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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."}],"type":"journal_article","date_published":"2015-06-03T00:00:00Z","citation":{"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.","apa":"Attali, D., Bauer, U., Devillers, O., Glisse, M., & Lieutier, A. (2015). Homological reconstruction and simplification in R3. Computational Geometry: Theory and Applications. 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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."}],"issue":"6","type":"journal_article","date_published":"2015-06-01T00:00:00Z","publication":"PLoS One","citation":{"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.","short":"O. Symonova, C. Topp, H. Edelsbrunner, PLoS One 10 (2015).","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.","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.","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","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.","ama":"Symonova O, Topp C, Edelsbrunner H. 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Root traits computed by DynamicRoots for the maize root shown in fig 2. 2015. doi: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.","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","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.","short":"O. Symonova, C. Topp, H. Edelsbrunner, (2015).","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.","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."},"month":"06","day":"01","article_processing_charge":"No"},{"quality_controlled":"1","page":"773 - 797","publication":"Journal of Complexity","citation":{"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.","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.","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","ista":"Pausinger F, Svane A. 2015. A Koksma-Hlawka inequality for general discrepancy systems. Journal of Complexity. 31(6), 773–797.","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","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."},"language":[{"iso":"eng"}],"date_published":"2015-12-01T00:00:00Z","doi":"10.1016/j.jco.2015.06.002","scopus_import":1,"day":"01","month":"12","publication_status":"published","title":"A Koksma-Hlawka inequality for general discrepancy systems","status":"public","publisher":"Academic Press","intvolume":" 31","department":[{"_id":"HeEd"}],"year":"2015","_id":"1792","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","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.","date_created":"2018-12-11T11:54:02Z","date_updated":"2023-09-07T11:41:25Z","oa_version":"None","volume":31,"author":[{"last_name":"Pausinger","first_name":"Florian","orcid":"0000-0002-8379-3768","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","full_name":"Pausinger, Florian"},{"full_name":"Svane, Anne","first_name":"Anne","last_name":"Svane"}],"related_material":{"record":[{"id":"1399","status":"public","relation":"dissertation_contains"}]},"type":"journal_article","abstract":[{"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.","lang":"eng"}],"issue":"6","publist_id":"5320"},{"_id":"1399","year":"2015","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","department":[{"_id":"HeEd"}],"publisher":"Institute of Science and Technology Austria","publication_status":"published","status":"public","title":"On the approximation of intrinsic volumes","related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"1662"},{"status":"public","relation":"part_of_dissertation","id":"1792"},{"id":"2255","status":"public","relation":"part_of_dissertation"}]},"author":[{"full_name":"Pausinger, Florian","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8379-3768","first_name":"Florian","last_name":"Pausinger"}],"oa_version":"None","date_created":"2018-12-11T11:51:48Z","date_updated":"2023-09-07T11:41:25Z","type":"dissertation","alternative_title":["ISTA Thesis"],"publist_id":"5808","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."}],"citation":{"chicago":"Pausinger, Florian. “On the Approximation of Intrinsic Volumes.” Institute of Science and Technology Austria, 2015.","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.","ista":"Pausinger F. 2015. On the approximation of intrinsic volumes. Institute of Science and Technology Austria.","ieee":"F. Pausinger, “On the approximation of intrinsic volumes,” Institute of Science and Technology Austria, 2015.","apa":"Pausinger, F. (2015). On the approximation of intrinsic volumes. Institute of Science and Technology Austria.","ama":"Pausinger F. On the approximation of intrinsic volumes. 