skeletons and Voronoi diagrams and reconstructing their input (pp. 37–46). Presented at the ISVD: Voronoi Diagrams in Science and Engineering, St. Petersburg, Russia: IEEE. https://doi.org/10.1109/ISVD.2013.11' chicago: Biedl, Therese, Martin Held, and Stefan Huber. “Recognizing Straight Skeletons and Voronoi Diagrams and Reconstructing Their Input,” 37–46. IEEE, 2013. https://doi.org/10.1109/ISVD.2013.11. ieee: 'T. Biedl, M. Held, and S. Huber, “Recognizing straight skeletons and Voronoi diagrams and reconstructing their input,” presented at the ISVD: Voronoi Diagrams in Science and Engineering, St. Petersburg, Russia, 2013, pp. 37–46.' ista: 'Biedl T, Held M, Huber S. 2013. Recognizing straight skeletons and Voronoi diagrams and reconstructing their input. ISVD: Voronoi Diagrams in Science and Engineering, 2013 10th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2013) , , 37–46.' mla: Biedl, Therese, et al. Recognizing Straight Skeletons and Voronoi Diagrams and Reconstructing Their Input. IEEE, 2013, pp. 37–46, doi:10.1109/ISVD.2013.11. short: T. Biedl, M. Held, S. Huber, in:, IEEE, 2013, pp. 37–46. conference: end_date: 2013-07-10 location: St. Petersburg, Russia name: 'ISVD: Voronoi Diagrams in Science and Engineering' start_date: 2013-07-08 date_created: 2018-12-11T11:56:20Z date_published: 2013-12-01T00:00:00Z date_updated: 2021-01-12T06:56:00Z day: '01' department: - _id: HeEd doi: 10.1109/ISVD.2013.11 language: - iso: eng month: '12' oa_version: None page: 37 - 46 publication_identifier: eisbn: - '978-0-7695-5037-4 ' publication_status: published publisher: IEEE publist_id: '4763' quality_controlled: '1' scopus_import: 1 status: public title: Recognizing straight skeletons and Voronoi diagrams and reconstructing their input type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2013' ... --- _id: '2210' abstract: - lang: eng text: 'A straight skeleton is a well-known geometric structure, and several algorithms exist to construct the straight skeleton for a given polygon. In this paper, we ask the reverse question: Given the straight skeleton (in form of a tree with a drawing in the plane, but with the exact position of the leaves unspecified), can we reconstruct the polygon? We show that in most cases there exists at most one polygon; in the remaining case there is an infinite number of polygons determined by one angle that can range in an interval. We can find this (set of) polygon(s) in linear time in the Real RAM computer model.' author: - first_name: Therese full_name: Biedl, Therese last_name: Biedl - first_name: Martin full_name: Held, Martin last_name: Held - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 citation: ama: 'Biedl T, Held M, Huber S. Reconstructing polygons from embedded straight skeletons. In: 29th European Workshop on Computational Geometry. TU Braunschweig; 2013:95-98.' apa: 'Biedl, T., Held, M., & Huber, S. (2013). Reconstructing polygons from embedded straight skeletons. In 29th European Workshop on Computational Geometry (pp. 95–98). Braunschweig, Germany: TU Braunschweig.' chicago: Biedl, Therese, Martin Held, and Stefan Huber. “Reconstructing Polygons from Embedded Straight Skeletons.” In 29th European Workshop on Computational Geometry, 95–98. TU Braunschweig, 2013. ieee: T. Biedl, M. Held, and S. Huber, “Reconstructing polygons from embedded straight skeletons,” in 29th European Workshop on Computational Geometry, Braunschweig, Germany, 2013, pp. 95–98. ista: 'Biedl T, Held M, Huber S. 2013. Reconstructing polygons from embedded straight skeletons. 29th European Workshop on Computational Geometry. EuroCG: European Workshop on Computational Geometry, 95–98.' mla: Biedl, Therese, et al. “Reconstructing Polygons from Embedded Straight Skeletons.” 29th European Workshop on Computational Geometry, TU Braunschweig, 2013, pp. 95–98. short: T. Biedl, M. Held, S. Huber, in:, 29th European Workshop on Computational Geometry, TU Braunschweig, 2013, pp. 95–98. conference: end_date: 2013-03-20 location: Braunschweig, Germany name: 'EuroCG: European Workshop on Computational Geometry' start_date: 2013-03-17 date_created: 2018-12-11T11:56:21Z date_published: 2013-03-01T00:00:00Z date_updated: 2021-01-12T06:56:00Z day: '01' department: - _id: HeEd language: - iso: eng main_file_link: - open_access: '1' url: http://www.ibr.cs.tu-bs.de/alg/eurocg13/booklet_eurocg13.pdf month: '03' oa: 1 oa_version: Submitted Version page: 95 - 98 publication: 29th European Workshop on Computational Geometry publication_status: published publisher: TU Braunschweig publist_id: '4762' status: public title: Reconstructing polygons from embedded straight skeletons type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2013' ... --- _id: '2304' abstract: - lang: eng text: This extended abstract is concerned with the irregularities of distribution of one-dimensional permuted van der Corput sequences that are generated from linear permutations. We show how to obtain upper bounds for the discrepancy and diaphony of these sequences, by relating them to Kronecker sequences and applying earlier results of Faure and Niederreiter. acknowledgement: This research is supported by the Graduate school of IST Austria (Institute of Science and Technology Austria). author: - first_name: Florian full_name: Pausinger, Florian id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87 last_name: Pausinger orcid: 0000-0002-8379-3768 citation: ama: Pausinger F. Van der Corput sequences and linear permutations. Electronic Notes in Discrete Mathematics. 2013;43:43-50. doi:10.1016/j.endm.2013.07.008 apa: Pausinger, F. (2013). Van der Corput sequences and linear permutations. Electronic Notes in Discrete Mathematics. Elsevier. https://doi.org/10.1016/j.endm.2013.07.008 chicago: Pausinger, Florian. “Van Der Corput Sequences and Linear Permutations.” Electronic Notes in Discrete Mathematics. Elsevier, 2013. https://doi.org/10.1016/j.endm.2013.07.008. ieee: F. Pausinger, “Van der Corput sequences and linear permutations,” Electronic Notes in Discrete Mathematics, vol. 43. Elsevier, pp. 43–50, 2013. ista: Pausinger F. 2013. Van der Corput sequences and linear permutations. Electronic Notes in Discrete Mathematics. 43, 43–50. mla: Pausinger, Florian. “Van Der Corput Sequences and Linear Permutations.” Electronic Notes in Discrete Mathematics, vol. 43, Elsevier, 2013, pp. 43–50, doi:10.1016/j.endm.2013.07.008. short: F. Pausinger, Electronic Notes in Discrete Mathematics 43 (2013) 43–50. date_created: 2018-12-11T11:56:53Z date_published: 2013-09-05T00:00:00Z date_updated: 2021-01-12T06:56:39Z day: '05' department: - _id: HeEd doi: 10.1016/j.endm.2013.07.008 intvolume: ' 43' language: - iso: eng month: '09' oa_version: None page: 43 - 50 publication: Electronic Notes in Discrete Mathematics publication_status: published publisher: Elsevier publist_id: '4623' quality_controlled: '1' scopus_import: 1 status: public title: Van der Corput sequences and linear permutations type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 43 year: '2013' ... --- _id: '2807' abstract: - lang: eng text: 'We consider several basic problems of algebraic topology, with connections to combinatorial and geometric questions, from the point of view of computational complexity. The extension problem asks, given topological spaces X; Y , a subspace A ⊆ X, and a (continuous) map f : A → Y , whether f can be extended to a map X → Y . For computational purposes, we assume that X and Y are represented as finite simplicial complexes, A is a subcomplex of X, and f is given as a simplicial map. In this generality the problem is undecidable, as follows from Novikov''s result from the 1950s on uncomputability of the fundamental group π1(Y ). We thus study the problem under the assumption that, for some k ≥ 2, Y is (k - 1)-connected; informally, this means that Y has \no holes up to dimension k-1" (a basic example of such a Y is the sphere Sk). We prove that, on the one hand, this problem is still undecidable for dimX = 2k. On the other hand, for every fixed k ≥ 2, we obtain an algorithm that solves the extension problem in polynomial time assuming Y (k - 1)-connected and dimX ≤ 2k - 1. For dimX ≤ 2k - 2, the algorithm also provides a classification of all extensions up to homotopy (continuous deformation). This relies on results of our SODA 2012 paper, and the main new ingredient is a machinery of objects with polynomial-time homology, which is a polynomial-time analog of objects with effective homology developed earlier by Sergeraert et al. We also consider the computation of the higher homotopy groups πk(Y ), k ≥ 2, for a 1-connected Y . Their computability was established by Brown in 1957; we show that πk(Y ) can be computed in polynomial time for every fixed k ≥ 2. On the other hand, Anick proved in 1989 that computing πk(Y ) is #P-hard if k is a part of input, where Y is a cell complex with certain rather compact encoding. We strengthen his result to #P-hardness for Y given as a simplicial complex. ' author: - first_name: Martin full_name: Čadek, Martin last_name: Čadek - first_name: Marek full_name: Krcál, Marek id: 33E21118-F248-11E8-B48F-1D18A9856A87 last_name: Krcál - first_name: Jiří full_name: Matoušek, Jiří last_name: Matoušek - first_name: Lukáš full_name: Vokřínek, Lukáš last_name: Vokřínek - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 citation: ama: 'Čadek M, Krcál M, Matoušek J, Vokřínek L, Wagner U. Extending continuous maps: Polynomiality and undecidability. In: 45th Annual ACM Symposium on Theory of Computing. ACM; 2013:595-604. doi:10.1145/2488608.2488683' apa: 'Čadek, M., Krcál, M., Matoušek, J., Vokřínek, L., & Wagner, U. (2013). Extending continuous maps: Polynomiality and undecidability. In 45th Annual ACM Symposium on theory of computing (pp. 595–604). Palo Alto, CA, United States: ACM. https://doi.org/10.1145/2488608.2488683' chicago: 'Čadek, Martin, Marek Krcál, Jiří Matoušek, Lukáš Vokřínek, and Uli Wagner. “Extending Continuous Maps: Polynomiality and Undecidability.” In 45th Annual ACM Symposium on Theory of Computing, 595–604. ACM, 2013. https://doi.org/10.1145/2488608.2488683.' ieee: 'M. Čadek, M. Krcál, J. Matoušek, L. Vokřínek, and U. Wagner, “Extending continuous maps: Polynomiality and undecidability,” in 45th Annual ACM Symposium on theory of computing, Palo Alto, CA, United States, 2013, pp. 595–604.' ista: 'Čadek M, Krcál M, Matoušek J, Vokřínek L, Wagner U. 2013. Extending continuous maps: Polynomiality and undecidability. 