--- _id: '1617' abstract: - lang: eng text: 'We study the discrepancy of jittered sampling sets: such a set P⊂ [0,1]d is generated for fixed m∈ℕ by partitioning [0,1]d into md axis aligned cubes of equal measure and placing a random point inside each of the N=md cubes. We prove that, for N sufficiently large, 1/10 d/N1/2+1/2d ≤EDN∗(P)≤ √d(log N) 1/2/N1/2+1/2d, where the upper bound with an unspecified constant Cd was proven earlier by Beck. Our proof makes crucial use of the sharp Dvoretzky-Kiefer-Wolfowitz inequality and a suitably taylored Bernstein inequality; we have reasons to believe that the upper bound has the sharp scaling in N. Additional heuristics suggest that jittered sampling should be able to improve known bounds on the inverse of the star-discrepancy in the regime N≳dd. We also prove a partition principle showing that every partition of [0,1]d combined with a jittered sampling construction gives rise to a set whose expected squared L2-discrepancy is smaller than that of purely random points.' acknowledgement: We are grateful to the referee whose suggestions greatly improved the quality and clarity of the exposition. author: - first_name: Florian full_name: Pausinger, Florian id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87 last_name: Pausinger orcid: 0000-0002-8379-3768 - first_name: Stefan full_name: Steinerberger, Stefan last_name: Steinerberger citation: ama: Pausinger F, Steinerberger S. On the discrepancy of jittered sampling. Journal of Complexity. 2016;33:199-216. doi:10.1016/j.jco.2015.11.003 apa: Pausinger, F., & Steinerberger, S. (2016). On the discrepancy of jittered sampling. Journal of Complexity. Academic Press. https://doi.org/10.1016/j.jco.2015.11.003 chicago: Pausinger, Florian, and Stefan Steinerberger. “On the Discrepancy of Jittered Sampling.” Journal of Complexity. Academic Press, 2016. https://doi.org/10.1016/j.jco.2015.11.003. ieee: F. Pausinger and S. Steinerberger, “On the discrepancy of jittered sampling,” Journal of Complexity, vol. 33. Academic Press, pp. 199–216, 2016. ista: Pausinger F, Steinerberger S. 2016. On the discrepancy of jittered sampling. Journal of Complexity. 33, 199–216. mla: Pausinger, Florian, and Stefan Steinerberger. “On the Discrepancy of Jittered Sampling.” Journal of Complexity, vol. 33, Academic Press, 2016, pp. 199–216, doi:10.1016/j.jco.2015.11.003. short: F. Pausinger, S. Steinerberger, Journal of Complexity 33 (2016) 199–216. date_created: 2018-12-11T11:53:03Z date_published: 2016-04-01T00:00:00Z date_updated: 2021-01-12T06:52:02Z day: '01' department: - _id: HeEd doi: 10.1016/j.jco.2015.11.003 intvolume: ' 33' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1510.00251 month: '04' oa: 1 oa_version: Submitted Version page: 199 - 216 publication: Journal of Complexity publication_status: published publisher: Academic Press publist_id: '5549' quality_controlled: '1' scopus_import: 1 status: public title: On the discrepancy of jittered sampling type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 33 year: '2016' ... --- _id: '1662' abstract: - lang: eng text: We introduce a modification of the classic notion of intrinsic volume using persistence moments of height functions. Evaluating the modified first intrinsic volume on digital approximations of a compact body with smoothly embedded boundary in Rn, we prove convergence to the first intrinsic volume of the body as the resolution of the approximation improves. We have weaker results for the other modified intrinsic volumes, proving they converge to the corresponding intrinsic volumes of the n-dimensional unit ball. acknowledgement: "This research is partially supported by the Toposys project FP7-ICT-318493-STREP, and by ESF under the ACAT Research Network Programme.