--- _id: '1682' abstract: - lang: eng text: 'We study the problem of robust satisfiability of systems of nonlinear equations, namely, whether for a given continuous function f:K→ ℝn on a finite simplicial complex K and α > 0, it holds that each function g: K → ℝn such that ||g - f || ∞ < α, has a root in K. Via a reduction to the extension problem of maps into a sphere, we particularly show that this problem is decidable in polynomial time for every fixed n, assuming dimK ≤ 2n - 3. This is a substantial extension of previous computational applications of topological degree and related concepts in numerical and interval analysis. Via a reverse reduction, we prove that the problem is undecidable when dim K > 2n - 2, where the threshold comes from the stable range in homotopy theory. For the lucidity of our exposition, we focus on the setting when f is simplexwise linear. Such functions can approximate general continuous functions, and thus we get approximation schemes and undecidability of the robust satisfiability in other possible settings.' article_number: '26' author: - first_name: Peter full_name: Franek, Peter last_name: Franek - first_name: Marek full_name: Krcál, Marek id: 33E21118-F248-11E8-B48F-1D18A9856A87 last_name: Krcál citation: ama: Franek P, Krcál M. Robust satisfiability of systems of equations. Journal of the ACM. 2015;62(4). doi:10.1145/2751524 apa: Franek, P., & Krcál, M. (2015). Robust satisfiability of systems of equations. Journal of the ACM. ACM. https://doi.org/10.1145/2751524 chicago: Franek, Peter, and Marek Krcál. “Robust Satisfiability of Systems of Equations.” Journal of the ACM. ACM, 2015. https://doi.org/10.1145/2751524. ieee: P. Franek and M. Krcál, “Robust satisfiability of systems of equations,” Journal of the ACM, vol. 62, no. 4. ACM, 2015. ista: Franek P, Krcál M. 2015. Robust satisfiability of systems of equations. Journal of the ACM. 62(4), 26. mla: Franek, Peter, and Marek Krcál. “Robust Satisfiability of Systems of Equations.” Journal of the ACM, vol. 62, no. 4, 26, ACM, 2015, doi:10.1145/2751524. short: P. Franek, M. Krcál, Journal of the ACM 62 (2015). date_created: 2018-12-11T11:53:27Z date_published: 2015-08-01T00:00:00Z date_updated: 2021-01-12T06:52:30Z day: '01' department: - _id: UlWa - _id: HeEd doi: 10.1145/2751524 intvolume: ' 62' issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1402.0858 month: '08' oa: 1 oa_version: Preprint publication: Journal of the ACM publication_status: published publisher: ACM publist_id: '5466' quality_controlled: '1' scopus_import: 1 status: public title: Robust satisfiability of systems of equations type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 62 year: '2015' ... --- _id: '1710' abstract: - lang: eng text: 'We consider the hollow on the half-plane {(x, y) : y ≤ 0} ⊂ ℝ2 defined by a function u : (-1, 1) → ℝ, u(x) < 0, and a vertical flow of point particles incident on the hollow. It is assumed that u satisfies the so-called single impact condition (SIC): each incident particle is elastically reflected by graph(u) and goes away without hitting the graph of u anymore. We solve the problem: find the function u minimizing the force of resistance created by the flow. We show that the graph of the minimizer is formed by two arcs of parabolas symmetric to each other with respect to the y-axis. Assuming that the resistance of u ≡ 0 equals 1, we show that the minimal resistance equals π/2 - 2arctan(1/2) ≈ 0.6435. This result completes the previously obtained result [SIAM J. Math. Anal., 46 (2014), pp. 2730-2742] stating in particular that the minimal resistance of a hollow in higher dimensions equals 0.5. We additionally consider a similar problem of minimal resistance, where the hollow in the half-space {(x1,...,xd,y) : y ≤ 0} ⊂ ℝd+1 is defined by a radial function U satisfying the SIC, U(x) = u(|x|), with x = (x1,...,xd), u(ξ) < 0 for 0 ≤ ξ < 1, and u(ξ) = 0 for ξ ≥ 1, and the flow is parallel to the y-axis. The minimal resistance is greater than 0.5 (and coincides with 0.6435 when d = 1) and converges to 0.5 as d → ∞.' author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Alexander full_name: Plakhov, Alexander last_name: Plakhov citation: ama: Akopyan A, Plakhov A. Minimal resistance of curves under the single impact assumption. Society for Industrial and Applied Mathematics. 