[{"page":"429 - 442","has_accepted_license":"1","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."}],"file":[{"date_created":"2018-12-12T10:17:36Z","file_name":"IST-2016-475-v1+1_1-s2.0-S092577211500005X-main.pdf","content_type":"application/pdf","file_id":"5292","file_size":508379,"access_level":"open_access","relation":"main_file","date_updated":"2020-07-14T12:45:03Z","checksum":"5b33719a86f7f4c8e5dc62c1b6893f49","creator":"system"}],"scopus_import":1,"license":"https://creativecommons.org/licenses/by/4.0/","oa":1,"ddc":["000"],"date_created":"2018-12-11T11:52:51Z","issue":"5","quality_controlled":"1","oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Elsevier","title":"Reprint of: Weighted straight skeletons in the plane","_id":"1584","department":[{"_id":"HeEd"}],"month":"07","date_published":"2015-07-01T00:00:00Z","date_updated":"2023-02-23T10:05:22Z","year":"2015","related_material":{"record":[{"id":"1582","relation":"other","status":"public"}]},"day":"01","language":[{"iso":"eng"}],"intvolume":" 48","doi":"10.1016/j.comgeo.2015.01.004","publication":"Computational Geometry: Theory and Applications","author":[{"full_name":"Biedl, Therese","first_name":"Therese","last_name":"Biedl"},{"full_name":"Held, Martin","first_name":"Martin","last_name":"Held"},{"full_name":"Huber, Stefan","orcid":"0000-0002-8871-5814","first_name":"Stefan","id":"4700A070-F248-11E8-B48F-1D18A9856A87","last_name":"Huber"},{"full_name":"Kaaser, Dominik","last_name":"Kaaser","first_name":"Dominik"},{"last_name":"Palfrader","first_name":"Peter","full_name":"Palfrader, Peter"}],"file_date_updated":"2020-07-14T12:45:03Z","publist_id":"5587","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"citation":{"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","short":"T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Computational Geometry: Theory and Applications 48 (2015) 429–442.","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.","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.","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.","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.","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"},"pubrep_id":"475","publication_status":"published","status":"public","volume":48,"type":"journal_article"},{"issue":"2","quality_controlled":"1","oa_version":"Published Version","publisher":"Elsevier","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Weighted straight skeletons in the plane","oa":1,"ddc":["000"],"date_created":"2018-12-11T11:52:51Z","scopus_import":1,"abstract":[{"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.","lang":"eng"}],"file":[{"date_created":"2018-12-12T10:16:28Z","file_name":"IST-2016-474-v1+1_1-s2.0-S0925772114000807-main.pdf","content_type":"application/pdf","file_id":"5215","file_size":505987,"access_level":"open_access","relation":"main_file","date_updated":"2020-07-14T12:45:02Z","creator":"system","checksum":"c1ef67f6ec925e12f73a96b8fe285ab4"}],"has_accepted_license":"1","page":"120 - 133","citation":{"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.","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.","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.","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","short":"T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Computational Geometry: Theory and Applications 48 (2015) 120–133.","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."},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"pubrep_id":"474","publication_status":"published","status":"public","volume":48,"type":"journal_article","intvolume":" 48","language":[{"iso":"eng"}],"doi":"10.1016/j.comgeo.2014.08.006","publication":"Computational Geometry: Theory and Applications","author":[{"full_name":"Biedl, Therese","last_name":"Biedl","first_name":"Therese"},{"full_name":"Held, Martin","first_name":"Martin","last_name":"Held"},{"orcid":"0000-0002-8871-5814","full_name":"Huber, Stefan","last_name":"Huber","first_name":"Stefan","id":"4700A070-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Dominik","last_name":"Kaaser","full_name":"Kaaser, Dominik"},{"full_name":"Palfrader, Peter","first_name":"Peter","last_name":"Palfrader"}],"file_date_updated":"2020-07-14T12:45:02Z","publist_id":"5589","date_updated":"2023-02-23T10:05:27Z","year":"2015","related_material":{"record":[{"status":"public","relation":"other","id":"1584"}]},"day":"01","_id":"1582","department":[{"_id":"HeEd"}],"month":"02","date_published":"2015-02-01T00:00:00Z"},{"issue":"2","quality_controlled":"1","oa_version":"Published Version","title":"A simple algorithm for computing positively weighted straight skeletons of monotone polygons","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Elsevier","ddc":["000"],"oa":1,"date_created":"2018-12-11T11:52:51Z","scopus_import":1,"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."