\r\nBoth authors thank Anne Marie Svane for her comments on an early version of this paper. The second author wishes to thank Eva B. Vedel Jensen and Markus Kiderlen from Aarhus University for enlightening discussions and their kind hospitality during a visit of their department in 2014." author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Florian full_name: Pausinger, Florian id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87 last_name: Pausinger orcid: 0000-0002-8379-3768 citation: ama: Edelsbrunner H, Pausinger F. Approximation and convergence of the intrinsic volume. Advances in Mathematics. 2016;287:674-703. doi:10.1016/j.aim.2015.10.004 apa: Edelsbrunner, H., & Pausinger, F. (2016). Approximation and convergence of the intrinsic volume. Advances in Mathematics. Academic Press. https://doi.org/10.1016/j.aim.2015.10.004 chicago: Edelsbrunner, Herbert, and Florian Pausinger. “Approximation and Convergence of the Intrinsic Volume.” Advances in Mathematics. Academic Press, 2016. https://doi.org/10.1016/j.aim.2015.10.004. ieee: H. Edelsbrunner and F. Pausinger, “Approximation and convergence of the intrinsic volume,” Advances in Mathematics, vol. 287. Academic Press, pp. 674–703, 2016. ista: Edelsbrunner H, Pausinger F. 2016. Approximation and convergence of the intrinsic volume. Advances in Mathematics. 287, 674–703. mla: Edelsbrunner, Herbert, and Florian Pausinger. “Approximation and Convergence of the Intrinsic Volume.” Advances in Mathematics, vol. 287, Academic Press, 2016, pp. 674–703, doi:10.1016/j.aim.2015.10.004. short: H. Edelsbrunner, F. Pausinger, Advances in Mathematics 287 (2016) 674–703. date_created: 2018-12-11T11:53:20Z date_published: 2016-01-10T00:00:00Z date_updated: 2023-09-07T11:41:25Z day: '10' ddc: - '004' department: - _id: HeEd doi: 10.1016/j.aim.2015.10.004 ec_funded: 1 file: - access_level: open_access checksum: f8869ec110c35c852ef6a37425374af7 content_type: application/pdf creator: system date_created: 2018-12-12T10:12:10Z date_updated: 2020-07-14T12:45:10Z file_id: '4928' file_name: IST-2017-774-v1+1_2016-J-03-FirstIntVolume.pdf file_size: 248985 relation: main_file file_date_updated: 2020-07-14T12:45:10Z has_accepted_license: '1' intvolume: ' 287' language: - iso: eng license: https://creativecommons.org/licenses/by-nc-nd/4.0/ month: '01' oa: 1 oa_version: Published Version page: 674 - 703 project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems publication: Advances in Mathematics publication_status: published publisher: Academic Press publist_id: '5488' pubrep_id: '774' quality_controlled: '1' related_material: record: - id: '1399' relation: dissertation_contains status: public scopus_import: 1 status: public title: Approximation and convergence of the intrinsic volume tmp: image: /images/cc_by_nc_nd.png legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) short: CC BY-NC-ND (4.0) type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 287 year: '2016' ... --- _id: '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: '1792' abstract: - lang: eng text: Motivated by recent ideas of Harman (Unif. Distrib. Theory, 2010) we develop a new concept of variation of multivariate functions on a compact Hausdorff space with respect to a collection D of subsets. We prove a general version of the Koksma-Hlawka theorem that holds for this notion of variation and discrepancy with respect to D. As special cases, we obtain Koksma-Hlawka inequalities for classical notions, such as extreme or isotropic discrepancy. For extreme discrepancy, our result coincides with the usual Koksma-Hlawka theorem. We show that the space of functions of bounded D-variation contains important discontinuous functions and is closed under natural algebraic operations. Finally, we illustrate the results on concrete integration problems from integral geometry and stereology. acknowledgement: F.P. is supported by the Graduate School of IST Austria, A.M.S is supported by the Centre for Stochastic Geometry and Advanced Bioimaging funded by a grant from the Villum Foundation. author: - first_name: Florian full_name: Pausinger, Florian id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87 last_name: Pausinger orcid: 0000-0002-8379-3768 - first_name: Anne full_name: Svane, Anne last_name: Svane citation: ama: Pausinger F, Svane A. A Koksma-Hlawka inequality for general discrepancy systems. Journal of Complexity. 