2015;47(4):2754-2769. doi:10.1137/140993843 apa: Akopyan, A., & Plakhov, A. (2015). Minimal resistance of curves under the single impact assumption. Society for Industrial and Applied Mathematics. SIAM. https://doi.org/10.1137/140993843 chicago: Akopyan, Arseniy, and Alexander Plakhov. “Minimal Resistance of Curves under the Single Impact Assumption.” Society for Industrial and Applied Mathematics. SIAM, 2015. https://doi.org/10.1137/140993843. ieee: A. Akopyan and A. Plakhov, “Minimal resistance of curves under the single impact assumption,” Society for Industrial and Applied Mathematics, vol. 47, no. 4. SIAM, pp. 2754–2769, 2015. ista: Akopyan A, Plakhov A. 2015. Minimal resistance of curves under the single impact assumption. Society for Industrial and Applied Mathematics. 47(4), 2754–2769. mla: Akopyan, Arseniy, and Alexander Plakhov. “Minimal Resistance of Curves under the Single Impact Assumption.” Society for Industrial and Applied Mathematics, vol. 47, no. 4, SIAM, 2015, pp. 2754–69, doi:10.1137/140993843. short: A. Akopyan, A. Plakhov, Society for Industrial and Applied Mathematics 47 (2015) 2754–2769. date_created: 2018-12-11T11:53:36Z date_published: 2015-07-14T00:00:00Z date_updated: 2021-01-12T06:52:41Z day: '14' department: - _id: HeEd doi: 10.1137/140993843 ec_funded: 1 intvolume: ' 47' issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1410.3736 month: '07' oa: 1 oa_version: Preprint page: 2754 - 2769 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Society for Industrial and Applied Mathematics publication_status: published publisher: SIAM publist_id: '5423' quality_controlled: '1' scopus_import: 1 status: public title: Minimal resistance of curves under the single impact assumption type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 47 year: '2015' ... --- _id: '1828' abstract: - lang: eng text: We construct a non-linear Markov process connected with a biological model of a bacterial genome recombination. The description of invariant measures of this process gives us the solution of one problem in elementary probability theory. article_processing_charge: No author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Sergey full_name: Pirogov, Sergey last_name: Pirogov - first_name: Aleksandr full_name: Rybko, Aleksandr last_name: Rybko citation: ama: Akopyan A, Pirogov S, Rybko A. Invariant measures of genetic recombination process. Journal of Statistical Physics. 2015;160(1):163-167. doi:10.1007/s10955-015-1238-5 apa: Akopyan, A., Pirogov, S., & Rybko, A. (2015). Invariant measures of genetic recombination process. Journal of Statistical Physics. Springer. https://doi.org/10.1007/s10955-015-1238-5 chicago: Akopyan, Arseniy, Sergey Pirogov, and Aleksandr Rybko. “Invariant Measures of Genetic Recombination Process.” Journal of Statistical Physics. Springer, 2015. https://doi.org/10.1007/s10955-015-1238-5. ieee: A. Akopyan, S. Pirogov, and A. Rybko, “Invariant measures of genetic recombination process,” Journal of Statistical Physics, vol. 160, no. 1. Springer, pp. 163–167, 2015. ista: Akopyan A, Pirogov S, Rybko A. 2015. Invariant measures of genetic recombination process. Journal of Statistical Physics. 160(1), 163–167. mla: Akopyan, Arseniy, et al. “Invariant Measures of Genetic Recombination Process.” Journal of Statistical Physics, vol. 160, no. 1, Springer, 2015, pp. 163–67, doi:10.1007/s10955-015-1238-5. short: A. Akopyan, S. Pirogov, A. Rybko, Journal of Statistical Physics 160 (2015) 163–167. date_created: 2018-12-11T11:54:14Z date_published: 2015-07-01T00:00:00Z date_updated: 2021-01-12T06:53:28Z day: '01' department: - _id: HeEd doi: 10.1007/s10955-015-1238-5 ec_funded: 1 intvolume: ' 160' issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: arxiv.org/abs/1406.5313 month: '07' oa: 1 oa_version: Preprint page: 163 - 167 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Journal of Statistical Physics publication_status: published publisher: Springer publist_id: '5276' quality_controlled: '1' scopus_import: 1 status: public title: Invariant measures of genetic recombination process type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 160 year: '2015' ... --- _id: '1938' abstract: - lang: eng text: 'We numerically investigate the distribution of extrema of ''chaotic'' Laplacian eigenfunctions on two-dimensional manifolds. Our contribution is two-fold: (a) we count extrema on grid graphs with a small number of randomly added edges and show the behavior to coincide with the 1957 prediction of Longuet-Higgins for the continuous case and (b) we compute the regularity of their spatial distribution using discrepancy, which is a classical measure from the theory of Monte Carlo integration. The first part suggests that grid graphs with randomly added edges should behave like two-dimensional surfaces with ergodic geodesic flow; in the second part we show that the extrema are more regularly distributed in space than the grid Z2.' acknowledgement: "F.P. was supported by the Graduate School of IST Austria. S.S. was partially supported by CRC1060 of the DFG\r\nThe authors thank Olga Symonova and Michael Kerber for sharing their implementation of the persistence algorithm. " author: - first_name: Florian full_name: Pausinger, Florian id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87 last_name: Pausinger orcid: 0000-0002-8379-3768 - first_name: Stefan full_name: Steinerberger, Stefan last_name: Steinerberger citation: ama: Pausinger F, Steinerberger S. On the distribution of local extrema in quantum chaos. Physics Letters, Section A. 2015;379(6):535-541. doi:10.1016/j.physleta.2014.12.010 apa: Pausinger, F., & Steinerberger, S. (2015). On the distribution of local extrema in quantum chaos. Physics Letters, Section A. Elsevier. https://doi.org/10.1016/j.physleta.2014.12.010 chicago: Pausinger, Florian, and Stefan Steinerberger. “On the Distribution of Local Extrema in Quantum Chaos.” Physics Letters, Section A. Elsevier, 2015. https://doi.org/10.1016/j.physleta.2014.12.010. ieee: F. Pausinger and S. Steinerberger, “On the distribution of local extrema in quantum chaos,” Physics Letters, Section A, vol. 379, no. 6. Elsevier, pp. 535–541, 2015. ista: Pausinger F, Steinerberger S. 2015. On the distribution of local extrema in quantum chaos. Physics Letters, Section A. 379(6), 535–541. mla: Pausinger, Florian, and Stefan Steinerberger. “On the Distribution of Local Extrema in Quantum Chaos.” Physics Letters, Section A, vol. 379, no. 6, Elsevier, 2015, pp. 535–41, doi:10.1016/j.physleta.2014.12.010. short: F. Pausinger, S. Steinerberger, Physics Letters, Section A 379 (2015) 535–541. date_created: 2018-12-11T11:54:49Z date_published: 2015-03-06T00:00:00Z date_updated: 2021-01-12T06:54:12Z day: '06' department: - _id: HeEd doi: 10.1016/j.physleta.2014.12.010 intvolume: ' 379' issue: '6' language: - iso: eng month: '03' oa_version: None page: 535 - 541 publication: Physics Letters, Section A publication_status: published publisher: Elsevier publist_id: '5152' quality_controlled: '1' scopus_import: 1 status: public title: On the distribution of local extrema in quantum chaos type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 379 year: '2015' ... --- _id: '2035' abstract: - lang: eng text: "Considering a continuous self-map and the induced endomorphism on homology, we study the eigenvalues and eigenspaces of the latter. Taking a filtration of representations, we define the persistence of the eigenspaces, effectively introducing a hierarchical organization of the map. The algorithm that computes this information for a finite sample is proved to be stable, and to give the correct answer for a sufficiently dense sample. Results computed with an implementation of the algorithm provide evidence of its practical utility.\r\n" acknowledgement: This research is partially supported by the Toposys project FP7-ICT-318493-STREP, by ESF under the ACAT Research Network Programme, by the Russian Government under mega project 11.G34.31.0053, and by the Polish National Science Center under Grant No. N201 419639. author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Grzegorz full_name: Jablonski, Grzegorz id: 4483EF78-F248-11E8-B48F-1D18A9856A87 last_name: Jablonski orcid: 0000-0002-3536-9866 - first_name: Marian full_name: Mrozek, Marian last_name: Mrozek citation: ama: Edelsbrunner H, Jablonski G, Mrozek M. The persistent homology of a self-map. Foundations of Computational Mathematics. 