--- _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 license: https://creativecommons.org/licenses/by/4.0/ 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' ...