2015;31(6):773-797. doi:10.1016/j.jco.2015.06.002 apa: Pausinger, F., & Svane, A. (2015). A Koksma-Hlawka inequality for general discrepancy systems. Journal of Complexity. Academic Press. https://doi.org/10.1016/j.jco.2015.06.002 chicago: Pausinger, Florian, and Anne Svane. “A Koksma-Hlawka Inequality for General Discrepancy Systems.” Journal of Complexity. Academic Press, 2015. https://doi.org/10.1016/j.jco.2015.06.002. ieee: F. Pausinger and A. Svane, “A Koksma-Hlawka inequality for general discrepancy systems,” Journal of Complexity, vol. 31, no. 6. Academic Press, pp. 773–797, 2015. ista: Pausinger F, Svane A. 2015. A Koksma-Hlawka inequality for general discrepancy systems. Journal of Complexity. 31(6), 773–797. mla: Pausinger, Florian, and Anne Svane. “A Koksma-Hlawka Inequality for General Discrepancy Systems.” Journal of Complexity, vol. 31, no. 6, Academic Press, 2015, pp. 773–97, doi:10.1016/j.jco.2015.06.002. short: F. Pausinger, A. Svane, Journal of Complexity 31 (2015) 773–797. date_created: 2018-12-11T11:54:02Z date_published: 2015-12-01T00:00:00Z date_updated: 2023-09-07T11:41:25Z day: '01' department: - _id: HeEd doi: 10.1016/j.jco.2015.06.002 intvolume: ' 31' issue: '6' language: - iso: eng month: '12' oa_version: None page: 773 - 797 publication: Journal of Complexity publication_status: published publisher: Academic Press publist_id: '5320' quality_controlled: '1' related_material: record: - id: '1399' relation: dissertation_contains status: public scopus_import: 1 status: public title: A Koksma-Hlawka inequality for general discrepancy systems type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 31 year: '2015' ... --- _id: '1399' abstract: - lang: eng text: This thesis is concerned with the computation and approximation of intrinsic volumes. Given a smooth body M and a certain digital approximation of it, we develop algorithms to approximate various intrinsic volumes of M using only measurements taken from its digital approximations. The crucial idea behind our novel algorithms is to link the recent theory of persistent homology to the theory of intrinsic volumes via the Crofton formula from integral geometry and, in particular, via Euler characteristic computations. Our main contributions are a multigrid convergent digital algorithm to compute the first intrinsic volume of a solid body in R^n as well as an appropriate integration pipeline to approximate integral-geometric integrals defined over the Grassmannian manifold. alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Florian full_name: Pausinger, Florian id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87 last_name: Pausinger orcid: 0000-0002-8379-3768 citation: ama: Pausinger F. On the approximation of intrinsic volumes. 2015. apa: Pausinger, F. (2015). On the approximation of intrinsic volumes. Institute of Science and Technology Austria. chicago: Pausinger, Florian. “On the Approximation of Intrinsic Volumes.” Institute of Science and Technology Austria, 2015. ieee: F. Pausinger, “On the approximation of intrinsic volumes,” Institute of Science and Technology Austria, 2015. ista: Pausinger F. 2015. On the approximation of intrinsic volumes. Institute of Science and Technology Austria. mla: Pausinger, Florian. On the Approximation of Intrinsic Volumes. Institute of Science and Technology Austria, 2015. short: F. Pausinger, On the Approximation of Intrinsic Volumes, Institute of Science and Technology Austria, 2015. date_created: 2018-12-11T11:51:48Z date_published: 2015-06-01T00:00:00Z date_updated: 2023-09-07T11:41:25Z day: '01' degree_awarded: PhD department: - _id: HeEd language: - iso: eng month: '06' oa_version: None