45th Annual ACM Symposium on theory of computing. STOC: Symposium on the Theory of Computing, 595–604.' mla: 'Čadek, Martin, et al. “Extending Continuous Maps: Polynomiality and Undecidability.” 45th Annual ACM Symposium on Theory of Computing, ACM, 2013, pp. 595–604, doi:10.1145/2488608.2488683.' short: M. Čadek, M. Krcál, J. Matoušek, L. Vokřínek, U. Wagner, in:, 45th Annual ACM Symposium on Theory of Computing, ACM, 2013, pp. 595–604. conference: end_date: 2013-06-04 location: Palo Alto, CA, United States name: 'STOC: Symposium on the Theory of Computing' start_date: 2013-06-01 date_created: 2018-12-11T11:59:42Z date_published: 2013-06-01T00:00:00Z date_updated: 2021-01-12T06:59:51Z day: '01' ddc: - '510' department: - _id: UlWa - _id: HeEd doi: 10.1145/2488608.2488683 file: - access_level: open_access checksum: 06c2ce5c1135fbc1f71ca15eeb242dcf content_type: application/pdf creator: system date_created: 2018-12-12T10:14:29Z date_updated: 2020-07-14T12:45:48Z file_id: '5081' file_name: IST-2016-533-v1+1_Extending_continuous_maps_polynomiality_and_undecidability.pdf file_size: 447945 relation: main_file file_date_updated: 2020-07-14T12:45:48Z has_accepted_license: '1' language: - iso: eng month: '06' oa: 1 oa_version: Submitted Version page: 595 - 604 publication: 45th Annual ACM Symposium on theory of computing publication_status: published publisher: ACM publist_id: '4078' pubrep_id: '533' quality_controlled: '1' scopus_import: 1 status: public title: 'Extending continuous maps: Polynomiality and undecidability' type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2013' ... --- _id: '2812' abstract: - lang: eng text: 'We consider the problem of deciding whether the persistent homology group of a simplicial pair (K, L) can be realized as the homology H* (X) of some complex X with L ⊂ X ⊂ K. We show that this problem is NP-complete even if K is embedded in ℝ3. As a consequence, we show that it is NP-hard to simplify level and sublevel sets of scalar functions on S3 within a given tolerance constraint. This problem has relevance to the visualization of medical images by isosurfaces. We also show an implication to the theory of well groups of scalar functions: not every well group can be realized by some level set, and deciding whether a well group can be realized is NP-hard.' acknowledgement: Some of the authors were partially supported by the GIGA ANR grant (contract ANR-09-BLAN-0331-01) and the European project CG-Learning (contract 255827). author: - first_name: Dominique full_name: Attali, Dominique last_name: Attali - first_name: Ulrich full_name: Bauer, Ulrich id: 2ADD483A-F248-11E8-B48F-1D18A9856A87 last_name: Bauer orcid: 0000-0002-9683-0724 - first_name: Olivier full_name: Devillers, Olivier last_name: Devillers - first_name: Marc full_name: Glisse, Marc last_name: Glisse - first_name: André full_name: Lieutier, André last_name: Lieutier citation: ama: 'Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. Homological reconstruction and simplification in R3. In: Proceedings of the 29th Annual Symposium on Computational Geometry. ACM; 2013:117-125. doi:10.1145/2462356.2462373' apa: 'Attali, D., Bauer, U., Devillers, O., Glisse, M., & Lieutier, A. (2013). Homological reconstruction and simplification in R3. In Proceedings of the 29th annual symposium on Computational Geometry (pp. 117–125). Rio de Janeiro, Brazil: ACM. https://doi.org/10.1145/2462356.2462373' chicago: Attali, Dominique, Ulrich Bauer, Olivier Devillers, Marc Glisse, and André Lieutier. “Homological Reconstruction and Simplification in R3.” In Proceedings of the 29th Annual Symposium on Computational Geometry, 117–25. ACM, 2013. https://doi.org/10.1145/2462356.2462373. ieee: D. Attali, U. Bauer, O. Devillers, M. Glisse, and A. Lieutier, “Homological reconstruction and simplification in R3,” in Proceedings of the 29th annual symposium on Computational Geometry, Rio de Janeiro, Brazil, 2013, pp. 117–125. ista: 'Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. 2013. Homological reconstruction and simplification in R3. Proceedings of the 29th annual symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, 117–125.' mla: Attali, Dominique, et al. “Homological Reconstruction and Simplification in R3.” Proceedings of the 29th Annual Symposium on Computational Geometry, ACM, 2013, pp. 117–25, doi:10.1145/2462356.2462373. short: D. Attali, U. Bauer, O. Devillers, M. Glisse, A. Lieutier, in:, Proceedings of the 29th Annual Symposium on Computational Geometry, ACM, 2013, pp. 117–125. conference: end_date: 2013-06-20 location: Rio de Janeiro, Brazil name: 'SoCG: Symposium on Computational Geometry' start_date: 2013-06-17 date_created: 2018-12-11T11:59:44Z date_published: 2013-06-01T00:00:00Z date_updated: 2023-02-23T10:15:15Z day: '01' department: - _id: HeEd doi: 10.1145/2462356.2462373 language: - iso: eng main_file_link: - open_access: '1' url: http://hal.archives-ouvertes.fr/hal-00833791/ month: '06' oa: 1 oa_version: Submitted Version page: 117 - 125 publication: Proceedings of the 29th annual symposium on Computational Geometry publication_status: published publisher: ACM publist_id: '4072' quality_controlled: '1' related_material: record: - id: '1805' relation: later_version status: public scopus_import: 1 status: public title: Homological reconstruction and simplification in R3 type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2013' ... --- _id: '2822' abstract: - lang: eng text: Identification of genes that control root system architecture in crop plants requires innovations that enable high-throughput and accurate measurements of root system architecture through time. We demonstrate the ability of a semiautomated 3D in vivo imaging and digital phenotyping pipeline to interrogate the quantitative genetic basis of root system growth in a rice biparental mapping population, Bala x Azucena. We phenotyped >1,400 3D root models and >57,000 2D images for a suite of 25 traits that quantified the distribution, shape, extent of exploration, and the intrinsic size of root networks at days 12, 14, and 16 of growth in a gellan gum medium. From these data we identified 89 quantitative trait loci, some of which correspond to those found previously in soil-grown plants, and provide evidence for genetic tradeoffs in root growth allocations, such as between the extent and thoroughness of exploration. We also developed a multivariate method for generating and mapping central root architecture phenotypes and used it to identify five major quantitative trait loci (r2 = 24-37%), two of which were not identified by our univariate analysis. Our imaging and analytical platform provides a means to identify genes with high potential for improving root traits and agronomic qualities of crops. author: - first_name: Christopher full_name: Topp, Christopher last_name: Topp - first_name: Anjali full_name: Iyer Pascuzzi, Anjali last_name: Iyer Pascuzzi - first_name: Jill full_name: Anderson, Jill last_name: Anderson - first_name: Cheng full_name: Lee, Cheng last_name: Lee - first_name: Paul full_name: Zurek, Paul last_name: Zurek - first_name: Olga full_name: Symonova, Olga id: 3C0C7BC6-F248-11E8-B48F-1D18A9856A87 last_name: Symonova - first_name: Ying full_name: Zheng, Ying last_name: Zheng - first_name: Alexander full_name: Bucksch, Alexander last_name: Bucksch - first_name: Yuriy full_name: Mileyko, Yuriy last_name: Mileyko - first_name: Taras full_name: Galkovskyi, Taras last_name: Galkovskyi - first_name: Brad full_name: Moore, Brad last_name: Moore - first_name: John full_name: Harer, John last_name: Harer - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Thomas full_name: Mitchell Olds, Thomas last_name: Mitchell Olds - first_name: Joshua full_name: Weitz, Joshua last_name: Weitz - first_name: Philip full_name: Benfey, Philip last_name: Benfey citation: ama: Topp C, Iyer Pascuzzi A, Anderson J, et al. 3D phenotyping and quantitative trait locus mapping identify core regions of the rice genome controlling root architecture. PNAS. 2013;110(18):E1695-E1704. doi:10.1073/pnas.1304354110 apa: Topp, C., Iyer Pascuzzi, A., Anderson, J., Lee, C., Zurek, P., Symonova, O., … Benfey, P. (2013). 3D phenotyping and quantitative trait locus mapping identify core regions of the rice genome controlling root architecture. PNAS. National Academy of Sciences. https://doi.org/10.1073/pnas.1304354110 chicago: Topp, Christopher, Anjali Iyer Pascuzzi, Jill Anderson, Cheng Lee, Paul Zurek, Olga Symonova, Ying Zheng, et al. “3D Phenotyping and Quantitative Trait Locus Mapping Identify Core Regions of the Rice Genome Controlling Root Architecture.” PNAS. National Academy of Sciences, 2013. https://doi.org/10.1073/pnas.1304354110. ieee: C. Topp et al., “3D phenotyping and quantitative trait locus mapping identify core regions of the rice genome controlling root architecture,” PNAS, vol. 110, no. 18. National Academy of Sciences, pp. E1695–E1704, 2013. ista: Topp C, Iyer Pascuzzi A, Anderson J, Lee C, Zurek P, Symonova O, Zheng Y, Bucksch A, Mileyko Y, Galkovskyi T, Moore B, Harer J, Edelsbrunner H, Mitchell Olds T, Weitz J, Benfey P. 2013. 