}],"has_accepted_license":"1","page":"243 - 247","file":[{"file_id":"5367","content_type":"application/pdf","file_name":"IST-2016-473-v1+1_1-s2.0-S0020019014001987-main.pdf","date_created":"2018-12-12T10:18:45Z","date_updated":"2020-07-14T12:45:03Z","creator":"system","checksum":"2779a648610c9b5c86d0b51a62816d23","file_size":270137,"relation":"main_file","access_level":"open_access"}],"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","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.","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.","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.","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.","short":"T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Information Processing Letters 115 (2015) 243–247.","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"},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"publication_status":"published","pubrep_id":"473","volume":115,"type":"journal_article","status":"public","language":[{"iso":"eng"}],"intvolume":" 115","publication":"Information Processing Letters","doi":"10.1016/j.ipl.2014.09.021","file_date_updated":"2020-07-14T12:45:03Z","author":[{"full_name":"Biedl, Therese","last_name":"Biedl","first_name":"Therese"},{"first_name":"Martin","last_name":"Held","full_name":"Held, Martin"},{"last_name":"Huber","first_name":"Stefan","id":"4700A070-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8871-5814","full_name":"Huber, Stefan"},{"last_name":"Kaaser","first_name":"Dominik","full_name":"Kaaser, Dominik"},{"first_name":"Peter","last_name":"Palfrader","full_name":"Palfrader, Peter"}],"publist_id":"5588","date_updated":"2021-01-12T06:51:45Z","year":"2015","day":"01","department":[{"_id":"HeEd"}],"_id":"1583","date_published":"2015-02-01T00:00:00Z","month":"02"},{"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1508.01076"}],"title":"Representing directed trees as straight skeletons","publisher":"Springer Nature","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","oa_version":"Preprint","quality_controlled":"1","oa":1,"date_created":"2018-12-11T11:52:54Z","scopus_import":"1","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."}],"page":"335 - 347","article_processing_charge":"No","citation":{"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.","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","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.","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","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.","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."},"volume":9411,"type":"book_chapter","status":"public","conference":{"name":"GD: International Symposium on Graph Drawing","location":"Los Angeles, CA, United States","start_date":"2015-09-24","end_date":"2015-09-26"},"publication_status":"published","publication":"Graph Drawing and Network Visualization","doi":"10.1007/978-3-319-27261-0_28","language":[{"iso":"eng"}],"intvolume":" 9411","publication_identifier":{"isbn":["978-3-319-27260-3"],"eisbn":["978-3-319-27261-0"]},"publist_id":"5581","author":[{"first_name":"Oswin","last_name":"Aichholzer","full_name":"Aichholzer, Oswin"},{"last_name":"Biedl","first_name":"Therese","full_name":"Biedl, Therese"},{"last_name":"Hackl","first_name":"Thomas","full_name":"Hackl, Thomas"},{"full_name":"Held, Martin","last_name":"Held","first_name":"Martin"},{"orcid":"0000-0002-8871-5814","full_name":"Huber, Stefan","last_name":"Huber","id":"4700A070-F248-11E8-B48F-1D18A9856A87","first_name":"Stefan"},{"full_name":"Palfrader, Peter","first_name":"Peter","last_name":"Palfrader"},{"full_name":"Vogtenhuber, Birgit","first_name":"Birgit","last_name":"Vogtenhuber"}],"year":"2015","date_updated":"2022-01-28T09:10:37Z","day":"27","department":[{"_id":"HeEd"}],"_id":"1590","date_published":"2015-11-27T00:00:00Z","month":"11","alternative_title":["LNCS"]},{"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."}],"department":[{"_id":"UlWa"},{"_id":"HeEd"}],"_id":"1682","date_published":"2015-08-01T00:00:00Z","month":"08","article_number":"26","year":"2015","date_updated":"2021-01-12T06:52:30Z","day":"01","scopus_import":1,"publication":"Journal of the ACM","doi":"10.1145/2751524","intvolume":" 62","language":[{"iso":"eng"}],"oa":1,"date_created":"2018-12-11T11:53:27Z","publist_id":"5466","author":[{"last_name":"Franek","first_name":"Peter","full_name":"Franek, Peter"},{"full_name":"Krcál, Marek","last_name":"Krcál","id":"33E21118-F248-11E8-B48F-1D18A9856A87","first_name":"Marek"}],"issue":"4","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1402.0858"}],"citation":{"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.","chicago":"Franek, Peter, and Marek Krcál. “Robust Satisfiability of Systems of Equations.” Journal of the ACM. ACM, 2015. https://doi.org/10.1145/2751524.","ista":"Franek P, Krcál M. 2015. Robust satisfiability of systems of equations. Journal of the ACM. 62(4), 26.","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","short":"P. Franek, M. Krcál, Journal of the ACM 62 (2015).","ieee":"P. Franek and M. Krcál, “Robust satisfiability of systems of equations,” Journal of the ACM, vol. 62, no. 4. ACM, 2015."},"type":"journal_article","volume":62,"title":"Robust satisfiability of systems of equations","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","publisher":"ACM","quality_controlled":"1","publication_status":"published","oa_version":"Preprint"},{"doi":"10.1137/140993843","publication":"Society for Industrial and Applied Mathematics","intvolume":" 47","language":[{"iso":"eng"}],"publist_id":"5423","author":[{"last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"last_name":"Plakhov","first_name":"Alexander","full_name":"Plakhov, Alexander"}],"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","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.","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.","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","short":"A. Akopyan, A. Plakhov, Society for Industrial and Applied Mathematics 47 (2015) 2754–2769."