page: '144' publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria publist_id: '5808' related_material: record: - id: '1662' relation: part_of_dissertation status: public - id: '1792' relation: part_of_dissertation status: public - id: '2255' relation: part_of_dissertation status: public status: public supervisor: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 title: On the approximation of intrinsic volumes type: dissertation user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2015' ... --- _id: '2255' abstract: - lang: eng text: Motivated by applications in biology, we present an algorithm for estimating the length of tube-like shapes in 3-dimensional Euclidean space. In a first step, we combine the tube formula of Weyl with integral geometric methods to obtain an integral representation of the length, which we approximate using a variant of the Koksma-Hlawka Theorem. In a second step, we use tools from computational topology to decrease the dependence on small perturbations of the shape. We present computational experiments that shed light on the stability and the convergence rate of our algorithm. author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Florian full_name: Pausinger, Florian id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87 last_name: Pausinger orcid: 0000-0002-8379-3768 citation: ama: Edelsbrunner H, Pausinger F. Stable length estimates of tube-like shapes. Journal of Mathematical Imaging and Vision. 2014;50(1):164-177. doi:10.1007/s10851-013-0468-x apa: Edelsbrunner, H., & Pausinger, F. (2014). Stable length estimates of tube-like shapes. Journal of Mathematical Imaging and Vision. Springer. https://doi.org/10.1007/s10851-013-0468-x chicago: Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like Shapes.” Journal of Mathematical Imaging and Vision. Springer, 2014. https://doi.org/10.1007/s10851-013-0468-x. ieee: H. Edelsbrunner and F. Pausinger, “Stable length estimates of tube-like shapes,” Journal of Mathematical Imaging and Vision, vol. 50, no. 1. Springer, pp. 164–177, 2014. ista: Edelsbrunner H, Pausinger F. 2014. Stable length estimates of tube-like shapes. Journal of Mathematical Imaging and Vision. 50(1), 164–177. mla: Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like Shapes.” Journal of Mathematical Imaging and Vision, vol. 50, no. 1, Springer, 2014, pp. 164–77, doi:10.1007/s10851-013-0468-x. short: H. Edelsbrunner, F. Pausinger, Journal of Mathematical Imaging and Vision 50 (2014) 164–177. date_created: 2018-12-11T11:56:36Z date_published: 2014-09-01T00:00:00Z date_updated: 2023-09-07T11:41:25Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1007/s10851-013-0468-x ec_funded: 1 file: - access_level: open_access checksum: 2f93f3e63a38a85cd4404d7953913b14 content_type: application/pdf creator: system date_created: 2018-12-12T10:16:18Z date_updated: 2020-07-14T12:45:35Z file_id: '5204' file_name: IST-2016-549-v1+1_2014-J-06-LengthEstimate.pdf file_size: 3941391 relation: main_file file_date_updated: 2020-07-14T12:45:35Z has_accepted_license: '1' intvolume: ' 50' issue: '1' language: - iso: eng month: '09' oa: 1 oa_version: Submitted Version page: 164 - 177 project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems publication: Journal of Mathematical Imaging and Vision publication_identifier: issn: - '09249907' publication_status: published publisher: Springer publist_id: '4691' pubrep_id: '549' quality_controlled: '1' related_material: record: - id: '2843' relation: earlier_version status: public - id: '1399' relation: dissertation_contains status: public scopus_import: 1 status: public title: Stable length estimates of tube-like shapes type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 50 year: '2014' ... --- _id: '2304' abstract: - lang: eng text: This extended abstract is concerned with the irregularities of distribution of one-dimensional permuted van der Corput sequences that are generated from linear