3D phenotyping and quantitative trait locus mapping identify core regions of the rice genome controlling root architecture. PNAS. 110(18), E1695–E1704. mla: Topp, Christopher, et al. “3D Phenotyping and Quantitative Trait Locus Mapping Identify Core Regions of the Rice Genome Controlling Root Architecture.” PNAS, vol. 110, no. 18, National Academy of Sciences, 2013, pp. E1695–704, doi:10.1073/pnas.1304354110. short: C. Topp, A. Iyer Pascuzzi, J. Anderson, C. Lee, P. Zurek, O. Symonova, Y. Zheng, A. Bucksch, Y. Mileyko, T. Galkovskyi, B. Moore, J. Harer, H. Edelsbrunner, T. Mitchell Olds, J. Weitz, P. Benfey, PNAS 110 (2013) E1695–E1704. date_created: 2018-12-11T11:59:47Z date_published: 2013-04-30T00:00:00Z date_updated: 2021-01-12T06:59:58Z day: '30' department: - _id: MaJö - _id: HeEd doi: 10.1073/pnas.1304354110 external_id: pmid: - '25673779' intvolume: ' 110' issue: '18' language: - iso: eng main_file_link: - open_access: '1' url: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4378147/ month: '04' oa: 1 oa_version: Submitted Version page: E1695 - E1704 pmid: 1 publication: PNAS publication_status: published publisher: National Academy of Sciences publist_id: '3979' quality_controlled: '1' scopus_import: 1 status: public title: 3D phenotyping and quantitative trait locus mapping identify core regions of the rice genome controlling root architecture type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 110 year: '2013' ... --- _id: '2843' abstract: - lang: eng text: 'Mathematical objects can be measured unambiguously, but not so objects from our physical world. Even the total length of tubelike shapes has its difficulties. We introduce a combination of geometric, probabilistic, and topological methods to design a stable length estimate for tube-like shapes; that is: one that is insensitive to small shape changes.' alternative_title: - LNCS author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Florian full_name: Pausinger, Florian id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87 last_name: Pausinger orcid: 0000-0002-8379-3768 citation: ama: 'Edelsbrunner H, Pausinger F. Stable length estimates of tube-like shapes. In: 17th IAPR International Conference on Discrete Geometry for Computer Imagery. Vol 7749. Springer; 2013:XV-XIX. doi:10.1007/978-3-642-37067-0' apa: 'Edelsbrunner, H., & Pausinger, F. (2013). Stable length estimates of tube-like shapes. In 17th IAPR International Conference on Discrete Geometry for Computer Imagery (Vol. 7749, pp. XV–XIX). Seville, Spain: Springer. https://doi.org/10.1007/978-3-642-37067-0' chicago: Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like Shapes.” In 17th IAPR International Conference on Discrete Geometry for Computer Imagery, 7749:XV–XIX. Springer, 2013. https://doi.org/10.1007/978-3-642-37067-0. ieee: H. Edelsbrunner and F. Pausinger, “Stable length estimates of tube-like shapes,” in 17th IAPR International Conference on Discrete Geometry for Computer Imagery, Seville, Spain, 2013, vol. 7749, pp. XV–XIX. ista: 'Edelsbrunner H, Pausinger F. 2013. Stable length estimates of tube-like shapes. 17th IAPR International Conference on Discrete Geometry for Computer Imagery. DGCI: Discrete Geometry for Computer Imagery, LNCS, vol. 7749, XV–XIX.' mla: Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like Shapes.” 17th IAPR International Conference on Discrete Geometry for Computer Imagery, vol. 7749, Springer, 2013, pp. XV–XIX, doi:10.1007/978-3-642-37067-0. short: H. Edelsbrunner, F. Pausinger, in:, 17th IAPR International Conference on Discrete Geometry for Computer Imagery, Springer, 2013, pp. XV–XIX. conference: end_date: 2013-03-22 location: Seville, Spain name: 'DGCI: Discrete Geometry for Computer Imagery' start_date: 2013-03-20 date_created: 2018-12-11T11:59:53Z date_published: 2013-02-21T00:00:00Z date_updated: 2023-02-23T10:35:00Z day: '21' department: - _id: HeEd doi: 10.1007/978-3-642-37067-0 intvolume: ' 7749' language: - iso: eng month: '02' oa_version: None page: XV - XIX publication: 17th IAPR International Conference on Discrete Geometry for Computer Imagery publication_status: published publisher: Springer publist_id: '3952' quality_controlled: '1' related_material: record: - id: '2255' relation: later_version status: public scopus_import: 1 status: public title: Stable length estimates of tube-like shapes type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 7749 year: '2013' ... --- _id: '2859' abstract: - lang: eng text: Given a continuous function f:X-R on a topological space, we consider the preimages of intervals and their homology groups and show how to read the ranks of these groups from the extended persistence diagram of f. In addition, we quantify the robustness of the homology classes under perturbations of f using well groups, and we show how to read the ranks of these groups from the same extended persistence diagram. The special case X=R3 has ramifications in the fields of medical imaging and scientific visualization. author: - first_name: Paul full_name: Bendich, Paul id: 43F6EC54-F248-11E8-B48F-1D18A9856A87 last_name: Bendich - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Dmitriy full_name: Morozov, Dmitriy last_name: Morozov - first_name: Amit full_name: Patel, Amit id: 34A254A0-F248-11E8-B48F-1D18A9856A87 last_name: Patel citation: ama: Bendich P, Edelsbrunner H, Morozov D, Patel A. Homology and robustness of level and interlevel sets. Homology, Homotopy and Applications. 2013;15(1):51-72. doi:10.4310/HHA.2013.v15.n1.a3 apa: Bendich, P., Edelsbrunner, H., Morozov, D., & Patel, A. (2013). Homology and robustness of level and interlevel sets. Homology, Homotopy and Applications. International Press. https://doi.org/10.4310/HHA.2013.v15.n1.a3 chicago: Bendich, Paul, Herbert Edelsbrunner, Dmitriy Morozov, and Amit Patel. “Homology and Robustness of Level and Interlevel Sets.” Homology, Homotopy and Applications. International Press, 2013. https://doi.org/10.4310/HHA.2013.v15.n1.a3. ieee: P. Bendich, H. Edelsbrunner, D. Morozov, and A. Patel, “Homology and robustness of level and interlevel sets,” Homology, Homotopy and Applications, vol. 15, no. 1. International Press, pp. 51–72, 2013. ista: Bendich P, Edelsbrunner H, Morozov D, Patel A. 2013. Homology and robustness of level and interlevel sets. Homology, Homotopy and Applications. 15(1), 51–72. mla: Bendich, Paul, et al. “Homology and Robustness of Level and Interlevel Sets.” Homology, Homotopy and Applications, vol. 15, no. 1, International Press, 2013, pp. 51–72, doi:10.4310/HHA.2013.v15.n1.a3. short: P. Bendich, H. Edelsbrunner, D. Morozov, A. Patel, Homology, Homotopy and Applications 15 (2013) 51–72. date_created: 2018-12-11T11:59:58Z date_published: 2013-05-01T00:00:00Z date_updated: 2021-01-12T07:00:18Z day: '01' department: - _id: HeEd doi: 10.4310/HHA.2013.v15.n1.a3 external_id: arxiv: - '1102.3389' intvolume: ' 15' issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1102.3389v1 month: '05' oa: 1 oa_version: Preprint page: 51 - 72 publication: Homology, Homotopy and Applications publication_status: published publisher: International Press publist_id: '3930' quality_controlled: '1' scopus_import: 1 status: public title: Homology and robustness of level and interlevel sets type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 15 year: '2013' ... --- _id: '2887' abstract: - lang: eng text: 'Root system growth and development is highly plastic and is influenced by the surrounding environment. Roots frequently grow in heterogeneous environments that include interactions from neighboring plants and physical impediments in the rhizosphere. To investigate how planting density and physical objects affect root system growth, we grew rice in a transparent gel system in close proximity with another plant or a physical object. Root systems were imaged and reconstructed in three dimensions. Root-root interaction strength was calculated using quantitative metrics that characterize the extent towhich the reconstructed root systems overlap each other. Surprisingly, we found the overlap of root systems of the same genotype was significantly higher than that of root systems of different genotypes. Root systems of the same genotype tended to grow toward each other but those of different genotypes appeared to avoid each other. Shoot separation experiments excluded the possibility of aerial interactions, suggesting root communication. Staggered plantings indicated that interactions likely occur at root tips in close proximity. Recognition of obstacles also occurred through root tips, but through physical contact in a size-dependent manner. These results indicate that root systems use two different forms of communication to recognize objects and alter root architecture: root-root recognition, possibly mediated through root exudates, and root-object recognition mediated by physical contact at the root tips. This finding suggests that root tips act as local sensors that integrate rhizosphere information into global root architectural changes.' article_processing_charge: No article_type: original author: - first_name: Suqin full_name: Fang, Suqin last_name: Fang - first_name: Randy full_name: Clark, Randy last_name: Clark - first_name: Ying full_name: Zheng, Ying last_name: Zheng - first_name: Anjali full_name: Iyer Pascuzzi, Anjali last_name: Iyer Pascuzzi - first_name: Joshua full_name: Weitz, Joshua last_name: Weitz - first_name: Leon full_name: Kochian, Leon last_name: Kochian - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Hong full_name: Liao, Hong last_name: Liao - first_name: Philip full_name: Benfey, Philip last_name: Benfey citation: ama: Fang S, Clark R, Zheng Y, et al. Genotypic recognition and spatial responses by rice roots. PNAS. 2013;110(7):2670-2675. doi:10.1073/pnas.1222821110 apa: Fang, S., Clark, R., Zheng, Y., Iyer Pascuzzi, A., Weitz, J., Kochian, L., … Benfey, P. (2013). Genotypic recognition and spatial responses by rice roots. PNAS. National Academy of Sciences. https://doi.org/10.1073/pnas.1222821110 chicago: Fang, Suqin, Randy