2015;15(5):1213-1244. doi:10.1007/s10208-014-9223-y apa: Edelsbrunner, H., Jablonski, G., & Mrozek, M. (2015). The persistent homology of a self-map. Foundations of Computational Mathematics. Springer. https://doi.org/10.1007/s10208-014-9223-y chicago: Edelsbrunner, Herbert, Grzegorz Jablonski, and Marian Mrozek. “The Persistent Homology of a Self-Map.” Foundations of Computational Mathematics. Springer, 2015. https://doi.org/10.1007/s10208-014-9223-y. ieee: H. Edelsbrunner, G. Jablonski, and M. Mrozek, “The persistent homology of a self-map,” Foundations of Computational Mathematics, vol. 15, no. 5. Springer, pp. 1213–1244, 2015. ista: Edelsbrunner H, Jablonski G, Mrozek M. 2015. The persistent homology of a self-map. Foundations of Computational Mathematics. 15(5), 1213–1244. mla: Edelsbrunner, Herbert, et al. “The Persistent Homology of a Self-Map.” Foundations of Computational Mathematics, vol. 15, no. 5, Springer, 2015, pp. 1213–44, doi:10.1007/s10208-014-9223-y. short: H. Edelsbrunner, G. Jablonski, M. Mrozek, Foundations of Computational Mathematics 15 (2015) 1213–1244. date_created: 2018-12-11T11:55:20Z date_published: 2015-10-01T00:00:00Z date_updated: 2021-01-12T06:54:53Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1007/s10208-014-9223-y ec_funded: 1 file: - access_level: open_access checksum: 3566f3a8b0c1bc550e62914a88c584ff content_type: application/pdf creator: system date_created: 2018-12-12T10:08:10Z date_updated: 2020-07-14T12:45:26Z file_id: '4670' file_name: IST-2016-486-v1+1_s10208-014-9223-y.pdf file_size: 1317546 relation: main_file file_date_updated: 2020-07-14T12:45:26Z has_accepted_license: '1' intvolume: ' 15' issue: '5' language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ month: '10' oa: 1 oa_version: Published Version page: 1213 - 1244 project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems publication: Foundations of Computational Mathematics publication_status: published publisher: Springer publist_id: '5022' pubrep_id: '486' quality_controlled: '1' scopus_import: 1 status: public title: The persistent homology of a self-map tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 15 year: '2015' ... --- _id: '1805' abstract: - lang: eng text: 'We consider the problem of deciding whether the persistent homology group of a simplicial pair (K,L) can be realized as the homology H∗(X) of some complex X with L ⊂ X ⊂ K. We show that this problem is NP-complete even if K is embedded in double-struck R3. As a consequence, we show that it is NP-hard to simplify level and sublevel sets of scalar functions on double-struck S3 within a given tolerance constraint. This problem has relevance to the visualization of medical images by isosurfaces. We also show an implication to the theory of well groups of scalar functions: not every well group can be realized by some level set, and deciding whether a well group can be realized is NP-hard.' author: - first_name: Dominique full_name: Attali, Dominique last_name: Attali - first_name: Ulrich full_name: Bauer, Ulrich id: 2ADD483A-F248-11E8-B48F-1D18A9856A87 last_name: Bauer orcid: 0000-0002-9683-0724 - first_name: Olivier full_name: Devillers, Olivier last_name: Devillers - first_name: Marc full_name: Glisse, Marc last_name: Glisse - first_name: André full_name: Lieutier, André last_name: Lieutier citation: ama: 'Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. Homological reconstruction and simplification in R3. Computational Geometry: Theory and Applications. 2015;48(8):606-621. doi:10.1016/j.comgeo.2014.08.010' apa: 'Attali, D., Bauer, U., Devillers, O., Glisse, M., & Lieutier, A. (2015). Homological reconstruction and simplification in R3. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2014.08.010' chicago: 'Attali, Dominique, Ulrich Bauer, Olivier Devillers, Marc Glisse, and André Lieutier. “Homological Reconstruction and Simplification in R3.” Computational Geometry: Theory and Applications. