--- _id: '1578' abstract: - lang: eng text: We prove that the dual of the digital Voronoi diagram constructed by flooding the plane from the data points gives a geometrically and topologically correct dual triangulation. This provides the proof of correctness for recently developed GPU algorithms that outperform traditional CPU algorithms for constructing two-dimensional Delaunay triangulations. acknowledgement: "The research of the second author is partially supported by NSF under grant DBI-0820624 and by DARPA under grants HR011-05-1-0057 and HR0011-09-006\r\n" author: - first_name: Thanhtung full_name: Cao, Thanhtung last_name: Cao - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Tiowseng full_name: Tan, Tiowseng last_name: Tan citation: ama: Cao T, Edelsbrunner H, Tan T. Triangulations from topologically correct digital Voronoi diagrams. Computational Geometry. 2015;48(7):507-519. doi:10.1016/j.comgeo.2015.04.001 apa: Cao, T., Edelsbrunner, H., & Tan, T. (2015). Triangulations from topologically correct digital Voronoi diagrams. Computational Geometry. Elsevier. https://doi.org/10.1016/j.comgeo.2015.04.001 chicago: Cao, Thanhtung, Herbert Edelsbrunner, and Tiowseng Tan. “Triangulations from Topologically Correct Digital Voronoi Diagrams.” Computational Geometry. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2015.04.001. ieee: T. Cao, H. Edelsbrunner, and T. Tan, “Triangulations from topologically correct digital Voronoi diagrams,” Computational Geometry, vol. 48, no. 7. Elsevier, pp. 507–519, 2015. ista: Cao T, Edelsbrunner H, Tan T. 2015. Triangulations from topologically correct digital Voronoi diagrams. Computational Geometry. 48(7), 507–519. mla: Cao, Thanhtung, et al. “Triangulations from Topologically Correct Digital Voronoi Diagrams.” Computational Geometry, vol. 48, no. 7, Elsevier, 2015, pp. 507–19, doi:10.1016/j.comgeo.2015.04.001. short: T. Cao, H. Edelsbrunner, T. Tan, Computational Geometry 48 (2015) 507–519. date_created: 2018-12-11T11:52:49Z date_published: 2015-08-01T00:00:00Z date_updated: 2021-01-12T06:51:43Z day: '01' department: - _id: HeEd doi: 10.1016/j.comgeo.2015.04.001 intvolume: ' 48' issue: '7' language: - iso: eng month: '08' oa_version: None page: 507 - 519 publication: Computational Geometry publication_status: published publisher: Elsevier publist_id: '5593' quality_controlled: '1' scopus_import: 1 status: public title: Triangulations from topologically correct digital Voronoi diagrams type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 48 year: '2015' ... --- _id: '1584' abstract: - lang: eng text: We investigate weighted straight skeletons from a geometric, graph-theoretical, and combinatorial point of view. We start with a thorough definition and shed light on some ambiguity issues in the procedural definition. We investigate the geometry, combinatorics, and topology of faces and the roof model, and we discuss in which cases a weighted straight skeleton is connected. Finally, we show that the weighted straight skeleton of even a simple polygon may be non-planar and may contain cycles, and we discuss under which restrictions on the weights and/or the input polygon the weighted straight skeleton still behaves similar to its unweighted counterpart. In particular, we obtain a non-procedural description and a linear-time construction algorithm for the straight skeleton of strictly convex polygons with arbitrary weights. author: - first_name: Therese full_name: Biedl, Therese last_name: Biedl - first_name: Martin full_name: Held, Martin last_name: Held - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Dominik full_name: Kaaser, Dominik last_name: Kaaser - first_name: Peter full_name: Palfrader, Peter last_name: Palfrader citation: ama: 'Biedl T, Held M, Huber S, Kaaser D, Palfrader P. Reprint of: Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 2015;48(5):429-442. doi:10.1016/j.comgeo.2015.01.004' apa: 'Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). Reprint of: Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2015.01.004' chicago: 'Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader. “Reprint of: Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory and Applications. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2015.01.004.' ieee: 'T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “Reprint of: Weighted straight skeletons in the plane,” Computational Geometry: Theory and Applications, vol. 48, no. 5. Elsevier, pp. 429–442, 2015.' ista: 'Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. Reprint of: Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 48(5), 429–442.' mla: 'Biedl, Therese, et al. “Reprint of: Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory and Applications, vol. 48, no. 5, Elsevier, 2015, pp. 429–42, doi:10.1016/j.comgeo.2015.01.004.' short: 'T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Computational Geometry: Theory and Applications 48 (2015) 429–442.' date_created: 2018-12-11T11:52:51Z