permutations. We show how to obtain upper bounds for the discrepancy and diaphony of these sequences, by relating them to Kronecker sequences and applying earlier results of Faure and Niederreiter. acknowledgement: This research is supported by the Graduate school of IST Austria (Institute of Science and Technology Austria). author: - first_name: Florian full_name: Pausinger, Florian id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87 last_name: Pausinger orcid: 0000-0002-8379-3768 citation: ama: Pausinger F. Van der Corput sequences and linear permutations. Electronic Notes in Discrete Mathematics. 2013;43:43-50. doi:10.1016/j.endm.2013.07.008 apa: Pausinger, F. (2013). Van der Corput sequences and linear permutations. Electronic Notes in Discrete Mathematics. Elsevier. https://doi.org/10.1016/j.endm.2013.07.008 chicago: Pausinger, Florian. “Van Der Corput Sequences and Linear Permutations.” Electronic Notes in Discrete Mathematics. Elsevier, 2013. https://doi.org/10.1016/j.endm.2013.07.008. ieee: F. Pausinger, “Van der Corput sequences and linear permutations,” Electronic Notes in Discrete Mathematics, vol. 43. Elsevier, pp. 43–50, 2013. ista: Pausinger F. 2013. Van der Corput sequences and linear permutations. Electronic Notes in Discrete Mathematics. 43, 43–50. mla: Pausinger, Florian. “Van Der Corput Sequences and Linear Permutations.” Electronic Notes in Discrete Mathematics, vol. 43, Elsevier, 2013, pp. 43–50, doi:10.1016/j.endm.2013.07.008. short: F. Pausinger, Electronic Notes in Discrete Mathematics 43 (2013) 43–50. date_created: 2018-12-11T11:56:53Z date_published: 2013-09-05T00:00:00Z date_updated: 2021-01-12T06:56:39Z day: '05' department: - _id: HeEd doi: 10.1016/j.endm.2013.07.008 intvolume: ' 43' language: - iso: eng month: '09' oa_version: None page: 43 - 50 publication: Electronic Notes in Discrete Mathematics publication_status: published publisher: Elsevier publist_id: '4623' quality_controlled: '1' scopus_import: 1 status: public title: Van der Corput sequences and linear permutations type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 43 year: '2013' ... --- _id: '2843' abstract: - lang: eng text: 'Mathematical objects can be measured unambiguously, but not so objects from our physical world. Even the total length of tubelike shapes has its difficulties. We introduce a combination of geometric, probabilistic, and topological methods to design a stable length estimate for tube-like shapes; that is: one that is insensitive to small shape changes.' alternative_title: - LNCS author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Florian full_name: Pausinger, Florian id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87 last_name: Pausinger orcid: 0000-0002-8379-3768 citation: ama: 'Edelsbrunner H, Pausinger F. Stable length estimates of tube-like shapes. In: 17th IAPR International Conference on Discrete Geometry for Computer Imagery. Vol 7749. Springer; 2013:XV-XIX. doi:10.1007/978-3-642-37067-0' apa: 'Edelsbrunner, H., & Pausinger, F. (2013). Stable length estimates of tube-like shapes. In 17th IAPR International Conference on Discrete Geometry for Computer Imagery (Vol. 7749, pp. XV–XIX). Seville, Spain: Springer. https://doi.org/10.1007/978-3-642-37067-0' chicago: Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like Shapes.” In 17th IAPR International Conference on Discrete Geometry for Computer Imagery, 7749:XV–XIX. Springer, 2013. https://doi.org/10.1007/978-3-642-37067-0. ieee: H. Edelsbrunner and F. Pausinger, “Stable length estimates of tube-like shapes,” in 17th IAPR International Conference on Discrete Geometry for Computer Imagery, Seville, Spain, 2013, vol. 7749, pp. XV–XIX. ista: 'Edelsbrunner H, Pausinger F. 2013. Stable length estimates of tube-like shapes. 17th IAPR International Conference on Discrete Geometry for Computer Imagery. DGCI: Discrete Geometry for Computer Imagery, LNCS, vol. 7749, XV–XIX.' mla: Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like Shapes.” 