},"status":"public","volume":47,"type":"journal_article","publication_status":"published","_id":"1710","department":[{"_id":"HeEd"}],"month":"07","date_published":"2015-07-14T00:00:00Z","year":"2015","date_updated":"2021-01-12T06:52:41Z","day":"14","oa":1,"ec_funded":1,"date_created":"2018-12-11T11:53:36Z","main_file_link":[{"url":"http://arxiv.org/abs/1410.3736","open_access":"1"}],"issue":"4","publisher":"SIAM","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Minimal resistance of curves under the single impact assumption","oa_version":"Preprint","quality_controlled":"1","page":"2754 - 2769","abstract":[{"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 → ∞.","lang":"eng"}],"project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7"}],"scopus_import":1},{"oa":1,"date_created":"2018-12-11T11:54:14Z","ec_funded":1,"issue":"1","main_file_link":[{"url":"arxiv.org/abs/1406.5313","open_access":"1"}],"title":"Invariant measures of genetic recombination process","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Springer","oa_version":"Preprint","quality_controlled":"1","abstract":[{"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.","lang":"eng"}],"page":"163 - 167","article_processing_charge":"No","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7"}],"scopus_import":1,"publication":"Journal of Statistical Physics","doi":"10.1007/s10955-015-1238-5","intvolume":" 160","language":[{"iso":"eng"}],"publist_id":"5276","author":[{"full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","last_name":"Akopyan"},{"full_name":"Pirogov, Sergey","first_name":"Sergey","last_name":"Pirogov"},{"full_name":"Rybko, Aleksandr","last_name":"Rybko","first_name":"Aleksandr"}],"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","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.","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.","short":"A. Akopyan, S. Pirogov, A. Rybko, Journal of Statistical Physics 160 (2015) 163–167.","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"},"type":"journal_article","volume":160,"status":"public","publication_status":"published","department":[{"_id":"HeEd"}],"_id":"1828","date_published":"2015-07-01T00:00:00Z","month":"07","year":"2015","date_updated":"2021-01-12T06:53:28Z","day":"01"},{"quality_controlled":"1","publication_status":"published","oa_version":"None","title":"On the distribution of local extrema in quantum chaos","volume":379,"type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Elsevier","status":"public","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","ista":"Pausinger F, Steinerberger S. 2015. On the distribution of local extrema in quantum chaos. Physics Letters, Section A. 379(6), 535–541.","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.","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.","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.","short":"F. Pausinger, S. Steinerberger, Physics Letters, Section A 379 (2015) 535–541.","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"},"issue":"6","author":[{"full_name":"Pausinger, Florian","orcid":"0000-0002-8379-3768","first_name":"Florian","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","last_name":"Pausinger"},{"full_name":"Steinerberger, Stefan","last_name":"Steinerberger","first_name":"Stefan"}],"date_created":"2018-12-11T11:54:49Z","publist_id":"5152","intvolume":" 379","language":[{"iso":"eng"}],"publication":"Physics Letters, Section A","doi":"10.1016/j.physleta.2014.12.010","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. ","scopus_import":1,"day":"06","date_updated":"2021-01-12T06:54:12Z","year":"2015","date_published":"2015-03-06T00:00:00Z","month":"03","department":[{"_id":"HeEd"}],"_id":"1938","page":"535 - 541","abstract":[{"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.","lang":"eng"}]},{"day":"01","year":"2015","date_updated":"2021-01-12T06:54:53Z","month":"10","date_published":"2015-10-01T00:00:00Z","_id":"2035","department":[{"_id":"HeEd"}],"status":"public","volume":15,"type":"journal_article","publication_status":"published","pubrep_id":"486","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","ista":"Edelsbrunner H, Jablonski G, Mrozek M. 2015. The persistent homology of a self-map. Foundations of Computational Mathematics. 15(5), 1213–1244.","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.","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.","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.","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","short":"H. Edelsbrunner, G. Jablonski, M. Mrozek, Foundations of Computational Mathematics 15 (2015) 1213–1244."