2015."},"page":"144","date_published":"2015-06-01T00:00:00Z","language":[{"iso":"eng"}],"degree_awarded":"PhD","supervisor":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"}],"article_processing_charge":"No","publication_identifier":{"issn":["2663-337X"]},"month":"06","day":"01"},{"oa_version":"None","title":"Toward the extraction of saddle periodic orbits","status":"public","intvolume":" 1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"10893","abstract":[{"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.","lang":"eng"}],"type":"book_chapter","date_published":"2014-03-19T00:00:00Z","page":"55-69","publication":"Topological Methods in Data Analysis and Visualization III ","citation":{"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.","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.","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.","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.","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","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.","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"},"day":"19","article_processing_charge":"No","series_title":"Mathematics and Visualization","scopus_import":"1","date_updated":"2022-06-21T12:01:47Z","date_created":"2022-03-21T07:11:23Z","volume":1,"author":[{"full_name":"Kasten, Jens","last_name":"Kasten","first_name":"Jens"},{"id":"4505473A-F248-11E8-B48F-1D18A9856A87","last_name":"Reininghaus","first_name":"Jan","full_name":"Reininghaus, Jan"},{"first_name":"Wieland","last_name":"Reich","full_name":"Reich, Wieland"},{"full_name":"Scheuermann, Gerik","last_name":"Scheuermann","first_name":"Gerik"}],"publication_status":"published","publisher":"Springer","editor":[{"full_name":"Bremer, Peer-Timo","first_name":"Peer-Timo","last_name":"Bremer"},{"full_name":"Hotz, Ingrid","first_name":"Ingrid","last_name":"Hotz"},{"first_name":"Valerio","last_name":"Pascucci","full_name":"Pascucci, Valerio"},{"last_name":"Peikert","first_name":"Ronald","full_name":"Peikert, Ronald"}],"department":[{"_id":"HeEd"}],"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.","year":"2014","ec_funded":1,"place":"Cham","language":[{"iso":"eng"}],"doi":"10.1007/978-3-319-04099-8_4","quality_controlled":"1","project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","call_identifier":"FP7","name":"Topological Complex Systems"}],"month":"03","publication_identifier":{"eissn":["2197-666X"],"isbn":["9783319040981"],"eisbn":["9783319040998"],"issn":["1612-3786"]}},{"pubrep_id":"443","file":[{"creator":"system","content_type":"application/pdf","file_size":991734,"file_name":"IST-2016-443-v1+1_S0218195914500034.pdf","access_level":"open_access","date_created":"2018-12-12T10:08:43Z","date_updated":"2020-07-14T12:45:17Z","checksum":"be45c133ab4d43351260e21beaa8f4b1","file_id":"4704","relation":"main_file"}],"oa_version":"Published Version","_id":"1816","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","intvolume":" 24","status":"public","title":"Topology-preserving watermarking of vector graphics","ddc":["000"],"issue":"1","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."}],"type":"journal_article","date_published":"2014-03-16T00:00:00Z","citation":{"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.","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","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.","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","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.","short":"S. Huber, M. Held, P. Meerwald, R. Kwitt, International Journal of Computational Geometry and Applications 24 (2014) 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."},"publication":"International Journal of Computational Geometry and Applications","page":"61 - 86","has_accepted_license":"1","day":"16","scopus_import":1,"author":[{"full_name":"Huber, Stefan","id":"4700A070-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8871-5814","first_name":"Stefan","last_name":"Huber"},{"last_name":"Held","first_name":"Martin","full_name":"Held, Martin"},{"first_name":"Peter","last_name":"Meerwald","full_name":"Meerwald, Peter"},{"last_name":"Kwitt","first_name":"Roland","full_name":"Kwitt, Roland"}],"volume":24,"date_updated":"2021-01-12T06:53:23Z","date_created":"2018-12-11T11:54:10Z","acknowledgement":"Work by Martin Held and Stefan Huber was supported by Austrian Science Fund (FWF): L367-N15 and P25816-N15.","year":"2014","publisher":"World Scientific Publishing","department":[{"_id":"HeEd"}],"publication_status":"published","publist_id":"5290","file_date_updated":"2020-07-14T12:45:17Z","doi":"10.1142/S0218195914500034","language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"quality_controlled":"1","month":"03"},{"scopus_import":1,"day":"14","month":"11","publication":"Discrete & Computational Geometry","citation":{"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","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.","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","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.","short":"J. Cibulka, P. Gao, M. Krcál, T. Valla, P. Valtr, Discrete & Computational Geometry 53 (2014) 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."