17th IAPR International Conference on Discrete Geometry for Computer Imagery, vol. 7749, Springer, 2013, pp. XV–XIX, doi:10.1007/978-3-642-37067-0. short: H. Edelsbrunner, F. Pausinger, in:, 17th IAPR International Conference on Discrete Geometry for Computer Imagery, Springer, 2013, pp. XV–XIX. conference: end_date: 2013-03-22 location: Seville, Spain name: 'DGCI: Discrete Geometry for Computer Imagery' start_date: 2013-03-20 date_created: 2018-12-11T11:59:53Z date_published: 2013-02-21T00:00:00Z date_updated: 2023-02-23T10:35:00Z day: '21' department: - _id: HeEd doi: 10.1007/978-3-642-37067-0 intvolume: ' 7749' language: - iso: eng month: '02' oa_version: None page: XV - XIX publication: 17th IAPR International Conference on Discrete Geometry for Computer Imagery publication_status: published publisher: Springer publist_id: '3952' quality_controlled: '1' related_material: record: - id: '2255' relation: later_version status: public scopus_import: 1 status: public title: Stable length estimates of tube-like shapes type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 7749 year: '2013' ... --- _id: '6588' abstract: - lang: eng text: First we note that the best polynomial approximation to vertical bar x vertical bar on the set, which consists of an interval on the positive half-axis and a point on the negative half-axis, can be given by means of the classical Chebyshev polynomials. Then we explore the cases when a solution of the related problem on two intervals can be given in elementary functions. acknowledgement: "This work is supported by the Austrian Science Fund (FWF), Project P22025-N18.\r\n" article_processing_charge: No article_type: original 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. Elementary solutions of the Bernstein problem on two intervals. Journal of Mathematical Physics, Analysis, Geometry. 2012;8(1):63-78. apa: Pausinger, F. (2012). Elementary solutions of the Bernstein problem on two intervals. Journal of Mathematical Physics, Analysis, Geometry. B. Verkin Institute for Low Temperature Physics and Engineering. chicago: Pausinger, Florian. “Elementary Solutions of the Bernstein Problem on Two Intervals.” Journal of Mathematical Physics, Analysis, Geometry. B. Verkin Institute for Low Temperature Physics and Engineering, 2012. ieee: F. Pausinger, “Elementary solutions of the Bernstein problem on two intervals,” Journal of Mathematical Physics, Analysis, Geometry, vol. 8, no. 1. B. Verkin Institute for Low Temperature Physics and Engineering, pp. 63–78, 2012. ista: Pausinger F. 2012. Elementary solutions of the Bernstein problem on two intervals. Journal of Mathematical Physics, Analysis, Geometry. 8(1), 63–78. mla: Pausinger, Florian. “Elementary Solutions of the Bernstein Problem on Two Intervals.” Journal of Mathematical Physics, Analysis, Geometry, vol. 8, no. 1, B. Verkin Institute for Low Temperature Physics and Engineering, 2012, pp. 63–78. short: F. Pausinger, Journal of Mathematical Physics, Analysis, Geometry 8 (2012) 63–78. date_created: 2019-06-27T08:16:56Z date_published: 2012-01-01T00:00:00Z date_updated: 2023-10-16T09:41:31Z day: '01' department: - _id: HeEd external_id: isi: - '000301173600004' intvolume: ' 8' isi: 1 issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: http://mi.mathnet.ru/eng/jmag525 month: '01' oa: 1 oa_version: Published Version page: 63-78 publication: Journal of Mathematical Physics, Analysis, Geometry publication_identifier: issn: - 1812-9471 publication_status: published publisher: B. Verkin Institute for Low Temperature Physics and Engineering quality_controlled: '1' scopus_import: '1' status: public title: Elementary solutions of the Bernstein problem on two intervals type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 8 year: '2012' ... --- _id: '2904' abstract: - lang: eng text: Generalized van der Corput sequences are onedimensional, infinite