date_published: 2015-07-01T00:00:00Z date_updated: 2023-02-23T10:05:22Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1016/j.comgeo.2015.01.004 file: - access_level: open_access checksum: 5b33719a86f7f4c8e5dc62c1b6893f49 content_type: application/pdf creator: system date_created: 2018-12-12T10:17:36Z date_updated: 2020-07-14T12:45:03Z file_id: '5292' file_name: IST-2016-475-v1+1_1-s2.0-S092577211500005X-main.pdf file_size: 508379 relation: main_file file_date_updated: 2020-07-14T12:45:03Z has_accepted_license: '1' intvolume: ' 48' issue: '5' language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: 429 - 442 publication: 'Computational Geometry: Theory and Applications' publication_status: published publisher: Elsevier publist_id: '5587' pubrep_id: '475' quality_controlled: '1' related_material: record: - id: '1582' relation: other status: public scopus_import: 1 status: public title: 'Reprint of: Weighted straight skeletons in the plane' 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: 48 year: '2015' ... --- _id: '1582' abstract: - lang: eng text: We investigate weighted straight skeletons from a geometric, graph-theoretical, and combinatorial point of view. We start with a thorough definition and shed light on some ambiguity issues in the procedural definition. We investigate the geometry, combinatorics, and topology of faces and the roof model, and we discuss in which cases a weighted straight skeleton is connected. Finally, we show that the weighted straight skeleton of even a simple polygon may be non-planar and may contain cycles, and we discuss under which restrictions on the weights and/or the input polygon the weighted straight skeleton still behaves similar to its unweighted counterpart. In particular, we obtain a non-procedural description and a linear-time construction algorithm for the straight skeleton of strictly convex polygons with arbitrary weights. author: - first_name: Therese full_name: Biedl, Therese last_name: Biedl - first_name: Martin full_name: Held, Martin last_name: Held - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Dominik full_name: Kaaser, Dominik last_name: Kaaser - first_name: Peter full_name: Palfrader, Peter last_name: Palfrader citation: ama: 'Biedl T, Held M, Huber S, Kaaser D, Palfrader P. Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 2015;48(2):120-133. doi:10.1016/j.comgeo.2014.08.006' apa: 'Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2014.08.006' chicago: 'Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader. “Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory and Applications. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2014.08.006.' ieee: 'T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “Weighted straight skeletons in the plane,” Computational Geometry: Theory and Applications, vol. 48, no. 2. Elsevier, pp. 120–133, 2015.' ista: 'Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 48(2), 120–133.' mla: 'Biedl, Therese, et al. “Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory and Applications, vol. 48, no. 2, Elsevier, 2015, pp. 120–33, doi:10.1016/j.comgeo.2014.08.006.' short: 'T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Computational Geometry: Theory and Applications 48 (2015) 120–133.' date_created: 2018-12-11T11:52:51Z date_published: 2015-02-01T00:00:00Z date_updated: 2023-02-23T10:05:27Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1016/j.comgeo.2014.08.006 file: - access_level: open_access checksum: c1ef67f6ec925e12f73a96b8fe285ab4 content_type: application/pdf creator: system date_created: 2018-12-12T10:16:28Z date_updated: 2020-07-14T12:45:02Z file_id: '5215' file_name: IST-2016-474-v1+1_1-s2.0-S0925772114000807-main.pdf file_size: 505987 relation: main_file file_date_updated: 2020-07-14T12:45:02Z has_accepted_license: '1' intvolume: ' 48' issue: '2' language: - iso: eng month: '02' oa: 1 oa_version: Published Version page: 120 - 133 publication: 'Computational Geometry: Theory and Applications' publication_status: published publisher: Elsevier publist_id: '5589' pubrep_id: '474' quality_controlled: '1' related_material: record: - id: '1584' relation: other status: public scopus_import: 1 status: public title: Weighted straight skeletons in the plane 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: 48 year: '2015' ... --- _id: '1583' abstract: - lang: eng text: We study the characteristics of straight skeletons of monotone polygonal chains and use them to devise an algorithm for computing positively weighted straight skeletons of monotone polygons. Our algorithm runs in O(nlogn) time and O(n) space, where n denotes the number of vertices of the polygon. author: - first_name: Therese full_name: Biedl, Therese last_name: Biedl - first_name: Martin full_name: Held, Martin last_name: Held - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Dominik full_name: Kaaser, Dominik last_name: Kaaser - first_name: Peter full_name: Palfrader, Peter last_name: Palfrader citation: ama: Biedl T, Held M, Huber S, Kaaser D, Palfrader P. A simple algorithm for computing positively weighted straight skeletons of monotone polygons. Information Processing Letters. 