},"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1310.7004"}],"oa":1,"page":"64 - 79","date_published":"2014-11-14T00:00:00Z","doi":"10.1007/s00454-014-9646-x","language":[{"iso":"eng"}],"type":"journal_article","abstract":[{"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.","lang":"eng"}],"publist_id":"5260","issue":"1","year":"2014","_id":"1842","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","acknowledgement":"Marek Krčál was supported by the ERC Advanced Grant No. 267165.","title":"On the geometric ramsey number of outerplanar graphs","status":"public","publication_status":"published","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"intvolume":" 53","publisher":"Springer","author":[{"last_name":"Cibulka","first_name":"Josef","full_name":"Cibulka, Josef"},{"full_name":"Gao, Pu","last_name":"Gao","first_name":"Pu"},{"id":"33E21118-F248-11E8-B48F-1D18A9856A87","last_name":"Krcál","first_name":"Marek","full_name":"Krcál, Marek"},{"full_name":"Valla, Tomáš","last_name":"Valla","first_name":"Tomáš"},{"full_name":"Valtr, Pavel","first_name":"Pavel","last_name":"Valtr"}],"date_updated":"2021-01-12T06:53:33Z","date_created":"2018-12-11T11:54:18Z","oa_version":"Submitted Version","volume":53},{"type":"journal_article","issue":"3","abstract":[{"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.","lang":"eng"}],"_id":"1876","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 14","title":"Functionals on triangulations of delaunay sets","status":"public","oa_version":"Submitted Version","scopus_import":"1","article_processing_charge":"No","day":"01","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","ista":"Dolbilin N, Edelsbrunner H, Glazyrin A, Musin O. 2014. Functionals on triangulations of delaunay sets. Moscow Mathematical Journal. 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.","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","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.","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."},"publication":"Moscow Mathematical Journal","page":"491 - 504","article_type":"original","date_published":"2014-07-01T00:00:00Z","publist_id":"5220","year":"2014","department":[{"_id":"HeEd"}],"publisher":"Independent University of Moscow","publication_status":"published","author":[{"full_name":"Dolbilin, Nikolai","last_name":"Dolbilin","first_name":"Nikolai"},{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"},{"first_name":"Alexey","last_name":"Glazyrin","full_name":"Glazyrin, Alexey"},{"first_name":"Oleg","last_name":"Musin","full_name":"Musin, Oleg"}],"volume":14,"date_created":"2018-12-11T11:54:29Z","date_updated":"2022-03-03T11:47:09Z","publication_identifier":{"issn":["16093321"]},"month":"07","main_file_link":[{"url":"http://arxiv.org/abs/1211.7053","open_access":"1"}],"external_id":{"arxiv":["1211.7053"]},"oa":1,"quality_controlled":"1","doi":"10.17323/1609-4514-2014-14-3-491-504","language":[{"iso":"eng"}]},{"type":"journal_article","abstract":[{"lang":"eng","text":"We propose an algorithm for the generalization of cartographic objects that can be used to represent maps on different scales."}],"issue":"6","_id":"1929","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","title":"An algorithm for cartographic generalization that preserves global topology","intvolume":" 203","oa_version":"None","scopus_import":"1","day":"16","article_processing_charge":"No","publication":"Journal of Mathematical Sciences","citation":{"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.","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.","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.","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","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."