},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"publist_id":"5022","author":[{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Grzegorz","id":"4483EF78-F248-11E8-B48F-1D18A9856A87","last_name":"Jablonski","full_name":"Jablonski, Grzegorz","orcid":"0000-0002-3536-9866"},{"full_name":"Mrozek, Marian","last_name":"Mrozek","first_name":"Marian"}],"file_date_updated":"2020-07-14T12:45:26Z","doi":"10.1007/s10208-014-9223-y","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.","publication":"Foundations of Computational Mathematics","language":[{"iso":"eng"}],"intvolume":" 15","scopus_import":1,"file":[{"file_name":"IST-2016-486-v1+1_s10208-014-9223-y.pdf","date_created":"2018-12-12T10:08:10Z","content_type":"application/pdf","file_id":"4670","date_updated":"2020-07-14T12:45:26Z","checksum":"3566f3a8b0c1bc550e62914a88c584ff","creator":"system","file_size":1317546,"relation":"main_file","access_level":"open_access"}],"page":"1213 - 1244","abstract":[{"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","lang":"eng"}],"has_accepted_license":"1","project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","call_identifier":"FP7","name":"Topological Complex Systems"}],"publisher":"Springer","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"The persistent homology of a self-map","quality_controlled":"1","oa_version":"Published Version","issue":"5","ec_funded":1,"date_created":"2018-12-11T11:55:20Z","oa":1,"ddc":["000"]},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Elsevier","title":"Homological reconstruction and simplification in R3","oa_version":"None","quality_controlled":"1","issue":"8","ec_funded":1,"date_created":"2018-12-11T11:54:06Z","scopus_import":1,"page":"606 - 621","abstract":[{"text":"We consider the problem of deciding whether the persistent homology group of a simplicial pair (K,L) can be realized as the homology H∗(X) of some complex X with L ⊂ X ⊂ K. We show that this problem is NP-complete even if K is embedded in double-struck R3. As a consequence, we show that it is NP-hard to simplify level and sublevel sets of scalar functions on double-struck S3 within a given tolerance constraint. This problem has relevance to the visualization of medical images by isosurfaces. We also show an implication to the theory of well groups of scalar functions: not every well group can be realized by some level set, and deciding whether a well group can be realized is NP-hard.","lang":"eng"}],"project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","name":"Topological Complex Systems","call_identifier":"FP7"}],"status":"public","type":"journal_article","volume":48,"publication_status":"published","citation":{"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.","short":"D. Attali, U. Bauer, O. Devillers, M. Glisse, A. Lieutier, Computational Geometry: Theory and Applications 48 (2015) 606–621.","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","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.","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","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.","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."},"publist_id":"5305","author":[{"full_name":"Attali, Dominique","first_name":"Dominique","last_name":"Attali"},{"full_name":"Bauer, Ulrich","orcid":"0000-0002-9683-0724","first_name":"Ulrich","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","last_name":"Bauer"},{"first_name":"Olivier","last_name":"Devillers","full_name":"Devillers, Olivier"},{"full_name":"Glisse, Marc","first_name":"Marc","last_name":"Glisse"},{"first_name":"André","last_name":"Lieutier","full_name":"Lieutier, André"}],"doi":"10.1016/j.comgeo.2014.08.010","publication":"Computational Geometry: Theory and Applications","intvolume":" 48","language":[{"iso":"eng"}],"day":"03","related_material":{"record":[{"status":"public","id":"2812","relation":"earlier_version"}]},"year":"2015","date_updated":"2023-02-23T10:59:19Z","month":"06","date_published":"2015-06-03T00:00:00Z","_id":"1805","department":[{"_id":"HeEd"}]},{"ddc":["000"],"oa":1,"date_created":"2018-12-11T11:54:02Z","issue":"6","quality_controlled":"1","oa_version":"Published Version","title":"DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Public Library of Science","file":[{"checksum":"d20f26461ca575276ad3ed9ce4bfc787","creator":"system","date_updated":"2020-07-14T12:45:16Z","access_level":"open_access","relation":"main_file","file_size":1850825,"file_id":"5150","content_type":"application/pdf","date_created":"2018-12-12T10:15:30Z","file_name":"IST-2016-454-v1+1_journal.pone.0127657.pdf"}],"has_accepted_license":"1","abstract":[{"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.","lang":"eng"}],"scopus_import":1,"intvolume":" 10","language":[{"iso":"eng"}],"publication":"PLoS One","doi":"10.1371/journal.pone.0127657","file_date_updated":"2020-07-14T12:45:16Z","author":[{"full_name":"Symonova, Olga","id":"3C0C7BC6-F248-11E8-B48F-1D18A9856A87","first_name":"Olga","last_name":"Symonova"},{"full_name":"Topp, Christopher","first_name":"Christopher","last_name":"Topp"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner"}],"publist_id":"5318","citation":{"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.","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","short":"O. Symonova, C. Topp, H. Edelsbrunner, PLoS One 10 (2015).","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","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.","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.","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."