2015;115(2):243-247. doi:10.1016/j.ipl.2014.09.021 apa: Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). A simple algorithm for computing positively weighted straight skeletons of monotone polygons. Information Processing Letters. Elsevier. https://doi.org/10.1016/j.ipl.2014.09.021 chicago: Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader. “A Simple Algorithm for Computing Positively Weighted Straight Skeletons of Monotone Polygons.” Information Processing Letters. Elsevier, 2015. https://doi.org/10.1016/j.ipl.2014.09.021. ieee: T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “A simple algorithm for computing positively weighted straight skeletons of monotone polygons,” Information Processing Letters, vol. 115, no. 2. Elsevier, pp. 243–247, 2015. ista: Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. A simple algorithm for computing positively weighted straight skeletons of monotone polygons. Information Processing Letters. 115(2), 243–247. mla: Biedl, Therese, et al. “A Simple Algorithm for Computing Positively Weighted Straight Skeletons of Monotone Polygons.” Information Processing Letters, vol. 115, no. 2, Elsevier, 2015, pp. 243–47, doi:10.1016/j.ipl.2014.09.021. short: T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Information Processing Letters 115 (2015) 243–247. date_created: 2018-12-11T11:52:51Z date_published: 2015-02-01T00:00:00Z date_updated: 2021-01-12T06:51:45Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1016/j.ipl.2014.09.021 file: - access_level: open_access checksum: 2779a648610c9b5c86d0b51a62816d23 content_type: application/pdf creator: system date_created: 2018-12-12T10:18:45Z date_updated: 2020-07-14T12:45:03Z file_id: '5367' file_name: IST-2016-473-v1+1_1-s2.0-S0020019014001987-main.pdf file_size: 270137 relation: main_file file_date_updated: 2020-07-14T12:45:03Z has_accepted_license: '1' intvolume: ' 115' issue: '2' language: - iso: eng month: '02' oa: 1 oa_version: Published Version page: 243 - 247 publication: Information Processing Letters publication_status: published publisher: Elsevier publist_id: '5588' pubrep_id: '473' quality_controlled: '1' scopus_import: 1 status: public title: A simple algorithm for computing positively weighted straight skeletons of monotone polygons 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: 115 year: '2015' ... --- _id: '1590' abstract: - lang: eng text: 'The straight skeleton of a polygon is the geometric graph obtained by tracing the vertices during a mitered offsetting process. It is known that the straight skeleton of a simple polygon is a tree, and one can naturally derive directions on the edges of the tree from the propagation of the shrinking process. In this paper, we ask the reverse question: Given a tree with directed edges, can it be the straight skeleton of a polygon? And if so, can we find a suitable simple polygon? We answer these questions for all directed trees where the order of edges around each node is fixed.' alternative_title: - LNCS article_processing_charge: No author: - first_name: Oswin full_name: Aichholzer, Oswin last_name: Aichholzer - first_name: Therese full_name: Biedl, Therese last_name: Biedl - first_name: Thomas full_name: Hackl, Thomas last_name: Hackl - first_name: Martin full_name: Held, Martin last_name: Held - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Peter full_name: Palfrader, Peter last_name: Palfrader - first_name: Birgit full_name: Vogtenhuber, Birgit last_name: Vogtenhuber citation: ama: 'Aichholzer O, Biedl T, Hackl T, et al. Representing directed trees as straight skeletons. In: Graph Drawing and Network Visualization. Vol 9411. Springer Nature; 2015:335-347. doi:10.1007/978-3-319-27261-0_28' apa: 'Aichholzer, O., Biedl, T., Hackl, T., Held, M., Huber, S., Palfrader, P., & Vogtenhuber, B. (2015). Representing directed trees as straight skeletons. In Graph Drawing and Network Visualization (Vol. 9411, pp. 335–347). Los Angeles, CA, United States: Springer Nature. https://doi.org/10.1007/978-3-319-27261-0_28' chicago: Aichholzer, Oswin, Therese Biedl, Thomas Hackl, Martin Held, Stefan Huber, Peter Palfrader, and Birgit Vogtenhuber. “Representing Directed Trees as Straight Skeletons.” In Graph Drawing and Network Visualization, 9411:335–47. Springer Nature, 2015. https://doi.org/10.1007/978-3-319-27261-0_28. ieee: O. Aichholzer et al., “Representing directed trees as straight skeletons,” in Graph Drawing and Network Visualization, vol. 9411, Springer Nature, 2015, pp. 335–347. ista: 'Aichholzer O, Biedl T, Hackl T, Held M, Huber S, Palfrader P, Vogtenhuber B. 2015.Representing directed trees as straight skeletons. In: Graph Drawing and Network Visualization. LNCS, vol. 9411, 335–347.' mla: Aichholzer, Oswin, et al. “Representing Directed Trees as Straight