Clark, Ying Zheng, Anjali Iyer Pascuzzi, Joshua Weitz, Leon Kochian, Herbert Edelsbrunner, Hong Liao, and Philip Benfey. “Genotypic Recognition and Spatial Responses by Rice Roots.” PNAS. National Academy of Sciences, 2013. https://doi.org/10.1073/pnas.1222821110. ieee: S. Fang et al., “Genotypic recognition and spatial responses by rice roots,” PNAS, vol. 110, no. 7. National Academy of Sciences, pp. 2670–2675, 2013. ista: Fang S, Clark R, Zheng Y, Iyer Pascuzzi A, Weitz J, Kochian L, Edelsbrunner H, Liao H, Benfey P. 2013. Genotypic recognition and spatial responses by rice roots. PNAS. 110(7), 2670–2675. mla: Fang, Suqin, et al. “Genotypic Recognition and Spatial Responses by Rice Roots.” PNAS, vol. 110, no. 7, National Academy of Sciences, 2013, pp. 2670–75, doi:10.1073/pnas.1222821110. short: S. Fang, R. Clark, Y. Zheng, A. Iyer Pascuzzi, J. Weitz, L. Kochian, H. Edelsbrunner, H. Liao, P. Benfey, PNAS 110 (2013) 2670–2675. date_created: 2018-12-11T12:00:09Z date_published: 2013-02-12T00:00:00Z date_updated: 2021-01-12T07:00:29Z day: '12' department: - _id: HeEd doi: 10.1073/pnas.1222821110 external_id: pmid: - '23362379' intvolume: ' 110' issue: '7' language: - iso: eng main_file_link: - open_access: '1' url: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3574932/ month: '02' oa: 1 oa_version: Published Version page: 2670 - 2675 pmid: 1 publication: PNAS publication_status: published publisher: National Academy of Sciences publist_id: '3872' quality_controlled: '1' scopus_import: 1 status: public title: Genotypic recognition and spatial responses by rice roots type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 110 year: '2013' ... --- _id: '2901' abstract: - lang: eng text: ' We introduce the M-modes problem for graphical models: predicting the M label configurations of highest probability that are at the same time local maxima of the probability landscape. M-modes have multiple possible applications: because they are intrinsically diverse, they provide a principled alternative to non-maximum suppression techniques for structured prediction, they can act as codebook vectors for quantizing the configuration space, or they can form component centers for mixture model approximation. We present two algorithms for solving the M-modes problem. The first algorithm solves the problem in polynomial time when the underlying graphical model is a simple chain. The second algorithm solves the problem for junction chains. In synthetic and real dataset, we demonstrate how M-modes can improve the performance of prediction. We also use the generated modes as a tool to understand the topography of the probability distribution of configurations, for example with relation to the training set size and amount of noise in the data. ' alternative_title: - ' JMLR: W&CP' author: - first_name: Chao full_name: Chen, Chao id: 3E92416E-F248-11E8-B48F-1D18A9856A87 last_name: Chen - first_name: Vladimir full_name: Kolmogorov, Vladimir id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87 last_name: Kolmogorov - first_name: Zhu full_name: Yan, Zhu last_name: Yan - first_name: Dimitris full_name: Metaxas, Dimitris last_name: Metaxas - first_name: Christoph full_name: Lampert, Christoph id: 40C20FD2-F248-11E8-B48F-1D18A9856A87 last_name: Lampert orcid: 0000-0001-8622-7887 citation: ama: 'Chen C, Kolmogorov V, Yan Z, Metaxas D, Lampert C. Computing the M most probable modes of a graphical model. In: Vol 31. JMLR; 2013:161-169.' apa: 'Chen, C., Kolmogorov, V., Yan, Z., Metaxas, D., & Lampert, C. (2013). Computing the M most probable modes of a graphical model (Vol. 31, pp. 161–169). Presented at the AISTATS: Conference on Uncertainty in Artificial Intelligence, Scottsdale, AZ, United States: JMLR.' chicago: Chen, Chao, Vladimir Kolmogorov, Zhu Yan, Dimitris Metaxas, and Christoph Lampert. “Computing the M Most Probable Modes of a Graphical Model,” 31:161–69. JMLR, 2013. ieee: 'C. Chen, V. Kolmogorov, Z. Yan, D. Metaxas, and C. Lampert, “Computing the M most probable modes of a graphical model,” presented at the AISTATS: Conference on Uncertainty in Artificial Intelligence, Scottsdale, AZ, United States, 2013, vol. 31, pp. 161–169.' ista: 'Chen C, Kolmogorov V, Yan Z, Metaxas D, Lampert C. 2013. Computing the M most probable modes of a graphical model. AISTATS: Conference on Uncertainty in Artificial Intelligence, JMLR: W&CP, vol. 31, 161–169.' mla: Chen, Chao, et al. Computing the M Most Probable Modes of a Graphical Model. Vol. 31, JMLR, 2013, pp. 161–69. short: C. Chen, V. Kolmogorov, Z. Yan, D. Metaxas, C. Lampert, in:, JMLR, 2013, pp. 161–169. conference: end_date: 2013-05-01 location: Scottsdale, AZ, United States name: ' AISTATS: Conference on Uncertainty in Artificial Intelligence' start_date: 2013-04-29 date_created: 2018-12-11T12:00:14Z date_published: 2013-01-01T00:00:00Z date_updated: 2021-01-12T07:00:35Z day: '01' department: - _id: HeEd - _id: VlKo - _id: ChLa intvolume: ' 31' language: - iso: eng main_file_link: - open_access: '1' url: http://jmlr.org/proceedings/papers/v31/chen13a.html month: '01' oa: 1 oa_version: None page: 161 - 169 publication_status: published publisher: JMLR publist_id: '3846' quality_controlled: '1' scopus_import: 1 status: public title: Computing the M most probable modes of a graphical model type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 31 year: '2013' ... --- _id: '2906' abstract: - lang: eng text: "Motivated by an application in cell biology, we describe an extension of the kinetic data structures framework from Delaunay triangulations to fixed-radius alpha complexes. Our algorithm is implemented\r\nusing CGAL, following the exact geometric computation paradigm. We report on several\r\ntechniques to accelerate the computation that turn our implementation applicable to the underlying biological\r\nproblem." alternative_title: - ALENEX author: - first_name: Michael full_name: Kerber, Michael id: 36E4574A-F248-11E8-B48F-1D18A9856A87 last_name: Kerber orcid: 0000-0002-8030-9299 - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 citation: ama: 'Kerber M, Edelsbrunner H. 3D kinetic alpha complexes and their implementation. In: 2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments. Society of Industrial and Applied Mathematics; 2013:70-77. doi:10.1137/1.9781611972931.6' apa: 'Kerber, M., & Edelsbrunner, H. (2013). 3D kinetic alpha complexes and their implementation. In 2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments (pp. 70–77). New Orleans, LA, United States: Society of Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611972931.6' chicago: Kerber, Michael, and Herbert Edelsbrunner. “3D Kinetic Alpha Complexes and Their Implementation.” In 2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments, 70–77. Society of Industrial and Applied Mathematics, 2013. https://doi.org/10.1137/1.9781611972931.6. ieee: M. Kerber and H. Edelsbrunner, “3D kinetic alpha complexes and their implementation,” in 2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments, New Orleans, LA, United States, 2013, pp. 70–77. ista: 'Kerber M, Edelsbrunner H. 2013. 3D kinetic alpha complexes and their implementation. 2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments. ALENEX: Algorithm Engineering and Experiments, ALENEX, , 70–77.' mla: Kerber, Michael, and Herbert Edelsbrunner. “3D Kinetic Alpha Complexes and Their Implementation.” 2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments, Society of Industrial and Applied Mathematics, 2013, pp. 70–77, doi:10.1137/1.9781611972931.6. short: M. Kerber, H. Edelsbrunner, in:, 2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments, Society of Industrial and Applied Mathematics, 2013, pp. 70–77. conference: end_date: 2013-01-07 location: New Orleans, LA, United States name: 'ALENEX: Algorithm Engineering and Experiments' start_date: 2013-01-07 date_created: 2018-12-11T12:00:16Z date_published: 2013-01-01T00:00:00Z date_updated: 2021-01-12T07:00:36Z day: '01' ddc: - '500' department: - _id: HeEd doi: 10.1137/1.9781611972931.6 file: - access_level: open_access checksum: a15a3ba22df9445731507f3e06c9fcee content_type: application/pdf creator: system date_created: 2018-12-12T10:08:57Z date_updated: 2020-07-14T12:45:52Z file_id: '4720' file_name: IST-2016-547-v1+1_2013-P-08-MedusaII.pdf file_size: 403013 relation: main_file file_date_updated: 2020-07-14T12:45:52Z has_accepted_license: '1' language: - iso: eng month: '01' oa: 1 oa_version: Submitted Version page: 70 - 77 publication: 2013 Proceedings of the 15th Workshop on Algorithm Engineering and Experiments publication_status: published publisher: Society of Industrial and Applied Mathematics publist_id: '3841' pubrep_id: '547' quality_controlled: '1' scopus_import: 1 status: public title: 3D kinetic alpha complexes and their implementation type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2013' ... --- _id: '2815' abstract: - lang: eng text: The fact that a sum of isotropic Gaussian kernels can have more modes than kernels is surprising. Extra (ghost) modes do not exist in ℝ1 and are generally not well studied in higher dimensions. We study a configuration of n+1 Gaussian kernels for which there are exactly n+2 modes. We show that all modes lie on a finite set of lines, which we call axes, and study the restriction of the Gaussian mixture to these axes in order to discover that there are an exponential number of critical points in this configuration. Although the existence of ghost modes remained unknown due to the difficulty of finding examples in ℝ2, we show that the resilience of ghost modes grows like the square root of the dimension. In addition, we exhibit finite configurations of isotropic Gaussian kernels with superlinearly many modes. acknowledgement: This research is partially supported by the National Science Foundation (NSF) under Grant DBI-0820624, by the European Science Foundation under the Research Networking Programme, and the Russian Government Project 11.G34.31.0053. article_processing_charge: No article_type: original author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Brittany Terese full_name: Fasy, Brittany Terese id: F65D502E-E68D-11E9-9252-C644099818F6 last_name: Fasy - first_name: Günter full_name: Rote, Günter last_name: Rote citation: ama: 'Edelsbrunner H, Fasy BT, Rote G. Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions. Discrete & Computational Geometry. 2013;49(4):797-822. doi:10.1007/s00454-013-9517-x' apa: 'Edelsbrunner, H., Fasy, B. T., & Rote, G. (2013). Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-013-9517-x' chicago: 'Edelsbrunner, Herbert, Brittany Terese Fasy, and Günter Rote. “Add Isotropic Gaussian Kernels at Own Risk: More and More Resilient Modes in Higher Dimensions.” Discrete & Computational Geometry. Springer, 2013. https://doi.org/10.1007/s00454-013-9517-x.' ieee: 'H. Edelsbrunner, B. T. Fasy, and G. Rote, “Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions,” Discrete & Computational Geometry, vol. 49, no. 4. Springer, pp. 797–822, 2013.' ista: 'Edelsbrunner H, Fasy BT, Rote G. 2013. Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions. Discrete & Computational Geometry. 49(4), 797–822.' mla: 'Edelsbrunner, Herbert, et al. “Add Isotropic Gaussian Kernels at Own Risk: More and More Resilient Modes in Higher Dimensions.” Discrete & Computational Geometry, vol. 49, no. 4, Springer, 2013, pp. 797–822, doi:10.1007/s00454-013-9517-x.' short: H. Edelsbrunner, B.T. Fasy, G. Rote, Discrete & Computational Geometry 49 (2013) 797–822. date_created: 2018-12-11T11:59:44Z date_published: 2013-06-01T00:00:00Z date_updated: 2023-02-23T11:13:49Z day: '01' department: - _id: HeEd doi: 10.1007/s00454-013-9517-x intvolume: ' 49' issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1007/s00454-013-9517-x month: '06' oa: 1 oa_version: Published Version page: 797 - 822 publication: Discrete & Computational Geometry publication_identifier: eissn: - 1432-0444 issn: - 0179-5376 publication_status: published publisher: Springer publist_id: '3991' quality_controlled: '1' related_material: record: - id: '3134' relation: earlier_version status: public scopus_import: '1' status: public title: 'Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions' type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 49 year: '2013' ... --- _id: '2939' abstract: - lang: eng text: In this paper, we present the first output-sensitive algorithm to compute the persistence diagram of a filtered simplicial complex. For any Γ > 0, it returns only those homology classes with persistence at least Γ. Instead of the classical reduction via column operations, our algorithm performs rank computations on submatrices of the boundary matrix. For an arbitrary constant δ ∈ (0, 1), the running time is O (C (1 - δ) Γ R d (n) log n), where C (1 - δ) Γ is the number of homology classes with persistence at least (1 - δ) Γ, n is the total number of simplices in the complex, d its dimension, and R d (n) is the complexity of computing the rank of an n × n matrix with O (d n) nonzero entries. Depending on the choice of the rank algorithm, this yields a deterministic O (C (1 - δ) Γ n 2.376) algorithm, an O (C (1 - δ) Γ n 2.28) Las-Vegas algorithm, or an O (C (1 - δ) Γ n 2 + ε{lunate}) Monte-Carlo algorithm for an arbitrary ε{lunate} > 0. The space complexity of the Monte-Carlo version is bounded by O (d n) = O (n log n). acknowledgement: The authors thank Herbert Edelsbrunner for many helpful discussions and suggestions. Moreover, they are grateful for the careful reviews that helped to improve the quality of the paper. author: - first_name: Chao full_name: Chen, Chao id: 3E92416E-F248-11E8-B48F-1D18A9856A87 last_name: Chen - first_name: Michael full_name: Kerber, Michael id: 36E4574A-F248-11E8-B48F-1D18A9856A87 last_name: Kerber orcid: 0000-0002-8030-9299 citation: ama: 'Chen C, Kerber M. An output sensitive algorithm for persistent homology. Computational Geometry: Theory and Applications. 2013;46(4):435-447. doi:10.1016/j.comgeo.2012.02.010' apa: 'Chen, C., & Kerber, M. (2013). An output sensitive algorithm for persistent homology. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2012.02.010' chicago: 'Chen, Chao, and Michael Kerber. “An Output Sensitive Algorithm for Persistent Homology.” Computational Geometry: Theory and Applications. Elsevier, 2013. https://doi.org/10.1016/j.comgeo.2012.02.010.' ieee: 'C. Chen and M. Kerber, “An output sensitive algorithm for persistent homology,” Computational Geometry: Theory and Applications, vol. 46, no. 4. Elsevier, pp. 435–447, 2013.' ista: 'Chen C, Kerber M. 2013. An output sensitive algorithm for persistent homology. Computational Geometry: Theory and Applications. 46(4), 435–447.' mla: 'Chen, Chao, and Michael Kerber. “An Output Sensitive Algorithm for Persistent Homology.” Computational Geometry: Theory and Applications, vol. 46, no. 4, Elsevier, 2013, pp. 435–47, doi:10.1016/j.comgeo.2012.02.010.' short: 'C. Chen, M. Kerber, Computational Geometry: Theory and Applications 46 (2013) 435–447.' date_created: 2018-12-11T12:00:27Z date_published: 2013-05-01T00:00:00Z date_updated: 2023-02-23T11:24:10Z day: '01' department: - _id: HeEd doi: 10.1016/j.comgeo.2012.02.010 intvolume: ' 46' issue: '4' language: - iso: eng month: '05' oa_version: None page: 435 - 447 publication: 'Computational Geometry: Theory and Applications' publication_status: published publisher: Elsevier publist_id: '3796' quality_controlled: '1' related_material: record: - id: '3367' relation: earlier_version status: public scopus_import: 1 status: public title: An output sensitive algorithm for persistent homology type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 46 year: '2013' ... --- _id: '10897' abstract: - lang: eng text: Taking images is an efficient way to collect data about the physical world. It can be done fast and in exquisite detail. By definition, image processing is the field that concerns itself with the computation aimed at harnessing the information contained in images [10]. This talk is concerned with topological information. Our main thesis is that persistent homology [5] is a useful method to quantify and summarize topological information, building a bridge that connects algebraic topology with applications. We provide supporting evidence for this thesis by touching upon four technical developments in the overlap between persistent homology and image processing. acknowledgement: This research is partially supported by the European Science Foundation (ESF) under the Research Network Programme, the European Union under the Toposys Project FP7-ICT-318493-STREP, the Russian Government under the Mega Project 11.G34.31.0053. article_processing_charge: No author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 citation: ama: 'Edelsbrunner H. Persistent homology in image processing. In: Graph-Based Representations in Pattern Recognition. Vol 7877. LNCS. Berlin, Heidelberg: Springer Nature; 2013:182-183. doi:10.1007/978-3-642-38221-5_19' apa: 'Edelsbrunner, H. (2013). Persistent homology in image processing. In Graph-Based Representations in Pattern Recognition (Vol. 7877, pp. 182–183). Berlin, Heidelberg: Springer Nature. https://doi.org/10.1007/978-3-642-38221-5_19' chicago: 'Edelsbrunner, Herbert. “Persistent Homology in Image Processing.” In Graph-Based Representations in Pattern Recognition, 7877:182–83. LNCS. Berlin, Heidelberg: Springer Nature, 2013. https://doi.org/10.1007/978-3-642-38221-5_19.' ieee: H. Edelsbrunner, “Persistent homology in image processing,” in Graph-Based Representations in Pattern Recognition, Vienna, Austria, 2013, vol. 7877, pp. 182–183. ista: 'Edelsbrunner H. 2013. Persistent homology in image processing. Graph-Based Representations in Pattern Recognition. GbRPR: Graph-based Representations in Pattern RecognitionLNCS vol. 7877, 182–183.' mla: Edelsbrunner, Herbert. “Persistent Homology in Image Processing.” Graph-Based Representations in Pattern Recognition, vol. 7877, Springer Nature, 2013, pp. 182–83, doi:10.1007/978-3-642-38221-5_19. short: H. Edelsbrunner, in:, Graph-Based Representations in Pattern Recognition, Springer Nature, Berlin, Heidelberg, 2013, pp. 182–183. conference: end_date: 2013-05-17 location: Vienna, Austria name: 'GbRPR: Graph-based Representations in Pattern Recognition' start_date: 2013-05-15 date_created: 2022-03-21T07:30:33Z date_published: 2013-06-01T00:00:00Z date_updated: 2023-09-05T15:10:20Z day: '01' department: - _id: HeEd doi: 10.1007/978-3-642-38221-5_19 ec_funded: 1 intvolume: ' 7877' language: - iso: eng month: '06' oa_version: None page: 182-183 place: Berlin, Heidelberg project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems publication: Graph-Based Representations in Pattern Recognition publication_identifier: eisbn: - '9783642382215' eissn: - 1611-3349 isbn: - '9783642382208' issn: - 0302-9743 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' series_title: LNCS status: public title: Persistent homology in image processing type: conference user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 7877 year: '2013' ... --- _id: '2849' author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Nataliya full_name: Strelkova, Nataliya last_name: Strelkova citation: ama: Edelsbrunner H, Strelkova N. On the configuration space of Steiner minimal trees. Russian Mathematical Surveys. 2012;67(6):1167-1168. doi:10.1070/RM2012v067n06ABEH004820 apa: Edelsbrunner, H., & Strelkova, N. (2012). On the configuration space of Steiner minimal trees. Russian Mathematical Surveys. IOP Publishing Ltd. https://doi.org/10.1070/RM2012v067n06ABEH004820 chicago: Edelsbrunner, Herbert, and Nataliya Strelkova. “On the Configuration Space of Steiner Minimal Trees.” Russian Mathematical Surveys. IOP Publishing Ltd., 2012. https://doi.org/10.1070/RM2012v067n06ABEH004820. ieee: H. Edelsbrunner and N. Strelkova, “On the configuration space of Steiner minimal trees,” Russian Mathematical Surveys, vol. 67, no. 6. IOP Publishing Ltd., pp. 1167–1168, 2012. ista: Edelsbrunner H, Strelkova N. 2012. On the configuration space of Steiner minimal trees. Russian Mathematical Surveys. 