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2014.08.010.' ieee: 'D. Attali, U. Bauer, O. Devillers, M. Glisse, and A. Lieutier, “Homological reconstruction and simplification in R3,” Computational Geometry: Theory and Applications, vol. 48, no. 8. Elsevier, pp. 606–621, 2015.' ista: 'Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. 2015. Homological reconstruction and simplification in R3. Computational Geometry: Theory and Applications. 48(8), 606–621.' mla: 'Attali, Dominique, et al. “Homological Reconstruction and Simplification in R3.” Computational Geometry: Theory and Applications, vol. 48, no. 8, Elsevier, 2015, pp. 606–21, doi:10.1016/j.comgeo.2014.08.010.' short: 'D. Attali, U. Bauer, O. Devillers, M. Glisse, A. Lieutier, Computational Geometry: Theory and Applications 48 (2015) 606–621.' date_created: 2018-12-11T11:54:06Z date_published: 2015-06-03T00:00:00Z date_updated: 2023-02-23T10:59:19Z day: '03' department: - _id: HeEd doi: 10.1016/j.comgeo.2014.08.010 ec_funded: 1 intvolume: ' 48' issue: '8' language: - iso: eng month: '06' oa_version: None page: 606 - 621 project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems publication: 'Computational Geometry: Theory and Applications' publication_status: published publisher: Elsevier publist_id: '5305' quality_controlled: '1' related_material: record: - id: '2812' relation: earlier_version status: public scopus_import: 1 status: public title: Homological reconstruction and simplification in R3 type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 48 year: '2015' ... --- _id: '1793' abstract: - lang: eng text: We present a software platform for reconstructing and analyzing the growth of a plant root system from a time-series of 3D voxelized shapes. It aligns the shapes with each other, constructs a geometric graph representation together with the function that records the time of growth, and organizes the branches into a hierarchy that reflects the order of creation. The software includes the automatic computation of structural and dynamic traits for each root in the system enabling the quantification of growth on fine-scale. These are important advances in plant phenotyping with applications to the study of genetic and environmental influences on growth. article_number: e0127657 author: - first_name: Olga full_name: Symonova, Olga id: 3C0C7BC6-F248-11E8-B48F-1D18A9856A87 last_name: Symonova - first_name: Christopher full_name: Topp, Christopher last_name: Topp - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 citation: ama: 'Symonova O, Topp C, Edelsbrunner H. DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots. PLoS One. 2015;10(6). doi:10.1371/journal.pone.0127657' apa: 'Symonova, O., Topp, C., & Edelsbrunner, H. (2015). DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots. PLoS One. Public Library of Science. https://doi.org/10.1371/journal.pone.0127657' chicago: 'Symonova, Olga, Christopher Topp, and Herbert Edelsbrunner. “DynamicRoots: A Software Platform for the Reconstruction and Analysis of Growing Plant Roots.” PLoS One. Public Library of Science, 2015. https://doi.org/10.1371/journal.pone.0127657.' ieee: 'O. Symonova, C. Topp, and H. Edelsbrunner, “DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots,” PLoS One, vol. 10, no. 6. Public Library of Science, 2015.' ista: 'Symonova O, Topp C, Edelsbrunner H. 2015. DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots. PLoS One. 10(6), e0127657.' mla: 'Symonova, Olga, et al. “DynamicRoots: A Software Platform for the Reconstruction and Analysis of Growing Plant Roots.” PLoS One, vol. 10, no. 6, e0127657, Public Library of Science, 2015, doi:10.1371/journal.pone.0127657.' short: O. Symonova, C. Topp, H. Edelsbrunner, PLoS One 10 (2015). date_created: 2018-12-11T11:54:02Z date_published: 2015-06-01T00:00:00Z date_updated: 2023-02-23T14:06:33Z day: '01' ddc: - '000' department: - _id: MaJö - _id: HeEd doi: 10.1371/journal.pone.0127657 file: - access_level: open_access checksum: d20f26461ca575276ad3ed9ce4bfc787 content_type: application/pdf