},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"pubrep_id":"454","publication_status":"published","type":"journal_article","volume":10,"status":"public","department":[{"_id":"MaJö"},{"_id":"HeEd"}],"_id":"1793","article_number":"e0127657","date_published":"2015-06-01T00:00:00Z","month":"06","date_updated":"2023-02-23T14:06:33Z","year":"2015","related_material":{"record":[{"relation":"research_data","id":"9737","status":"public"}]},"day":"01"},{"oa_version":"Published Version","type":"research_data_reference","title":"Root traits computed by DynamicRoots for the maize root shown in fig 2","status":"public","publisher":"Public Library of Science","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","citation":{"short":"O. Symonova, C. Topp, H. Edelsbrunner, (2015).","apa":"Symonova, O., Topp, C., & Edelsbrunner, H. (2015). Root traits computed by DynamicRoots for the maize root shown in fig 2. Public Library of Science. https://doi.org/10.1371/journal.pone.0127657.s001","ieee":"O. Symonova, C. Topp, and H. Edelsbrunner, “Root traits computed by DynamicRoots for the maize root shown in fig 2.” Public Library of Science, 2015.","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.","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.","ama":"Symonova O, Topp C, Edelsbrunner H. Root traits computed by DynamicRoots for the maize root shown in fig 2. 2015. doi:10.1371/journal.pone.0127657.s001","ista":"Symonova O, Topp C, Edelsbrunner H. 2015. Root traits computed by DynamicRoots for the maize root shown in fig 2, Public Library of Science, 10.1371/journal.pone.0127657.s001."},"author":[{"full_name":"Symonova, Olga","last_name":"Symonova","first_name":"Olga","id":"3C0C7BC6-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Topp, Christopher","last_name":"Topp","first_name":"Christopher"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner"}],"date_created":"2021-07-28T06:20:13Z","doi":"10.1371/journal.pone.0127657.s001","related_material":{"record":[{"status":"public","relation":"used_in_publication","id":"1793"}]},"day":"01","date_updated":"2023-02-23T10:14:42Z","year":"2015","date_published":"2015-06-01T00:00:00Z","month":"06","department":[{"_id":"MaJö"},{"_id":"HeEd"}],"article_processing_charge":"No","_id":"9737"},{"issue":"6","citation":{"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.","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.","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","ista":"Pausinger F, Svane A. 2015. A Koksma-Hlawka inequality for general discrepancy systems. Journal of Complexity. 31(6), 773–797.","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","short":"F. Pausinger, A. Svane, Journal of Complexity 31 (2015) 773–797.","ieee":"F. Pausinger and A. Svane, “A Koksma-Hlawka inequality for general discrepancy systems,” Journal of Complexity, vol. 31, no. 6. Academic Press, pp. 773–797, 2015."},"type":"journal_article","title":"A Koksma-Hlawka inequality for general discrepancy systems","volume":31,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","publisher":"Academic Press","oa_version":"None","publication_status":"published","quality_controlled":"1","publication":"Journal of Complexity","doi":"10.1016/j.jco.2015.06.002","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.","language":[{"iso":"eng"}],"intvolume":" 31","date_created":"2018-12-11T11:54:02Z","publist_id":"5320","author":[{"first_name":"Florian","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","last_name":"Pausinger","full_name":"Pausinger, Florian","orcid":"0000-0002-8379-3768"},{"full_name":"Svane, Anne","last_name":"Svane","first_name":"Anne"}],"year":"2015","date_updated":"2023-09-07T11:41:25Z","day":"01","scopus_import":1,"related_material":{"record":[{"id":"1399","relation":"dissertation_contains","status":"public"}]},"page":"773 - 797","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."}],"department":[{"_id":"HeEd"}],"_id":"1792","date_published":"2015-12-01T00:00:00Z","month":"12"},{"title":"On the approximation of intrinsic volumes","type":"dissertation","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publisher":"Institute of Science and Technology Austria","status":"public","oa_version":"None","publication_status":"published","supervisor":[{"last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"}],"citation":{"chicago":"Pausinger, Florian. “On the Approximation of Intrinsic Volumes.” Institute of Science and Technology Austria, 2015.","mla":"Pausinger, Florian. On the Approximation of Intrinsic Volumes. Institute of Science and Technology Austria, 2015.","ama":"Pausinger F. On the approximation of intrinsic volumes. 2015.","ista":"Pausinger F. 2015. On the approximation of intrinsic volumes. Institute of Science and Technology Austria.","apa":"Pausinger, F. (2015). On the approximation of intrinsic volumes. Institute of Science and Technology Austria.","short":"F. Pausinger, 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."