67(6), 1167–1168. mla: Edelsbrunner, Herbert, and Nataliya Strelkova. “On the Configuration Space of Steiner Minimal Trees.” Russian Mathematical Surveys, vol. 67, no. 6, IOP Publishing Ltd., 2012, pp. 1167–68, doi:10.1070/RM2012v067n06ABEH004820. short: H. Edelsbrunner, N. Strelkova, Russian Mathematical Surveys 67 (2012) 1167–1168. date_created: 2018-12-11T11:59:55Z date_published: 2012-01-01T00:00:00Z date_updated: 2021-01-12T07:00:13Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1070/RM2012v067n06ABEH004820 file: - access_level: open_access checksum: 44ee8d173487e8ed41a51136816bbeb4 content_type: application/pdf creator: system date_created: 2018-12-12T10:14:26Z date_updated: 2020-07-14T12:45:51Z file_id: '5078' file_name: IST-2016-546-v1+1_2014-J-05-SteinerMinTrees.pdf file_size: 392021 relation: main_file file_date_updated: 2020-07-14T12:45:51Z has_accepted_license: '1' intvolume: ' 67' issue: '6' language: - iso: eng month: '01' oa: 1 oa_version: Submitted Version page: 1167 - 1168 publication: Russian Mathematical Surveys publication_status: published publisher: IOP Publishing Ltd. publist_id: '3943' pubrep_id: '546' quality_controlled: '1' scopus_import: 1 status: public title: On the configuration space of Steiner minimal trees type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 67 year: '2012' ... --- _id: '2903' abstract: - lang: eng text: In order to enjoy a digital version of the Jordan Curve Theorem, it is common to use the closed topology for the foreground and the open topology for the background of a 2-dimensional binary image. In this paper, we introduce a single topology that enjoys this theorem for all thresholds decomposing a real-valued image into foreground and background. This topology is easy to construct and it generalizes to n-dimensional images. author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Olga full_name: Symonova, Olga id: 3C0C7BC6-F248-11E8-B48F-1D18A9856A87 last_name: Symonova citation: ama: 'Edelsbrunner H, Symonova O. The adaptive topology of a digital image. In: IEEE; 2012:41-48. doi:10.1109/ISVD.2012.11' apa: 'Edelsbrunner, H., & Symonova, O. (2012). The adaptive topology of a digital image (pp. 41–48). Presented at the ISVD: International Symposium on Voronoi Diagrams in Science and Engineering, New Brunswick, NJ, USA : IEEE. https://doi.org/10.1109/ISVD.2012.11' chicago: Edelsbrunner, Herbert, and Olga Symonova. “The Adaptive Topology of a Digital Image,” 41–48. IEEE, 2012. https://doi.org/10.1109/ISVD.2012.11. ieee: 'H. Edelsbrunner and O. Symonova, “The adaptive topology of a digital image,” presented at the ISVD: International Symposium on Voronoi Diagrams in Science and Engineering, New Brunswick, NJ, USA , 2012, pp. 41–48.' ista: 'Edelsbrunner H, Symonova O. 2012. The adaptive topology of a digital image. ISVD: International Symposium on Voronoi Diagrams in Science and Engineering, 41–48.' mla: Edelsbrunner, Herbert, and Olga Symonova. The Adaptive Topology of a Digital Image. IEEE, 2012, pp. 41–48, doi:10.1109/ISVD.2012.11. short: H. Edelsbrunner, O. Symonova, in:, IEEE, 2012, pp. 41–48. conference: end_date: 2012-06-29 location: 'New Brunswick, NJ, USA ' name: 'ISVD: International Symposium on Voronoi Diagrams in Science and Engineering' start_date: 2012-06-27 date_created: 2018-12-11T12:00:15Z date_published: 2012-08-06T00:00:00Z date_updated: 2021-01-12T07:00:35Z day: '06' ddc: - '000' department: - _id: HeEd - _id: MaJö doi: 10.1109/ISVD.2012.11 file: - access_level: open_access checksum: 444869a4e8abf07834f88b6e5cb5e9c3 content_type: application/pdf creator: system date_created: 2018-12-12T10:09:41Z date_updated: 2020-07-14T12:45:52Z file_id: '4765' file_name: IST-2016-545-v1+1_2012-P-10-AdaptiveTopology.pdf file_size: 760548 relation: main_file file_date_updated: 2020-07-14T12:45:52Z has_accepted_license: '1' language: - iso: eng month: '08' oa: 1 oa_version: Submitted Version page: 41 - 48 publication_status: published publisher: IEEE publist_id: '3844' pubrep_id: '545' quality_controlled: '1' scopus_import: 1 status: public title: The adaptive topology of a digital image type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 year: '2012' ... --- _id: '2941' author: - first_name: Nikolai full_name: Dolbilin, Nikolai last_name: Dolbilin - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Oleg full_name: Musin, Oleg last_name: Musin citation: ama: Dolbilin N, Edelsbrunner H, Musin O. On the optimality of functionals over triangulations of Delaunay sets. Russian Mathematical Surveys. 2012;67(4):781-783. doi:10.1070/RM2012v067n04ABEH004807 apa: Dolbilin, N., Edelsbrunner, H., & Musin, O. (2012). On the optimality of functionals over triangulations of Delaunay sets. Russian Mathematical Surveys. IOP Publishing. https://doi.org/10.1070/RM2012v067n04ABEH004807 chicago: Dolbilin, Nikolai, Herbert Edelsbrunner, and Oleg Musin. “On the Optimality of Functionals over Triangulations of Delaunay Sets.” Russian Mathematical Surveys. IOP Publishing, 2012. https://doi.org/10.1070/RM2012v067n04ABEH004807. ieee: N. Dolbilin, H. Edelsbrunner, and O. Musin, “On the optimality of functionals over triangulations of Delaunay sets,” Russian Mathematical Surveys, vol. 67, no. 4. IOP Publishing, pp. 781–783, 2012. ista: Dolbilin N, Edelsbrunner H, Musin O. 2012. On the optimality of functionals over triangulations of Delaunay sets. Russian Mathematical Surveys. 67(4), 781–783. mla: Dolbilin, Nikolai, et al. “On the Optimality of Functionals over Triangulations of Delaunay Sets.” Russian Mathematical Surveys, vol. 67, no. 4, IOP Publishing, 2012, pp. 781–83, doi:10.1070/RM2012v067n04ABEH004807. short: N. Dolbilin, H. Edelsbrunner, O. Musin, Russian Mathematical Surveys 67 (2012) 781–783. date_created: 2018-12-11T12:00:28Z date_published: 2012-11-01T00:00:00Z date_updated: 2021-01-12T07:39:55Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.1070/RM2012v067n04ABEH004807 file: - access_level: open_access checksum: 389a5ae53d6347de36c3468034f2821d content_type: application/pdf creator: system date_created: 2018-12-12T10:16:49Z date_updated: 2020-07-14T12:45:55Z file_id: '5239' file_name: IST-2013-132-v1+1_2012-J-04-Functional-E.pdf file_size: 253816 relation: main_file file_date_updated: 2020-07-14T12:45:55Z has_accepted_license: '1' intvolume: ' 67' issue: '4' language: - iso: eng month: '11' oa: 1 oa_version: Submitted Version page: 781 - 783 publication: Russian Mathematical Surveys publication_status: published publisher: IOP Publishing publist_id: '3792' pubrep_id: '132' quality_controlled: '1' scopus_import: 1 status: public title: On the optimality of functionals over triangulations of Delaunay sets type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 67 year: '2012' ... --- _id: '2971' abstract: - lang: eng text: 'We study the task of interactive semantic labeling of a segmentation hierarchy. To this end we propose a framework interleaving two components: an automatic labeling step, based on a Conditional Random Field whose dependencies are defined by the inclusion tree of the segmentation hierarchy, and an interaction step that integrates incremental input from a human user. Evaluated on two distinct datasets, the proposed interactive approach efficiently integrates human interventions and illustrates the advantages of structured prediction in an interactive framework. ' author: - first_name: Georg full_name: Zankl, Georg last_name: Zankl - first_name: Yll full_name: Haxhimusa, Yll last_name: Haxhimusa - first_name: Adrian full_name: Ion, Adrian id: 29F89302-F248-11E8-B48F-1D18A9856A87 last_name: Ion citation: ama: 'Zankl G, Haxhimusa Y, Ion A. Interactive labeling of image segmentation hierarchies. In: Vol 7476. Springer; 2012:11-20. doi:10.1007/978-3-642-32717-9_2' apa: 'Zankl, G., Haxhimusa, Y., & Ion, A. (2012). Interactive labeling of image segmentation hierarchies (Vol. 7476, pp. 11–20). Presented at the Pattern Recognition, Graz, Austria: Springer. https://doi.org/10.1007/978-3-642-32717-9_2' chicago: Zankl, Georg, Yll Haxhimusa, and Adrian Ion. “Interactive Labeling of Image Segmentation Hierarchies,” 7476:11–20. Springer, 2012. https://doi.org/10.1007/978-3-642-32717-9_2. ieee: G. Zankl, Y. Haxhimusa, and A. Ion, “Interactive labeling of image segmentation hierarchies,” presented at the Pattern Recognition, Graz, Austria, 2012, vol. 7476, pp. 11–20. ista: Zankl G, Haxhimusa Y, Ion A. 2012. Interactive labeling of image segmentation hierarchies. Pattern Recognition vol. 7476, 11–20. mla: Zankl, Georg, et al. Interactive Labeling of Image Segmentation Hierarchies. Vol. 7476, Springer, 2012, pp. 11–20, doi:10.1007/978-3-642-32717-9_2. short: G. Zankl, Y. Haxhimusa, A. Ion, in:, Springer, 2012, pp. 11–20. conference: end_date: 2012-08-31 location: Graz, Austria name: Pattern Recognition start_date: 2012-08-28 date_created: 2018-12-11T12:00:37Z date_published: 2012-01-01T00:00:00Z date_updated: 2021-01-12T07:40:10Z day: '01' department: - _id: HeEd doi: 10.1007/978-3-642-32717-9_2 intvolume: ' 7476' language: - iso: eng month: '01' oa_version: None page: 11 - 20 publication_status: published publisher: Springer publist_id: '3737' quality_controlled: '1' scopus_import: 1 status: public title: Interactive labeling of image segmentation hierarchies type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 7476 year: '2012' ... --- _id: '3120' abstract: - lang: eng text: We introduce a strategy based on Kustin-Miller unprojection that allows us to construct many hundreds of Gorenstein codimension 4 ideals with 9 × 16 resolutions (that is, nine equations and sixteen first syzygies). Our two basic games are called Tom and Jerry; the main application is the biregular construction of most of the anticanonically polarised Mori Fano 3-folds of Altinok's thesis. There are 115 cases whose numerical data (in effect, the Hilbert series) allow a Type I projection. In every case, at least one Tom and one Jerry construction works, providing at least two deformation families of quasismooth Fano 3-folds having the same numerics but different topology. © 2012 Copyright Foundation Compositio Mathematica. acknowledgement: This research is supported by the Korean Government WCU Grant R33-2008-000-10101-0. author: - first_name: Gavin full_name: Brown, Gavin last_name: Brown - first_name: Michael full_name: Kerber, Michael id: 36E4574A-F248-11E8-B48F-1D18A9856A87 last_name: Kerber orcid: 0000-0002-8030-9299 - first_name: Miles full_name: Reid, Miles last_name: Reid citation: ama: Brown G, Kerber M, Reid M. Fano 3 folds in codimension 4 Tom and Jerry Part I. Compositio Mathematica. 