Skeletons.” Graph Drawing and Network Visualization, vol. 9411, Springer Nature, 2015, pp. 335–47, doi:10.1007/978-3-319-27261-0_28. short: O. Aichholzer, T. Biedl, T. Hackl, M. Held, S. Huber, P. Palfrader, B. Vogtenhuber, in:, Graph Drawing and Network Visualization, Springer Nature, 2015, pp. 335–347. conference: end_date: 2015-09-26 location: Los Angeles, CA, United States name: 'GD: International Symposium on Graph Drawing' start_date: 2015-09-24 date_created: 2018-12-11T11:52:54Z date_published: 2015-11-27T00:00:00Z date_updated: 2022-01-28T09:10:37Z day: '27' department: - _id: HeEd doi: 10.1007/978-3-319-27261-0_28 intvolume: ' 9411' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1508.01076 month: '11' oa: 1 oa_version: Preprint page: 335 - 347 publication: Graph Drawing and Network Visualization publication_identifier: eisbn: - 978-3-319-27261-0 isbn: - 978-3-319-27260-3 publication_status: published publisher: Springer Nature publist_id: '5581' quality_controlled: '1' scopus_import: '1' status: public title: Representing directed trees as straight skeletons type: book_chapter user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 volume: 9411 year: '2015' ... --- _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 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' ... --- _id: '10893' abstract: - lang: eng 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. 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. article_processing_charge: No author: - first_name: Jens full_name: Kasten, Jens last_name: Kasten - first_name: Jan full_name: Reininghaus, Jan id: 4505473A-F248-11E8-B48F-1D18A9856A87 last_name: Reininghaus - first_name: Wieland full_name: Reich, Wieland last_name: Reich - first_name: Gerik full_name: Scheuermann, Gerik last_name: Scheuermann citation: 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' 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' 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.' 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.' 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.' 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. 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. date_created: 2022-03-21T07:11:23Z date_published: 2014-03-19T00:00:00Z date_updated: 2022-06-21T12:01:47Z day: '19' department: - _id: HeEd doi: 10.1007/978-3-319-04099-8_4 ec_funded: 1 editor: - first_name: Peer-Timo full_name: Bremer, Peer-Timo last_name: Bremer - first_name: Ingrid full_name: Hotz, Ingrid last_name: Hotz - first_name: Valerio full_name: Pascucci, Valerio last_name: Pascucci - first_name: Ronald full_name: Peikert, Ronald last_name: Peikert intvolume: ' 1' language: - iso: eng month: '03' oa_version: None page: 55-69 place: Cham project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems publication: 'Topological Methods in Data Analysis and Visualization III ' publication_identifier: eisbn: - '9783319040998' eissn: - 2197-666X isbn: - '9783319040981' issn: - 1612-3786 publication_status: published publisher: Springer quality_controlled: '1' scopus_import: '1' series_title: Mathematics and Visualization status: public title: Toward the extraction of saddle periodic orbits type: book_chapter user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 1 year: '2014' ... --- _id: '1816' 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. acknowledgement: 'Work by Martin Held and Stefan Huber was supported by Austrian Science Fund (FWF): L367-N15 and P25816-N15.' author: - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Martin full_name: Held, Martin last_name: Held - first_name: Peter full_name: Meerwald, Peter last_name: Meerwald - first_name: Roland full_name: Kwitt, Roland last_name: Kwitt citation: 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 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 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. 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. 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. 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. short: S. Huber, M. Held, P. Meerwald, R. Kwitt, International Journal of Computational Geometry and Applications 24 (2014) 61–86. date_created: 2018-12-11T11:54:10Z date_published: 2014-03-16T00:00:00Z date_updated: 2021-01-12T06:53:23Z day: '16' ddc: - '000' department: - _id: HeEd doi: 10.1142/S0218195914500034 file: - access_level: open_access checksum: be45c133ab4d43351260e21beaa8f4b1 content_type: application/pdf creator: system date_created: 2018-12-12T10:08:43Z date_updated: 2020-07-14T12:45:17Z file_id: '4704' file_name: IST-2016-443-v1+1_S0218195914500034.pdf file_size: 991734 relation: main_file file_date_updated: 2020-07-14T12:45:17Z has_accepted_license: '1' intvolume: ' 24' issue: '1' language: - iso: eng month: '03' oa: 1 oa_version: Published Version page: 61 - 86 publication: International Journal of Computational Geometry and Applications publication_status: published publisher: World Scientific Publishing publist_id: '5290' pubrep_id: '443' quality_controlled: '1' scopus_import: 1 status: public title: Topology-preserving watermarking of vector graphics 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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 24 year: '2014' ... --- _id: '1842' abstract: - lang: eng 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. acknowledgement: Marek Krčál was supported by the ERC Advanced Grant No. 267165. author: - first_name: Josef full_name: Cibulka, Josef last_name: Cibulka - first_name: Pu full_name: Gao, Pu last_name: Gao - first_name: Marek full_name: Krcál, Marek id: 33E21118-F248-11E8-B48F-1D18A9856A87 last_name: Krcál - first_name: Tomáš full_name: Valla, Tomáš last_name: Valla - first_name: Pavel full_name: Valtr, Pavel last_name: Valtr citation: 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 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 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. 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. 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. short: J. Cibulka, P. Gao, M. Krcál, T. Valla, P. Valtr, Discrete & Computational Geometry 53 (2014) 64–79. date_created: 2018-12-11T11:54:18Z date_published: 2014-11-14T00:00:00Z date_updated: 2021-01-12T06:53:33Z day: '14' department: - _id: UlWa - _id: HeEd doi: 10.1007/s00454-014-9646-x intvolume: ' 53' issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1310.7004 month: '11' oa: 1 oa_version: Submitted Version page: 64 - 79 publication: Discrete & Computational Geometry publication_status: published publisher: Springer publist_id: '5260' scopus_import: 1 status: public title: On the geometric ramsey number of outerplanar graphs type: journal_article user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 53 year: '2014' ... --- _id: '1876' abstract: - lang: eng 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. article_processing_charge: No article_type: original author: - first_name: Nikolai full_name: Dolbilin, Nikolai last_name: Dolbilin - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Alexey full_name: Glazyrin, Alexey last_name: Glazyrin - first_name: Oleg full_name: Musin, Oleg last_name: Musin 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 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 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. 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. ista: Dolbilin N, Edelsbrunner H, Glazyrin A, Musin O. 2014. Functionals on triangulations of delaunay sets. Moscow Mathematical Journal. 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. date_created: 2018-12-11T11:54:29Z date_published: 2014-07-01T00:00:00Z date_updated: 2022-03-03T11:47:09Z day: '01' department: - _id: HeEd doi: 10.17323/1609-4514-2014-14-3-491-504 external_id: arxiv: - '1211.7053' intvolume: ' 14' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1211.7053 month: '07' oa: 1 oa_version: Submitted Version page: 491 - 504 publication: Moscow Mathematical Journal publication_identifier: issn: - '16093321' publication_status: published publisher: Independent University of Moscow publist_id: '5220' quality_controlled: '1' scopus_import: '1' status: public title: Functionals on triangulations of delaunay sets type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 14 year: '2014' ... --- _id: '1929' abstract: - lang: eng text: We propose an algorithm for the generalization of cartographic objects that can be used to represent maps on different scales. 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. article_processing_charge: No article_type: original author: - first_name: V V full_name: Alexeev, V V last_name: Alexeev - first_name: V G full_name: Bogaevskaya, V G last_name: Bogaevskaya - first_name: M M full_name: Preobrazhenskaya, M M last_name: Preobrazhenskaya - first_name: A Y full_name: Ukhalov, A Y last_name: Ukhalov - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Olga full_name: Yakimova, Olga last_name: Yakimova citation: 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 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. 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. 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. 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. date_created: 2018-12-11T11:54:46Z date_published: 2014-11-16T00:00:00Z date_updated: 2022-05-24T10:39:06Z day: '16' department: - _id: HeEd doi: 10.1007/s10958-014-2165-8 intvolume: ' 203' issue: '6' language: - iso: eng month: '11' oa_version: None page: 754 - 760 publication: Journal of Mathematical Sciences publication_identifier: eissn: - 1573-8795 issn: - 1072-3374 publication_status: published publisher: Springer publist_id: '5165' quality_controlled: '1' scopus_import: '1' status: public title: An algorithm for cartographic generalization that preserves global topology type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 203 year: '2014' ...