},"article_type":"original","page":"754 - 760","date_published":"2014-11-16T00:00:00Z","publist_id":"5165","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.","year":"2014","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Springer","author":[{"full_name":"Alexeev, V V","last_name":"Alexeev","first_name":"V V"},{"full_name":"Bogaevskaya, V G","last_name":"Bogaevskaya","first_name":"V G"},{"full_name":"Preobrazhenskaya, M M","first_name":"M M","last_name":"Preobrazhenskaya"},{"full_name":"Ukhalov, A Y","last_name":"Ukhalov","first_name":"A Y"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert"},{"first_name":"Olga","last_name":"Yakimova","full_name":"Yakimova, Olga"}],"date_created":"2018-12-11T11:54:46Z","date_updated":"2022-05-24T10:39:06Z","volume":203,"month":"11","publication_identifier":{"eissn":["1573-8795"],"issn":["1072-3374"]},"quality_controlled":"1","doi":"10.1007/s10958-014-2165-8","language":[{"iso":"eng"}]},{"_id":"1930","year":"2014","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","acknowledgement":"RTRA Digiteoproject; ERC grant; SNF award; Intel Doctoral Fellowship; MPC-VCC","publication_status":"published","title":"Fast and memory-efficient topological denoising of 2D and 3D scalar fields","status":"public","publisher":"IEEE","intvolume":" 20","department":[{"_id":"HeEd"}],"author":[{"last_name":"Günther","first_name":"David","full_name":"Günther, David"},{"full_name":"Jacobson, Alec","first_name":"Alec","last_name":"Jacobson"},{"first_name":"Jan","last_name":"Reininghaus","id":"4505473A-F248-11E8-B48F-1D18A9856A87","full_name":"Reininghaus, Jan"},{"first_name":"Hans","last_name":"Seidel","full_name":"Seidel, Hans"},{"full_name":"Sorkine Hornung, Olga","last_name":"Sorkine Hornung","first_name":"Olga"},{"full_name":"Weinkauf, Tino","last_name":"Weinkauf","first_name":"Tino"}],"date_updated":"2021-01-12T06:54:09Z","date_created":"2018-12-11T11:54:46Z","oa_version":"None","volume":20,"type":"journal_article","abstract":[{"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.","lang":"eng"}],"publist_id":"5164","issue":"12","publication":"IEEE Transactions on Visualization and Computer Graphics","citation":{"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.","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.","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.","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.","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","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"},"quality_controlled":"1","page":"2585 - 2594","date_published":"2014-12-31T00:00:00Z","doi":"10.1109/TVCG.2014.2346432","language":[{"iso":"eng"}],"scopus_import":1,"month":"12","day":"31"},{"day":"01","scopus_import":1,"date_published":"2014-01-01T00:00:00Z","page":"31 - 38","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","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.","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","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.","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.","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."},"publication":"Proceedings of the Workshop on Algorithm Engineering and Experiments","abstract":[{"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.","lang":"eng"}],"type":"conference","oa_version":"Submitted Version","title":"Distributed computation of persistent homology","status":"public","_id":"2043","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","month":"01","language":[{"iso":"eng"}],"doi":"10.1137/1.9781611973198.4","conference":{"start_date":"2014-01-05","location":"Portland, USA","end_date":"2014-01-05","name":"ALENEX: Algorithm Engineering and Experiments"},"project":[{"name":"Topological Complex Systems","call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493"}],"quality_controlled":"1","oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1310.0710"}],"ec_funded":1,"publist_id":"5008","date_created":"2018-12-11T11:55:23Z","date_updated":"2021-01-12T06:54:56Z","author":[{"first_name":"Ulrich","last_name":"Bauer","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9683-0724","full_name":"Bauer, Ulrich"},{"first_name":"Michael","last_name":"Kerber","orcid":"0000-0002-8030-9299","full_name":"Kerber, Michael"},{"id":"4505473A-F248-11E8-B48F-1D18A9856A87","last_name":"Reininghaus","first_name":"Jan","full_name":"Reininghaus, Jan"}],"department":[{"_id":"HeEd"}],"editor":[{"full_name":" McGeoch, Catherine","first_name":"Catherine","last_name":" McGeoch"},{"first_name":"Ulrich","last_name":"Meyer","full_name":"Meyer, Ulrich"}],"publisher":"Society of Industrial and Applied