2012;148(4):1171-1194. doi:10.1112/S0010437X11007226 apa: Brown, G., Kerber, M., & Reid, M. (2012). Fano 3 folds in codimension 4 Tom and Jerry Part I. Compositio Mathematica. Cambridge University Press. https://doi.org/10.1112/S0010437X11007226 chicago: Brown, Gavin, Michael Kerber, and Miles Reid. “Fano 3 Folds in Codimension 4 Tom and Jerry Part I.” Compositio Mathematica. Cambridge University Press, 2012. https://doi.org/10.1112/S0010437X11007226. ieee: G. Brown, M. Kerber, and M. Reid, “Fano 3 folds in codimension 4 Tom and Jerry Part I,” Compositio Mathematica, vol. 148, no. 4. Cambridge University Press, pp. 1171–1194, 2012. ista: Brown G, Kerber M, Reid M. 2012. Fano 3 folds in codimension 4 Tom and Jerry Part I. Compositio Mathematica. 148(4), 1171–1194. mla: Brown, Gavin, et al. “Fano 3 Folds in Codimension 4 Tom and Jerry Part I.” Compositio Mathematica, vol. 148, no. 4, Cambridge University Press, 2012, pp. 1171–94, doi:10.1112/S0010437X11007226. short: G. Brown, M. Kerber, M. Reid, Compositio Mathematica 148 (2012) 1171–1194. date_created: 2018-12-11T12:01:30Z date_published: 2012-07-01T00:00:00Z date_updated: 2021-01-12T07:41:12Z day: '01' department: - _id: HeEd doi: 10.1112/S0010437X11007226 intvolume: ' 148' issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1009.4313 month: '07' oa: 1 oa_version: Preprint page: 1171 - 1194 publication: Compositio Mathematica publication_status: published publisher: Cambridge University Press publist_id: '3579' quality_controlled: '1' scopus_import: 1 status: public title: Fano 3 folds in codimension 4 Tom and Jerry Part I type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 148 year: '2012' ... --- _id: '3133' abstract: - lang: eng text: 'This note contributes to the point calculus of persistent homology by extending Alexander duality from spaces to real-valued functions. Given a perfect Morse function f: S n+1 →[0, 1 and a decomposition S n+1 = U ∪ V into two (n + 1)-manifolds with common boundary M, we prove elementary relationships between the persistence diagrams of f restricted to U, to V, and to M. ' acknowledgement: "his research is partially supported by the National Science Foundation (NSF) under grant DBI-0820624, the European Science Foundation under the Research Networking Programme, and the Russian Government Project 11.G34.31.0053.\r\nThe authors thank an anonymous referee for suggesting the simplified proof of the Contravariant PE Theorem given in this paper. They also thank Frederick Cohen, Yuriy Mileyko and Amit Patel for helpful discussions." author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Michael full_name: Kerber, Michael id: 36E4574A-F248-11E8-B48F-1D18A9856A87 last_name: Kerber orcid: 0000-0002-8030-9299 citation: ama: 'Edelsbrunner H, Kerber M. Alexander duality for functions: The persistent behavior of land and water and shore. In: Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry . ACM; 2012:249-258. doi:10.1145/2261250.2261287' apa: 'Edelsbrunner, H., & Kerber, M. (2012). Alexander duality for functions: The persistent behavior of land and water and shore. In Proceedings of the twenty-eighth annual symposium on Computational geometry (pp. 249–258). Chapel Hill, NC, USA: ACM. https://doi.org/10.1145/2261250.2261287' chicago: 'Edelsbrunner, Herbert, and Michael Kerber. “Alexander Duality for Functions: The Persistent Behavior of Land and Water and Shore.” In Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry , 249–58. ACM, 2012. https://doi.org/10.1145/2261250.2261287.' ieee: 'H. Edelsbrunner and M. Kerber, “Alexander duality for functions: The persistent behavior of land and water and shore,” in Proceedings of the twenty-eighth annual symposium on Computational geometry , Chapel Hill, NC, USA, 2012, pp. 249–258.' ista: 'Edelsbrunner H, Kerber M. 2012. Alexander duality for functions: The persistent behavior of land and water and shore. Proceedings of the twenty-eighth annual symposium on Computational geometry . SCG: Symposium on Computational Geometry, 249–258.' mla: 'Edelsbrunner, Herbert, and Michael Kerber. “Alexander Duality for Functions: The Persistent Behavior of Land and Water and Shore.” Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry , ACM, 2012, pp. 249–58, doi:10.1145/2261250.2261287.' short: H. Edelsbrunner, M. Kerber, in:, Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry , ACM, 2012, pp. 249–258. conference: end_date: 2012-06-20 location: Chapel Hill, NC, USA name: 'SCG: Symposium on Computational Geometry' start_date: 2012-06-17 date_created: 2018-12-11T12:01:35Z date_published: 2012-06-20T00:00:00Z date_updated: 2021-01-12T07:41:17Z day: '20' department: - _id: HeEd doi: 10.1145/2261250.2261287 language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1109.5052 month: '06' oa: 1 oa_version: Preprint page: 249 - 258 publication: 'Proceedings of the twenty-eighth annual symposium on Computational geometry ' publication_status: published publisher: ACM publist_id: '3564' quality_controlled: '1' scopus_import: 1 status: public title: 'Alexander duality for functions: The persistent behavior of land and water and shore' type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 year: '2012' ... --- _id: '3134' abstract: - lang: eng text: 'It has been an open question whether the sum of finitely many isotropic Gaussian kernels in n ≥ 2 dimensions can have more modes than kernels, until in 2003 Carreira-Perpiñán and Williams exhibited n +1 isotropic Gaussian kernels in ℝ n with n + 2 modes. We give a detailed analysis of this example, showing that it has exponentially many critical points and that the resilience of the extra mode grows like √n. In addition, we exhibit finite configurations of isotropic Gaussian kernels with superlinearly many modes. ' acknowledgement: This research is partially supported by the National Science Foun- dation (NSF) under grant DBI-0820624, by the European Science Foundation under the Research Networking Programme, and the Russian Government Project 11.G34.31.0053. author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Brittany full_name: Fasy, Brittany last_name: Fasy - first_name: Günter full_name: Rote, Günter last_name: Rote citation: ama: 'Edelsbrunner H, Fasy B, Rote G. Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions. In: Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry . ACM; 2012:91-100. doi:10.1145/2261250.2261265' apa: 'Edelsbrunner, H., Fasy, B., & Rote, G. (2012). Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions. In Proceedings of the twenty-eighth annual symposium on Computational geometry (pp. 91–100). Chapel Hill, NC, USA: ACM. https://doi.org/10.1145/2261250.2261265' chicago: 'Edelsbrunner, Herbert, Brittany Fasy, and Günter Rote. “Add Isotropic Gaussian Kernels at Own Risk: More and More Resilient Modes in Higher Dimensions.” In Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry , 91–100. ACM, 2012. https://doi.org/10.1145/2261250.2261265.' ieee: 'H. Edelsbrunner, B. Fasy, and G. Rote, “Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions,” in Proceedings of the twenty-eighth annual symposium on Computational geometry , Chapel Hill, NC, USA, 2012, pp. 91–100.' ista: 'Edelsbrunner H, Fasy B, Rote G. 2012. Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions. Proceedings of the twenty-eighth annual symposium on Computational geometry . SCG: Symposium on Computational Geometry, 91–100.' mla: 'Edelsbrunner, Herbert, et al. “Add Isotropic Gaussian Kernels at Own Risk: More and More Resilient Modes in Higher Dimensions.” Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry , ACM, 2012, pp. 91–100, doi:10.1145/2261250.2261265.' short: H. Edelsbrunner, B. Fasy, G. Rote, in:, Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry , ACM, 2012, pp. 91–100. conference: end_date: 2012-06-20 location: Chapel Hill, NC, USA name: 'SCG: Symposium on Computational Geometry' start_date: 2012-06-17 date_created: 2018-12-11T12:01:35Z date_published: 2012-06-20T00:00:00Z date_updated: 2023-02-23T10:59:27Z day: '20' department: - _id: HeEd doi: 10.1145/2261250.2261265 language: - iso: eng month: '06' oa_version: None page: 91 - 100 publication: 'Proceedings of the twenty-eighth annual symposium on Computational geometry ' publication_status: published publisher: ACM publist_id: '3563' quality_controlled: '1' related_material: record: - id: '2815' relation: later_version status: public scopus_import: 1 status: public title: 'Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions' type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 year: '2012' ... --- _id: '3256' abstract: - lang: eng text: We use a distortion to define the dual complex of a cubical subdivision of ℝ n as an n-dimensional subcomplex of the nerve of the set of n-cubes. Motivated by the topological analysis of high-dimensional digital image data, we consider such subdivisions defined by generalizations of quad- and oct-trees to n dimensions. Assuming the subdivision is balanced, we show that mapping each vertex to the center of the corresponding n-cube gives a geometric realization of the dual complex in ℝ n. acknowledgement: This research is partially supported by the Defense Advanced Research Projects Agency (DARPA) under grants HR0011-05-1-0057 and HR0011-09-0065 as well as the National Science Foundation (NSF) under grant DBI-0820624. author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Michael full_name: Kerber, Michael id: 36E4574A-F248-11E8-B48F-1D18A9856A87 last_name: Kerber orcid: 0000-0002-8030-9299 citation: ama: Edelsbrunner H, Kerber M. Dual complexes of cubical subdivisions of ℝn. Discrete & Computational Geometry. 