},"date_created":"2018-12-11T11:51:48Z","publist_id":"5808","author":[{"id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","first_name":"Florian","last_name":"Pausinger","full_name":"Pausinger, Florian","orcid":"0000-0002-8379-3768"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["2663-337X"]},"day":"01","related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"1662"},{"id":"1792","relation":"part_of_dissertation","status":"public"},{"status":"public","id":"2255","relation":"part_of_dissertation"}]},"degree_awarded":"PhD","year":"2015","date_updated":"2023-09-07T11:41:25Z","date_published":"2015-06-01T00:00:00Z","month":"06","alternative_title":["ISTA Thesis"],"page":"144","abstract":[{"text":"This thesis is concerned with the computation and approximation of intrinsic volumes. Given a smooth body M and a certain digital approximation of it, we develop algorithms to approximate various intrinsic volumes of M using only measurements taken from its digital approximations. The crucial idea behind our novel algorithms is to link the recent theory of persistent homology to the theory of intrinsic volumes via the Crofton formula from integral geometry and, in particular, via Euler characteristic computations. Our main contributions are a multigrid convergent digital algorithm to compute the first intrinsic volume of a solid body in R^n as well as an appropriate integration pipeline to approximate integral-geometric integrals defined over the Grassmannian manifold.","lang":"eng"}],"department":[{"_id":"HeEd"}],"article_processing_charge":"No","_id":"1399"},{"abstract":[{"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.","lang":"eng"}],"page":"55-69","article_processing_charge":"No","project":[{"grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425","name":"Topological Complex Systems","call_identifier":"FP7"}],"scopus_import":"1","date_created":"2022-03-21T07:11:23Z","ec_funded":1,"title":"Toward the extraction of saddle periodic orbits","publisher":"Springer","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","oa_version":"None","date_published":"2014-03-19T00:00:00Z","month":"03","place":"Cham","department":[{"_id":"HeEd"}],"_id":"10893","day":"19","year":"2014","date_updated":"2022-06-21T12:01:47Z","author":[{"full_name":"Kasten, Jens","first_name":"Jens","last_name":"Kasten"},{"id":"4505473A-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","last_name":"Reininghaus","full_name":"Reininghaus, Jan"},{"full_name":"Reich, Wieland","first_name":"Wieland","last_name":"Reich"},{"last_name":"Scheuermann","first_name":"Gerik","full_name":"Scheuermann, Gerik"}],"series_title":"Mathematics and Visualization","publication":"Topological Methods in Data Analysis and Visualization III ","doi":"10.1007/978-3-319-04099-8_4","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.","language":[{"iso":"eng"}],"intvolume":" 1","publication_identifier":{"eissn":["2197-666X"],"isbn":["9783319040981"],"eisbn":["9783319040998"],"issn":["1612-3786"]},"volume":1,"type":"book_chapter","editor":[{"full_name":"Bremer, Peer-Timo","first_name":"Peer-Timo","last_name":"Bremer"},{"full_name":"Hotz, Ingrid","first_name":"Ingrid","last_name":"Hotz"},{"full_name":"Pascucci, Valerio","first_name":"Valerio","last_name":"Pascucci"},{"full_name":"Peikert, Ronald","last_name":"Peikert","first_name":"Ronald"}],"status":"public","publication_status":"published","citation":{"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.","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.","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","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.","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.","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","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."}},{"publist_id":"5290","file_date_updated":"2020-07-14T12:45:17Z","author":[{"last_name":"Huber","id":"4700A070-F248-11E8-B48F-1D18A9856A87","first_name":"Stefan","orcid":"0000-0002-8871-5814","full_name":"Huber, Stefan"},{"first_name":"Martin","last_name":"Held","full_name":"Held, Martin"},{"full_name":"Meerwald, Peter","last_name":"Meerwald","first_name":"Peter"},{"full_name":"Kwitt, Roland","first_name":"Roland","last_name":"Kwitt"}],"publication":"International Journal of Computational Geometry and Applications","acknowledgement":"Work by Martin Held and Stefan Huber was supported by Austrian Science Fund (FWF): L367-N15 and P25816-N15.","doi":"10.1142/S0218195914500034","language":[{"iso":"eng"}],"intvolume":" 24","volume":24,"type":"journal_article","status":"public","publication_status":"published","pubrep_id":"443","citation":{"short":"S. Huber, M. Held, P. Meerwald, R. Kwitt, International Journal of Computational Geometry and Applications 24 (2014) 61–86.","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","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.","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.","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.","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","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."},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"date_published":"2014-03-16T00:00:00Z","month":"03","department":[{"_id":"HeEd"}],"_id":"1816","day":"16","year":"2014","date_updated":"2021-01-12T06:53:23Z","date_created":"2018-12-11T11:54:10Z","ddc":["000"],"oa":1,"title":"Topology-preserving watermarking of vector graphics","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publisher":"World Scientific Publishing","quality_controlled":"1","oa_version":"Published Version","issue":"1","page":"61 - 86","has_accepted_license":"1","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."