Mathematics","publication_status":"published","year":"2014"},{"publist_id":"5007","ec_funded":1,"author":[{"first_name":"Ulrich","last_name":"Bauer","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9683-0724","full_name":"Bauer, Ulrich"},{"full_name":"Kerber, Michael","orcid":"0000-0002-8030-9299","last_name":"Kerber","first_name":"Michael"},{"full_name":"Reininghaus, Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","last_name":"Reininghaus","first_name":"Jan"}],"date_created":"2018-12-11T11:55:23Z","date_updated":"2021-01-12T06:54:56Z","year":"2014","publication_status":"published","department":[{"_id":"HeEd"}],"editor":[{"last_name":"Bremer","first_name":"Peer-Timo","full_name":"Bremer, Peer-Timo"},{"full_name":"Hotz, Ingrid","first_name":"Ingrid","last_name":"Hotz"},{"first_name":"Valerio","last_name":"Pascucci","full_name":"Pascucci, Valerio"},{"full_name":"Peikert, Ronald","first_name":"Ronald","last_name":"Peikert"}],"publisher":"Springer","month":"03","doi":"10.1007/978-3-319-04099-8_7","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1303.0477"}],"quality_controlled":"1","project":[{"grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425","name":"Topological Complex Systems","call_identifier":"FP7"}],"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."}],"type":"book_chapter","oa_version":"Submitted Version","_id":"2044","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","title":"Clear and Compress: Computing Persistent Homology in Chunks","status":"public","day":"19","scopus_import":1,"series_title":"Mathematics and Visualization","date_published":"2014-03-19T00:00:00Z","publication":"Topological Methods in Data Analysis and Visualization III","citation":{"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.","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","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.","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","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.","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."},"page":"103 - 117"},{"citation":{"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.","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.","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.","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","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.","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"},"main_file_link":[{"url":"http://arxiv.org/abs/1311.3681","open_access":"1"}],"oa":1,"publication":"Proceedings of the Annual Symposium on Computational Geometry","project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","name":"Topological Complex Systems","call_identifier":"FP7"}],"page":"355 - 364","quality_controlled":"1","doi":"10.1145/2582112.2582168","date_published":"2014-06-01T00:00:00Z","conference":{"name":"SoCG: Symposium on Computational Geometry","end_date":"2014-06-11","start_date":"2014-06-08","location":"Kyoto, Japan"},"language":[{"iso":"eng"}],"scopus_import":1,"day":"01","month":"06","year":"2014","_id":"2153","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"publisher":"ACM","status":"public","title":"Induced matchings of barcodes and the algebraic stability of persistence","publication_status":"published","author":[{"full_name":"Bauer, Ulrich","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9683-0724","first_name":"Ulrich","last_name":"Bauer"},{"last_name":"Lesnick","first_name":"Michael","full_name":"Lesnick, Michael"}],"oa_version":"Submitted Version","date_created":"2018-12-11T11:56:01Z","date_updated":"2021-01-12T06:55:38Z","type":"conference","ec_funded":1,"publist_id":"4853","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)."}]},{"day":"01","scopus_import":1,"date_published":"2014-06-01T00:00:00Z","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","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.","short":"U. Bauer, X. Ge, Y. Wang, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 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.","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."},"publication":"Proceedings of the Annual Symposium on Computational Geometry","page":"464 - 473","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)."