2012;47(2):393-414. doi:10.1007/s00454-011-9382-4 apa: Edelsbrunner, H., & Kerber, M. (2012). Dual complexes of cubical subdivisions of ℝn. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-011-9382-4 chicago: Edelsbrunner, Herbert, and Michael Kerber. “Dual Complexes of Cubical Subdivisions of ℝn.” Discrete & Computational Geometry. Springer, 2012. https://doi.org/10.1007/s00454-011-9382-4. ieee: H. Edelsbrunner and M. Kerber, “Dual complexes of cubical subdivisions of ℝn,” Discrete & Computational Geometry, vol. 47, no. 2. Springer, pp. 393–414, 2012. ista: Edelsbrunner H, Kerber M. 2012. Dual complexes of cubical subdivisions of ℝn. Discrete & Computational Geometry. 47(2), 393–414. mla: Edelsbrunner, Herbert, and Michael Kerber. “Dual Complexes of Cubical Subdivisions of ℝn.” Discrete & Computational Geometry, vol. 47, no. 2, Springer, 2012, pp. 393–414, doi:10.1007/s00454-011-9382-4. short: H. Edelsbrunner, M. Kerber, Discrete & Computational Geometry 47 (2012) 393–414. date_created: 2018-12-11T12:02:17Z date_published: 2012-03-01T00:00:00Z date_updated: 2021-01-12T07:42:10Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1007/s00454-011-9382-4 file: - access_level: open_access checksum: 76486f3b2c9e7fd81342f3832ca387e7 content_type: application/pdf creator: system date_created: 2018-12-12T10:08:15Z date_updated: 2020-07-14T12:46:05Z file_id: '4675' file_name: IST-2016-543-v1+1_2012-J-08-HierarchyCubeComplex.pdf file_size: 203636 relation: main_file file_date_updated: 2020-07-14T12:46:05Z has_accepted_license: '1' intvolume: ' 47' issue: '2' language: - iso: eng month: '03' oa: 1 oa_version: Submitted Version page: 393 - 414 publication: Discrete & Computational Geometry publication_status: published publisher: Springer publist_id: '3398' pubrep_id: '543' quality_controlled: '1' scopus_import: 1 status: public title: Dual complexes of cubical subdivisions of ℝn type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 47 year: '2012' ... --- _id: '3265' abstract: - lang: eng text: We propose a mid-level statistical model for image segmentation that composes multiple figure-ground hypotheses (FG) obtained by applying constraints at different locations and scales, into larger interpretations (tilings) of the entire image. Inference is cast as optimization over sets of maximal cliques sampled from a graph connecting all non-overlapping figure-ground segment hypotheses. Potential functions over cliques combine unary, Gestalt-based figure qualities, and pairwise compatibilities among spatially neighboring segments, constrained by T-junctions and the boundary interface statistics of real scenes. Learning the model parameters is based on maximum likelihood, alternating between sampling image tilings and optimizing their potential function parameters. State of the art results are reported on the Berkeley and Stanford segmentation datasets, as well as VOC2009, where a 28% improvement was achieved. article_number: '6126486' author: - first_name: Adrian full_name: Ion, Adrian id: 29F89302-F248-11E8-B48F-1D18A9856A87 last_name: Ion - first_name: Joao full_name: Carreira, Joao last_name: Carreira - first_name: Cristian full_name: Sminchisescu, Cristian last_name: Sminchisescu citation: ama: 'Ion A, Carreira J, Sminchisescu C. Image segmentation by figure-ground composition into maximal cliques. In: IEEE; 2012. doi:10.1109/ICCV.2011.6126486' apa: 'Ion, A., Carreira, J., & Sminchisescu, C. (2012). Image segmentation by figure-ground composition into maximal cliques. Presented at the ICCV: International Conference on Computer Vision, Barcelona, Spain: IEEE. https://doi.org/10.1109/ICCV.2011.6126486' chicago: Ion, Adrian, Joao Carreira, and Cristian Sminchisescu. “Image Segmentation by Figure-Ground Composition into Maximal Cliques.” IEEE, 2012. https://doi.org/10.1109/ICCV.2011.6126486. ieee: 'A. Ion, J. Carreira, and C. Sminchisescu, “Image segmentation by figure-ground composition into maximal cliques,” presented at the ICCV: International Conference on Computer Vision, Barcelona, Spain, 2012.' ista: 'Ion A, Carreira J, Sminchisescu C. 2012. Image segmentation by figure-ground composition into maximal cliques. ICCV: International Conference on Computer Vision, 6126486.' mla: Ion, Adrian, et al. Image Segmentation by Figure-Ground Composition into Maximal Cliques. 6126486, IEEE, 2012, doi:10.1109/ICCV.2011.6126486. short: A. Ion, J. Carreira, C. Sminchisescu, in:, IEEE, 2012. conference: end_date: 2011-11-13 location: Barcelona, Spain name: 'ICCV: International Conference on Computer Vision' start_date: 2011-11-06 date_created: 2018-12-11T12:02:21Z date_published: 2012-01-12T00:00:00Z date_updated: 2021-01-12T07:42:15Z day: '12' department: - _id: HeEd doi: 10.1109/ICCV.2011.6126486 language: - iso: eng month: '01' oa_version: None publication_status: published publisher: IEEE publist_id: '3382' quality_controlled: '1' status: public title: Image segmentation by figure-ground composition into maximal cliques type: conference user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 year: '2012' ... --- _id: '3115' abstract: - lang: eng text: 'We consider the offset-deconstruction problem: Given a polygonal shape Q with n vertices, can it be expressed, up to a tolerance ε in Hausdorff distance, as the Minkowski sum of another polygonal shape P with a disk of fixed radius? If it does, we also seek a preferably simple-looking solution P; then, P''s offset constitutes an accurate, vertex-reduced, and smoothened approximation of Q. We give an O(nlogn)-time exact decision algorithm that handles any polygonal shape, assuming the real-RAM model of computation. A variant of the algorithm, which we have implemented using the cgal library, is based on rational arithmetic and answers the same deconstruction problem up to an uncertainty parameter δ its running time additionally depends on δ. If the input shape is found to be approximable, this algorithm also computes an approximate solution for the problem. It also allows us to solve parameter-optimization problems induced by the offset-deconstruction problem. For convex shapes, the complexity of the exact decision algorithm drops to O(n), which is also the time required to compute a solution P with at most one more vertex than a vertex-minimal one.' acknowledgement: "We thank Eyal Flato (Plataine Ltd.) for raising the offset-deconstruction problem in connection with wood cutting. We also thank Tim Bretl (UIUC) for suggesting the digital-pen offset-deconstruction problem. This work has been supported in part by the Israel Science Foundation (grant no. 1102/11), by the German–Israeli Foundation (grant no. 969/07), by the Hermann Minkowski–Minerva Center for Geometry at Tel Aviv University, and by the EU Project under Contract No. 255827 (CGL—Computational Geometry Learning).\r\n" author: - first_name: Eric full_name: Berberich, Eric last_name: Berberich - first_name: Dan full_name: Halperin, Dan last_name: Halperin - first_name: Michael full_name: Kerber, Michael id: 36E4574A-F248-11E8-B48F-1D18A9856A87 last_name: Kerber orcid: 0000-0002-8030-9299 - first_name: Roza full_name: Pogalnikova, Roza last_name: Pogalnikova citation: ama: Berberich E, Halperin D, Kerber M, Pogalnikova R. Deconstructing approximate offsets. Discrete & Computational Geometry. 2012;48(4):964-989. doi:10.1007/s00454-012-9441-5 apa: Berberich, E., Halperin, D., Kerber, M., & Pogalnikova, R. (2012). Deconstructing approximate offsets. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-012-9441-5 chicago: Berberich, Eric, Dan Halperin, Michael Kerber, and Roza Pogalnikova. “Deconstructing Approximate Offsets.” Discrete & Computational Geometry. Springer, 2012. https://doi.org/10.1007/s00454-012-9441-5. ieee: E. Berberich, D. Halperin, M. Kerber, and R. Pogalnikova, “Deconstructing approximate offsets,” Discrete & Computational Geometry, vol. 48, no. 4. Springer, pp. 964–989, 2012. ista: Berberich E, Halperin D, Kerber M, Pogalnikova R. 2012. Deconstructing approximate offsets. Discrete & Computational Geometry. 48(4), 964–989. mla: Berberich, Eric, et al. “Deconstructing Approximate Offsets.” Discrete & Computational Geometry, vol. 48, no. 4, Springer, 2012, pp. 964–89, doi:10.1007/s00454-012-9441-5. short: E. Berberich, D. Halperin, M. Kerber, R. Pogalnikova, Discrete & Computational Geometry 48 (2012) 964–989. date_created: 2018-12-11T12:01:28Z date_published: 2012-12-01T00:00:00Z date_updated: 2023-02-23T11:22:30Z day: '01' department: - _id: HeEd doi: 10.1007/s00454-012-9441-5 external_id: arxiv: - '1109.2158' intvolume: ' 48' issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1109.2158 month: '12' oa: 1 oa_version: Preprint page: 964 - 989 publication: Discrete & Computational Geometry publication_status: published publisher: Springer publist_id: '3584' quality_controlled: '1' related_material: record: - id: '3329' relation: earlier_version status: public scopus_import: 1 status: public title: Deconstructing approximate offsets type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 48 year: '2012' ...