creator: system date_created: 2018-12-12T10:15:30Z date_updated: 2020-07-14T12:45:16Z file_id: '5150' file_name: IST-2016-454-v1+1_journal.pone.0127657.pdf file_size: 1850825 relation: main_file file_date_updated: 2020-07-14T12:45:16Z has_accepted_license: '1' intvolume: ' 10' issue: '6' language: - iso: eng month: '06' oa: 1 oa_version: Published Version publication: PLoS One publication_status: published publisher: Public Library of Science publist_id: '5318' pubrep_id: '454' quality_controlled: '1' related_material: record: - id: '9737' relation: research_data status: public scopus_import: 1 status: public title: 'DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots' tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 10 year: '2015' ... --- _id: '9737' article_processing_charge: No author: - first_name: Olga full_name: Symonova, Olga id: 3C0C7BC6-F248-11E8-B48F-1D18A9856A87 last_name: Symonova - first_name: Christopher full_name: Topp, Christopher last_name: Topp - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 citation: ama: Symonova O, Topp C, Edelsbrunner H. Root traits computed by DynamicRoots for the maize root shown in fig 2. 2015. doi:10.1371/journal.pone.0127657.s001 apa: Symonova, O., Topp, C., & Edelsbrunner, H. (2015). Root traits computed by DynamicRoots for the maize root shown in fig 2. Public Library of Science. https://doi.org/10.1371/journal.pone.0127657.s001 chicago: Symonova, Olga, Christopher Topp, and Herbert Edelsbrunner. “Root Traits Computed by DynamicRoots for the Maize Root Shown in Fig 2.” Public Library of Science, 2015. https://doi.org/10.1371/journal.pone.0127657.s001. ieee: O. Symonova, C. Topp, and H. Edelsbrunner, “Root traits computed by DynamicRoots for the maize root shown in fig 2.” Public Library of Science, 2015. ista: Symonova O, Topp C, Edelsbrunner H. 2015. Root traits computed by DynamicRoots for the maize root shown in fig 2, Public Library of Science, 10.1371/journal.pone.0127657.s001. mla: Symonova, Olga, et al. Root Traits Computed by DynamicRoots for the Maize Root Shown in Fig 2. Public Library of Science, 2015, doi:10.1371/journal.pone.0127657.s001. short: O. Symonova, C. Topp, H. Edelsbrunner, (2015). date_created: 2021-07-28T06:20:13Z date_published: 2015-06-01T00:00:00Z date_updated: 2023-02-23T10:14:42Z day: '01' department: - _id: MaJö - _id: HeEd doi: 10.1371/journal.pone.0127657.s001 month: '06' oa_version: Published Version publisher: Public Library of Science related_material: record: - id: '1793' relation: used_in_publication status: public status: public title: Root traits computed by DynamicRoots for the maize root shown in fig 2 type: research_data_reference user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf year: '2015' ... --- _id: '1792' abstract: - lang: eng text: Motivated by recent ideas of Harman (Unif. Distrib. Theory, 2010) we develop a new concept of variation of multivariate functions on a compact Hausdorff space with respect to a collection D of subsets. We prove a general version of the Koksma-Hlawka theorem that holds for this notion of variation and discrepancy with respect to D. As special cases, we obtain Koksma-Hlawka inequalities for classical notions, such as extreme or isotropic discrepancy. For extreme discrepancy, our result coincides with the usual Koksma-Hlawka theorem. We show that the space of functions of bounded D-variation contains important discontinuous functions and is closed under natural algebraic operations. Finally, we illustrate the results on concrete integration problems from integral geometry and stereology. acknowledgement: F.P. is supported by the Graduate School of IST Austria, A.M.S is supported by the Centre for Stochastic Geometry and Advanced Bioimaging funded by a grant from the Villum Foundation. author: - first_name: Florian full_name: Pausinger, Florian id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87 last_name: Pausinger orcid: 0000-0002-8379-3768 - first_name: Anne full_name: Svane, Anne last_name: Svane citation: ama: Pausinger F, Svane A. A Koksma-Hlawka inequality for general discrepancy systems. Journal of Complexity. 