}],"file":[{"relation":"main_file","access_level":"open_access","file_size":991734,"creator":"system","checksum":"be45c133ab4d43351260e21beaa8f4b1","date_updated":"2020-07-14T12:45:17Z","date_created":"2018-12-12T10:08:43Z","file_name":"IST-2016-443-v1+1_S0218195914500034.pdf","file_id":"4704","content_type":"application/pdf"}],"scopus_import":1},{"oa_version":"Submitted Version","publication_status":"published","status":"public","publisher":"Springer","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","title":"On the geometric ramsey number of outerplanar graphs","type":"journal_article","volume":53,"citation":{"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.","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.","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","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.","short":"J. Cibulka, P. Gao, M. Krcál, T. Valla, P. Valtr, Discrete & Computational Geometry 53 (2014) 64–79.","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","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."},"main_file_link":[{"url":"http://arxiv.org/abs/1310.7004","open_access":"1"}],"issue":"1","author":[{"full_name":"Cibulka, Josef","last_name":"Cibulka","first_name":"Josef"},{"full_name":"Gao, Pu","last_name":"Gao","first_name":"Pu"},{"last_name":"Krcál","id":"33E21118-F248-11E8-B48F-1D18A9856A87","first_name":"Marek","full_name":"Krcál, Marek"},{"last_name":"Valla","first_name":"Tomáš","full_name":"Valla, Tomáš"},{"full_name":"Valtr, Pavel","last_name":"Valtr","first_name":"Pavel"}],"publist_id":"5260","date_created":"2018-12-11T11:54:18Z","oa":1,"language":[{"iso":"eng"}],"intvolume":" 53","doi":"10.1007/s00454-014-9646-x","acknowledgement":"Marek Krčál was supported by the ERC Advanced Grant No. 267165.","publication":"Discrete & Computational Geometry","scopus_import":1,"day":"14","date_updated":"2021-01-12T06:53:33Z","year":"2014","month":"11","date_published":"2014-11-14T00:00:00Z","_id":"1842","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"page":"64 - 79","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."}]},{"scopus_import":"1","external_id":{"arxiv":["1211.7053"]},"page":"491 - 504","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","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Independent University of Moscow","title":"Functionals on triangulations of delaunay sets","oa_version":"Submitted Version","quality_controlled":"1","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1211.7053"}],"issue":"3","date_created":"2018-12-11T11:54:29Z","oa":1,"article_type":"original","day":"01","year":"2014","date_updated":"2022-03-03T11:47:09Z","month":"07","date_published":"2014-07-01T00:00:00Z","_id":"1876","department":[{"_id":"HeEd"}],"status":"public","type":"journal_article","volume":14,"publication_status":"published","citation":{"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","short":"N. Dolbilin, H. Edelsbrunner, A. Glazyrin, O. Musin, Moscow Mathematical Journal 14 (2014) 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.","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.","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.","ista":"Dolbilin N, Edelsbrunner H, Glazyrin A, Musin O. 2014. Functionals on triangulations of delaunay sets. Moscow Mathematical Journal. 14(3), 491–504.","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"},"publist_id":"5220","author":[{"first_name":"Nikolai","last_name":"Dolbilin","full_name":"Dolbilin, Nikolai"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner"},{"last_name":"Glazyrin","first_name":"Alexey","full_name":"Glazyrin, Alexey"},{"last_name":"Musin","first_name":"Oleg","full_name":"Musin, Oleg"}],"doi":"10.17323/1609-4514-2014-14-3-491-504","publication":"Moscow Mathematical Journal","publication_identifier":{"issn":["16093321"]},"intvolume":" 14","language":[{"iso":"eng"}]},{"date_created":"2018-12-11T11:54:46Z","article_type":"original","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Springer","title":"An algorithm for cartographic generalization that preserves global topology","oa_version":"None","quality_controlled":"1","issue":"6","page":"754 - 760","abstract":[{"lang":"eng","text":"We propose an algorithm for the generalization of cartographic objects that can be used to represent maps on different scales."}],"article_processing_charge":"No","scopus_import":"1","publist_id":"5165","author":[{"full_name":"Alexeev, V V","last_name":"Alexeev","first_name":"V V"},{"first_name":"V G","last_name":"Bogaevskaya","full_name":"Bogaevskaya, V G"},{"last_name":"Preobrazhenskaya","first_name":"M M","full_name":"Preobrazhenskaya, M M"},{"last_name":"Ukhalov","first_name":"A Y","full_name":"Ukhalov, A Y"},{"last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Yakimova, Olga","last_name":"Yakimova","first_name":"Olga"}],"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.","doi":"10.1007/s10958-014-2165-8","publication":"Journal of Mathematical Sciences","publication_identifier":{"issn":["1072-3374"],"eissn":["1573-8795"]},"intvolume":" 203","language":[{"iso":"eng"}],"status":"public","type":"journal_article","volume":203,"publication_status":"published","citation":{"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.","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","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.","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.","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.","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","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."