}],"type":"conference","oa_version":"Submitted Version","_id":"2156","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","title":"Measuring distance between Reeb graphs","status":"public","month":"06","doi":"10.1145/2582112.2582169","conference":{"end_date":"2014-06-11","start_date":"2014-06-08","location":"Kyoto, Japan","name":"SoCG: Symposium on Computational Geometry"},"language":[{"iso":"eng"}],"main_file_link":[{"url":"http://arxiv.org/abs/1307.2839","open_access":"1"}],"oa":1,"project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","name":"Topological Complex Systems","call_identifier":"FP7"}],"quality_controlled":"1","ec_funded":1,"publist_id":"4850","author":[{"full_name":"Bauer, Ulrich","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9683-0724","first_name":"Ulrich","last_name":"Bauer"},{"full_name":"Ge, Xiaoyin","first_name":"Xiaoyin","last_name":"Ge"},{"full_name":"Wang, Yusu","first_name":"Yusu","last_name":"Wang"}],"date_updated":"2021-01-12T06:55:39Z","date_created":"2018-12-11T11:56:02Z","year":"2014","acknowledgement":"National Science Foundation under grants CCF-1319406, CCF-1116258.","publisher":"ACM","department":[{"_id":"HeEd"}],"publication_status":"published"},{"month":"06","oa":1,"main_file_link":[{"url":"http://arxiv.org/abs/1312.1231","open_access":"1"}],"project":[{"grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425","name":"Topological Complex Systems","call_identifier":"FP7"}],"quality_controlled":"1","doi":"10.1145/2582112.2582167","conference":{"end_date":"2014-06-11","location":"Kyoto, Japan","start_date":"2014-06-08","name":"SoCG: Symposium on Computational Geometry"},"language":[{"iso":"eng"}],"publist_id":"4851","ec_funded":1,"year":"2014","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","department":[{"_id":"HeEd"}],"publisher":"ACM","publication_status":"published","author":[{"orcid":"0000-0002-9683-0724","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","last_name":"Bauer","first_name":"Ulrich","full_name":"Bauer, Ulrich"},{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"}],"date_updated":"2021-01-12T06:55:38Z","date_created":"2018-12-11T11:56:01Z","scopus_import":1,"day":"01","citation":{"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.","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.","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","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.","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.","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"},"publication":"Proceedings of the Annual Symposium on Computational Geometry","page":"484 - 490","date_published":"2014-06-01T00:00:00Z","type":"conference","abstract":[{"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).","lang":"eng"}],"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","_id":"2155","title":"The morse theory of Čech and Delaunay filtrations","status":"public","oa_version":"Submitted Version"},{"author":[{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"last_name":"Parsa","first_name":"Salman","id":"4BDBD4F2-F248-11E8-B48F-1D18A9856A87","full_name":"Parsa, Salman"}],"oa_version":"None","date_created":"2018-12-11T11:56:09Z","date_updated":"2021-01-12T06:55:48Z","_id":"2177","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","year":"2014","publisher":"SIAM","department":[{"_id":"HeEd"}],"publication_status":"published","status":"public","title":"On the computational complexity of betti numbers reductions from matrix rank","publist_id":"4805","abstract":[{"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.","lang":"eng"}],"type":"conference","doi":"10.1137/1.9781611973402.11","date_published":"2014-01-01T00:00:00Z","conference":{"name":"SODA: Symposium on Discrete Algorithms","location":"Portland, USA","start_date":"2014-01-05","end_date":"2014-01-07"},"language":[{"iso":"eng"}],"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","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.","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.","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","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.","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."},"publication":"Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms","page":"152 - 160","quality_controlled":"1","month":"01","day":"01","scopus_import":1},{"publist_id":"4797","article_number":"17 ","volume":61,"date_updated":"2021-01-12T06:55:50Z","date_created":"2018-12-11T11:56:12Z","author":[{"last_name":"Čadek","first_name":"Martin","full_name":"Čadek, Martin"},{"full_name":"Krcál, Marek","id":"33E21118-F248-11E8-B48F-1D18A9856A87","first_name":"Marek","last_name":"Krcál"},{"first_name":"Jiří","last_name":"Matoušek","full_name":"Matoušek, Jiří"},{"full_name":"Sergeraert, Francis","first_name":"Francis","last_name":"Sergeraert"},{"last_name":"Vokřínek","first_name":"Lukáš","full_name":"Vokřínek, Lukáš"},{"full_name":"Wagner, Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568","first_name":"Uli","last_name":"Wagner"}],"publisher":"ACM","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"publication_status":"published","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).","year":"2014","month":"05","language":[{"iso":"eng"}],"doi":"10.1145/2597629","quality_controlled":"1","oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1105.6257"}],"issue":"3","abstract":[{"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.","lang":"eng"}],"type":"journal_article","oa_version":"Preprint","intvolume":" 