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Computational Geometry: Theory and Applications. 2015;48(8):606-621. doi: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.","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."},"page":"606 - 621","date_published":"2015-06-03T00:00:00Z","type":"journal_article","abstract":[{"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.","lang":"eng"}],"issue":"8","_id":"1805","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","title":"Homological reconstruction and simplification in R3","intvolume":" 48","oa_version":"None","month":"06","quality_controlled":"1","project":[{"call_identifier":"FP7","name":"Topological Complex Systems","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"doi":"10.1016/j.comgeo.2014.08.010","language":[{"iso":"eng"}],"ec_funded":1,"publist_id":"5305","year":"2015","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Elsevier","author":[{"full_name":"Attali, Dominique","first_name":"Dominique","last_name":"Attali"},{"id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9683-0724","first_name":"Ulrich","last_name":"Bauer","full_name":"Bauer, Ulrich"},{"first_name":"Olivier","last_name":"Devillers","full_name":"Devillers, Olivier"},{"first_name":"Marc","last_name":"Glisse","full_name":"Glisse, Marc"},{"first_name":"André","last_name":"Lieutier","full_name":"Lieutier, André"}],"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"2812"}]},"date_updated":"2023-02-23T10:59:19Z","date_created":"2018-12-11T11:54:06Z","volume":48},{"scopus_import":1,"has_accepted_license":"1","day":"01","citation":{"chicago":"Symonova, Olga, Christopher Topp, and Herbert Edelsbrunner. “DynamicRoots: A Software Platform for the Reconstruction and Analysis of Growing Plant Roots.” PLoS One. 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These are important advances in plant phenotyping with applications to the study of genetic and environmental influences on growth."}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"1793","intvolume":" 10","ddc":["000"],"title":"DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots","status":"public","pubrep_id":"454","oa_version":"Published Version","file":[{"file_size":1850825,"content_type":"application/pdf","creator":"system","file_name":"IST-2016-454-v1+1_journal.pone.0127657.pdf","access_level":"open_access","date_updated":"2020-07-14T12:45:16Z","date_created":"2018-12-12T10:15:30Z","checksum":"d20f26461ca575276ad3ed9ce4bfc787","relation":"main_file","file_id":"5150"}],"month":"06","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","doi":"10.1371/journal.pone.0127657","language":[{"iso":"eng"}],"article_number":"e0127657","publist_id":"5318","file_date_updated":"2020-07-14T12:45:16Z","year":"2015","publisher":"Public Library of Science","department":[{"_id":"MaJö"},{"_id":"HeEd"}],"publication_status":"published","related_material":{"record":[{"status":"public","relation":"research_data","id":"9737"}]},"author":[{"first_name":"Olga","last_name":"Symonova","id":"3C0C7BC6-F248-11E8-B48F-1D18A9856A87","full_name":"Symonova, Olga"},{"full_name":"Topp, Christopher","last_name":"Topp","first_name":"Christopher"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"}],"volume":10,"date_created":"2018-12-11T11:54:02Z","date_updated":"2023-02-23T14:06:33Z"},{"type":"research_data_reference","author":[{"last_name":"Symonova","first_name":"Olga","id":"3C0C7BC6-F248-11E8-B48F-1D18A9856A87","full_name":"Symonova, Olga"},{"last_name":"Topp","first_name":"Christopher","full_name":"Topp, Christopher"},{"last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"}],"related_material":{"record":[{"id":"1793","status":"public","relation":"used_in_publication"}]},"date_created":"2021-07-28T06:20:13Z","date_updated":"2023-02-23T10:14:42Z","oa_version":"Published Version","year":"2015","_id":"9737","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","title":"Root traits computed by DynamicRoots for the maize root shown in fig 2","status":"public","publisher":"Public Library of Science","department":[{"_id":"MaJö"},{"_id":"HeEd"}],"month":"06","day":"01","article_processing_charge":"No","date_published":"2015-06-01T00:00:00Z","doi":"10.1371/journal.pone.0127657.s001","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","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.","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","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.","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).","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."}},{"day":"01","month":"12","scopus_import":1,"doi":"10.1016/j.jco.2015.06.002","date_published":"2015-12-01T00:00:00Z","language":[{"iso":"eng"}],"publication":"Journal of Complexity","citation":{"ista":"Pausinger F, Svane A. 2015. A Koksma-Hlawka inequality for general discrepancy systems. Journal of Complexity. 31(6), 773–797.","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.","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","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","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.","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."},"quality_controlled":"1","page":"773 - 797","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"}],"publist_id":"5320","issue":"6","type":"journal_article","author":[{"full_name":"Pausinger, Florian","last_name":"Pausinger","first_name":"Florian","orcid":"0000-0002-8379-3768","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Svane","first_name":"Anne","full_name":"Svane, Anne"}],"related_material":{"record":[{"id":"1399","relation":"dissertation_contains","status":"public"}]},"date_updated":"2023-09-07T11:41:25Z","date_created":"2018-12-11T11:54:02Z","oa_version":"None","volume":31,"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.","title":"A Koksma-Hlawka inequality for general discrepancy systems","publication_status":"published","status":"public","department":[{"_id":"HeEd"}],"intvolume":" 31","publisher":"Academic Press"},{"article_processing_charge":"No","publication_identifier":{"issn":["2663-337X"]},"month":"06","day":"01","citation":{"chicago":"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.","mla":"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.","apa":"Pausinger, F. (2015). On the approximation of intrinsic volumes. Institute of Science and Technology Austria.","ista":"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"}],"supervisor":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"}],"degree_awarded":"PhD","type":"dissertation","alternative_title":["ISTA Thesis"],"publist_id":"5808","abstract":[{"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.","lang":"eng"}],"year":"2015","_id":"1399","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","department":[{"_id":"HeEd"}],"publisher":"Institute of Science and Technology Austria","status":"public","publication_status":"published","title":"On the approximation of intrinsic volumes","related_material":{"record":[{"id":"1662","relation":"part_of_dissertation","status":"public"},{"status":"public","relation":"part_of_dissertation","id":"1792"},{"relation":"part_of_dissertation","status":"public","id":"2255"}]},"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"}]