},"month":"11","date_published":"2014-11-16T00:00:00Z","_id":"1929","department":[{"_id":"HeEd"}],"day":"16","year":"2014","date_updated":"2022-05-24T10:39:06Z"},{"day":"31","scopus_import":1,"year":"2014","date_updated":"2021-01-12T06:54:09Z","date_published":"2014-12-31T00:00:00Z","month":"12","page":"2585 - 2594","abstract":[{"text":"(Figure Presented) Data acquisition, numerical inaccuracies, and sampling often introduce noise in measurements and simulations. Removing this noise is often necessary for efficient analysis and visualization of this data, yet many denoising techniques change the minima and maxima of a scalar field. For example, the extrema can appear or disappear, spatially move, and change their value. This can lead to wrong interpretations of the data, e.g., when the maximum temperature over an area is falsely reported being a few degrees cooler because the denoising method is unaware of these features. Recently, a topological denoising technique based on a global energy optimization was proposed, which allows the topology-controlled denoising of 2D scalar fields. While this method preserves the minima and maxima, it is constrained by the size of the data. We extend this work to large 2D data and medium-sized 3D data by introducing a novel domain decomposition approach. It allows processing small patches of the domain independently while still avoiding the introduction of new critical points. Furthermore, we propose an iterative refinement of the solution, which decreases the optimization energy compared to the previous approach and therefore gives smoother results that are closer to the input. We illustrate our technique on synthetic and real-world 2D and 3D data sets that highlight potential applications.","lang":"eng"}],"department":[{"_id":"HeEd"}],"_id":"1930","type":"journal_article","volume":20,"title":"Fast and memory-efficient topological denoising of 2D and 3D scalar fields","status":"public","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","publisher":"IEEE","quality_controlled":"1","oa_version":"None","publication_status":"published","issue":"12","citation":{"ieee":"D. Günther, A. Jacobson, J. Reininghaus, H. Seidel, O. Sorkine Hornung, and T. Weinkauf, “Fast and memory-efficient topological denoising of 2D and 3D scalar fields,” IEEE Transactions on Visualization and Computer Graphics, vol. 20, no. 12. IEEE, pp. 2585–2594, 2014.","short":"D. Günther, A. Jacobson, J. Reininghaus, H. Seidel, O. Sorkine Hornung, T. Weinkauf, IEEE Transactions on Visualization and Computer Graphics 20 (2014) 2585–2594.","apa":"Günther, D., Jacobson, A., Reininghaus, J., Seidel, H., Sorkine Hornung, O., & Weinkauf, T. (2014). Fast and memory-efficient topological denoising of 2D and 3D scalar fields. IEEE Transactions on Visualization and Computer Graphics. IEEE. https://doi.org/10.1109/TVCG.2014.2346432","ama":"Günther D, Jacobson A, Reininghaus J, Seidel H, Sorkine Hornung O, Weinkauf T. Fast and memory-efficient topological denoising of 2D and 3D scalar fields. IEEE Transactions on Visualization and Computer Graphics. 2014;20(12):2585-2594. doi:10.1109/TVCG.2014.2346432","ista":"Günther D, Jacobson A, Reininghaus J, Seidel H, Sorkine Hornung O, Weinkauf T. 2014. Fast and memory-efficient topological denoising of 2D and 3D scalar fields. IEEE Transactions on Visualization and Computer Graphics. 20(12), 2585–2594.","chicago":"Günther, David, Alec Jacobson, Jan Reininghaus, Hans Seidel, Olga Sorkine Hornung, and Tino Weinkauf. “Fast and Memory-Efficient Topological Denoising of 2D and 3D Scalar Fields.” IEEE Transactions on Visualization and Computer Graphics. IEEE, 2014. https://doi.org/10.1109/TVCG.2014.2346432.","mla":"Günther, David, et al. “Fast and Memory-Efficient Topological Denoising of 2D and 3D Scalar Fields.” IEEE Transactions on Visualization and Computer Graphics, vol. 20, no. 12, IEEE, 2014, pp. 2585–94, doi:10.1109/TVCG.2014.2346432."},"date_created":"2018-12-11T11:54:46Z","publist_id":"5164","author":[{"full_name":"Günther, David","last_name":"Günther","first_name":"David"},{"full_name":"Jacobson, Alec","first_name":"Alec","last_name":"Jacobson"},{"first_name":"Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","last_name":"Reininghaus","full_name":"Reininghaus, Jan"},{"first_name":"Hans","last_name":"Seidel","full_name":"Seidel, Hans"},{"last_name":"Sorkine Hornung","first_name":"Olga","full_name":"Sorkine Hornung, Olga"},{"full_name":"Weinkauf, Tino","last_name":"Weinkauf","first_name":"Tino"}],"publication":"IEEE Transactions on Visualization and Computer Graphics","doi":"10.1109/TVCG.2014.2346432","acknowledgement":"RTRA Digiteoproject; ERC grant; SNF award; Intel Doctoral Fellowship; MPC-VCC","language":[{"iso":"eng"}],"intvolume":" 20"}]