61","status":"public","title":"Computing all maps into a sphere","_id":"2184","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","day":"01","scopus_import":1,"date_published":"2014-05-01T00:00:00Z","citation":{"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).","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.","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","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.","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.","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"},"publication":"Journal of the ACM"},{"month":"01","language":[{"iso":"eng"}],"conference":{"end_date":"2012-07-07","start_date":"2012-07-02","location":"Kraków, Poland","name":"ECM: European Congress of Mathematics"},"doi":"10.4171/120-1/3","quality_controlled":"1","oa":1,"file_date_updated":"2020-07-14T12:45:52Z","publist_id":"3842","date_updated":"2021-01-12T07:00:36Z","date_created":"2018-12-11T12:00:16Z","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"full_name":"Morozovy, Dmitriy","last_name":"Morozovy","first_name":"Dmitriy"}],"publication_status":"published","publisher":"European Mathematical Society Publishing House","department":[{"_id":"HeEd"}],"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.","year":"2014","day":"01","has_accepted_license":"1","article_processing_charge":"No","date_published":"2014-01-01T00:00:00Z","page":"31 - 50","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","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.","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","ista":"Edelsbrunner H, Morozovy D. 2014. Persistent homology: Theory and practice. ECM: European Congress of Mathematics, 31–50.","short":"H. Edelsbrunner, D. Morozovy, in:, European Mathematical Society Publishing House, 2014, pp. 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.","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."},"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."}],"type":"conference","file":[{"checksum":"1d4a046f1af945c407c5c4d411d4c5e4","date_updated":"2020-07-14T12:45:52Z","date_created":"2018-12-12T10:16:43Z","relation":"main_file","file_id":"5232","content_type":"application/pdf","file_size":435320,"creator":"system","access_level":"open_access","file_name":"IST-2016-544-v1+1_2012-P-11-PHTheoryPractice.pdf"}],"oa_version":"Submitted Version","pubrep_id":"544","status":"public","title":"Persistent homology: Theory and practice","ddc":["000"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"2905"},{"page":"117-127","citation":{"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.","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.","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.","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.","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","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"},"publication":"25th International Symposium, ISAAC 2014","date_published":"2014-11-08T00:00:00Z","scopus_import":"1","article_processing_charge":"No","day":"08","intvolume":" 8889","status":"public","title":"Planar matchings for weighted straight skeletons","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"10892","oa_version":"None","alternative_title":["LNCS"],"type":"conference","abstract":[{"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.","lang":"eng"}],"quality_controlled":"1","language":[{"iso":"eng"}],"doi":"10.1007/978-3-319-13075-0_10","conference":{"end_date":"2014-12-17","start_date":"2014-12-15","location":"Jeonju, Korea","name":"ISAAC: International Symposium on Algorithms and Computation"},"publication_identifier":{"eissn":["1611-3349"],"isbn":["9783319130743"],"eisbn":["9783319130750"],"issn":["0302-9743"]},"month":"11","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"publication_status":"published","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.","year":"2014","volume":8889,"date_created":"2022-03-21T07:09:03Z","date_updated":"2023-02-23T12:20:55Z","related_material":{"record":[{"relation":"later_version","status":"public","id":"481"}]},"author":[{"full_name":"Biedl, Therese","last_name":"Biedl","first_name":"Therese"},{"first_name":"Stefan","last_name":"Huber","id":"4700A070-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8871-5814","full_name":"Huber, Stefan"},{"first_name":"Peter","last_name":"Palfrader","full_name":"Palfrader, Peter"}]}]