2015;31(6):773-797. doi:10.1016/j.jco.2015.06.002 apa: Pausinger, F., & Svane, A. (2015). A Koksma-Hlawka inequality for general discrepancy systems. Journal of Complexity. Academic Press. https://doi.org/10.1016/j.jco.2015.06.002 chicago: Pausinger, Florian, and Anne Svane. “A Koksma-Hlawka Inequality for General Discrepancy Systems.” Journal of Complexity. Academic Press, 2015. https://doi.org/10.1016/j.jco.2015.06.002. ieee: F. Pausinger and A. Svane, “A Koksma-Hlawka inequality for general discrepancy systems,” Journal of Complexity, vol. 31, no. 6. Academic Press, pp. 773–797, 2015. ista: Pausinger F, Svane A. 2015. A Koksma-Hlawka inequality for general discrepancy systems. Journal of Complexity. 31(6), 773–797. mla: Pausinger, Florian, and Anne Svane. “A Koksma-Hlawka Inequality for General Discrepancy Systems.” Journal of Complexity, vol. 31, no. 6, Academic Press, 2015, pp. 773–97, doi:10.1016/j.jco.2015.06.002. short: F. Pausinger, A. Svane, Journal of Complexity 31 (2015) 773–797. date_created: 2018-12-11T11:54:02Z date_published: 2015-12-01T00:00:00Z date_updated: 2023-09-07T11:41:25Z day: '01' department: - _id: HeEd doi: 10.1016/j.jco.2015.06.002 intvolume: ' 31' issue: '6' language: - iso: eng month: '12' oa_version: None page: 773 - 797 publication: Journal of Complexity publication_status: published publisher: Academic Press publist_id: '5320' quality_controlled: '1' related_material: record: - id: '1399' relation: dissertation_contains status: public scopus_import: 1 status: public title: A Koksma-Hlawka inequality for general discrepancy systems type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 31 year: '2015' ... --- _id: '1399' abstract: - lang: eng text: This thesis is concerned with the computation and approximation of intrinsic volumes. Given a smooth body M and a certain digital approximation of it, we develop algorithms to approximate various intrinsic volumes of M using only measurements taken from its digital approximations. The crucial idea behind our novel algorithms is to link the recent theory of persistent homology to the theory of intrinsic volumes via the Crofton formula from integral geometry and, in particular, via Euler characteristic computations. Our main contributions are a multigrid convergent digital algorithm to compute the first intrinsic volume of a solid body in R^n as well as an appropriate integration pipeline to approximate integral-geometric integrals defined over the Grassmannian manifold. alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Florian full_name: Pausinger, Florian id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87 last_name: Pausinger orcid: 0000-0002-8379-3768 citation: ama: Pausinger F. On the approximation of intrinsic volumes. 2015. apa: Pausinger, F. (2015). On the approximation of intrinsic volumes. Institute of Science and Technology Austria. chicago: Pausinger, Florian. “On the Approximation of Intrinsic Volumes.” Institute of Science and Technology Austria, 2015. ieee: F. Pausinger, “On the approximation of intrinsic volumes,” Institute of Science and Technology Austria, 2015. ista: Pausinger F. 2015. On the approximation of intrinsic volumes. Institute of Science and Technology Austria. mla: Pausinger, Florian. On the Approximation of Intrinsic Volumes. Institute of Science and Technology Austria, 2015. short: F. Pausinger, On the Approximation of Intrinsic Volumes, Institute of Science and Technology Austria, 2015. date_created: 2018-12-11T11:51:48Z date_published: 2015-06-01T00:00:00Z date_updated: 2023-09-07T11:41:25Z day: '01' degree_awarded: PhD department: - _id: HeEd language: - iso: eng month: '06' oa_version: None page: '144' publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria publist_id: '5808' related_material: record: - id: '1662' relation: part_of_dissertation status: public - id: '1792' relation: part_of_dissertation status: public - id: '2255' relation: part_of_dissertation status: public status: public supervisor: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 title: On the approximation of intrinsic volumes type: dissertation user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2015' ...