sequences in the unit interval. They are generated from permutations in integer base b and are the building blocks of the multi-dimensional Halton sequences. Motivated by recent progress of Atanassov on the uniform distribution behavior of Halton sequences, we study, among others, permutations of the form P(i) = ai (mod b) for coprime integers a and b. We show that multipliers a that either divide b - 1 or b + 1 generate van der Corput sequences with weak distribution properties. We give explicit lower bounds for the asymptotic distribution behavior of these sequences and relate them to sequences generated from the identity permutation in smaller bases, which are, due to Faure, the weakest distributed generalized van der Corput sequences. - lang: fre text: Les suites de Van der Corput généralisées sont dessuites unidimensionnelles et infinies dans l’intervalle de l’unité.Elles sont générées par permutations des entiers de la basebetsont les éléments constitutifs des suites multi-dimensionnelles deHalton. Suites aux progrès récents d’Atanassov concernant le com-portement de distribution uniforme des suites de Halton nous nousintéressons aux permutations de la formuleP(i) =ai(modb)pour les entiers premiers entre euxaetb. Dans cet article nousidentifions des multiplicateursagénérant des suites de Van derCorput ayant une mauvaise distribution. Nous donnons les bornesinférieures explicites pour cette distribution asymptotique asso-ciée à ces suites et relions ces dernières aux suites générées parpermutation d’identité, qui sont, selon Faure, les moins bien dis-tribuées des suites généralisées de Van der Corput dans une basedonnée. article_processing_charge: No article_type: original 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. Weak multipliers for generalized van der Corput sequences. Journal de Theorie des Nombres des Bordeaux. 2012;24(3):729-749. doi:10.5802/jtnb.819 apa: Pausinger, F. (2012). Weak multipliers for generalized van der Corput sequences. Journal de Theorie Des Nombres Des Bordeaux. Université de Bordeaux. https://doi.org/10.5802/jtnb.819 chicago: Pausinger, Florian. “Weak Multipliers for Generalized van Der Corput Sequences.” Journal de Theorie Des Nombres Des Bordeaux. Université de Bordeaux, 2012. https://doi.org/10.5802/jtnb.819. ieee: F. Pausinger, “Weak multipliers for generalized van der Corput sequences,” Journal de Theorie des Nombres des Bordeaux, vol. 24, no. 3. Université de Bordeaux, pp. 729–749, 2012. ista: Pausinger F. 2012. Weak multipliers for generalized van der Corput sequences. Journal de Theorie des Nombres des Bordeaux. 24(3), 729–749. mla: Pausinger, Florian. “Weak Multipliers for Generalized van Der Corput Sequences.” Journal de Theorie Des Nombres Des Bordeaux, vol. 24, no. 3, Université de Bordeaux, 2012, pp. 729–49, doi:10.5802/jtnb.819. short: F. Pausinger, Journal de Theorie Des Nombres Des Bordeaux 24 (2012) 729–749. date_created: 2018-12-11T12:00:15Z date_published: 2012-01-01T00:00:00Z date_updated: 2023-10-18T07:53:47Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.5802/jtnb.819 file: - access_level: open_access checksum: 6954bfe9d7f4119fbdda7a11cf0f5c67 content_type: application/pdf creator: dernst date_created: 2020-05-11T12:40:39Z date_updated: 2020-07-14T12:45:52Z file_id: '7819' file_name: JTNB_2012__24_3_729_0.pdf file_size: 819275 relation: main_file file_date_updated: 2020-07-14T12:45:52Z has_accepted_license: '1' intvolume: ' 24' issue: '3' language: - iso: eng month: '01' oa: 1 oa_version: Published Version page: 729 - 749 publication: Journal de Theorie des Nombres des Bordeaux publication_identifier: eissn: - 2118-8572 issn: - 1246-7405 publication_status: published publisher: Université de Bordeaux publist_id: '3843' quality_controlled: '1' scopus_import: '1' status: public title: Weak multipliers for generalized van der Corput sequences type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 24 year: '2012' ...